Tennessee
Valley
Authority
United States
Environmental Protection
Agency
Division of
Environmental Planning
Chattanooga, Tennessee 37401
Office of Research and Development
Office of Energy, Minerals and Industry
Washington, D.C. 20460
TVA/EP-78/02
EPA-600/7-77-0 89
August 1977
LEAST-SQUARES RESOLUTION
OF GAMMA-RAY SPECTRA
IN ENVIRONMENTAL SAMPLES
Interagency
Energy-Environment
Research and Development
Program Report
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REPORTING
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4 Environmental Monitoring
5. Socioeconomic Environmental Studies
6 Scientific and Technical Assessment Reports (STAR)
7 Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects, assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide range of energy-related environ-
mental issues.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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TVA/EP-78/02
EPA-600/7-77-089
August 1977
LEAST-SQUARES RESOLUTION OF GAMMA-RAY SPECTRA
IN ENVIRONMENTAL MONITORING
by
Larry G. Kanipe, Stephen K. Seale, and Walter S. Liggett
Division of Environmental Planning
Tennessee Valley Authority
Muscle Shoals, Alabama 35660
Interagency Agreement No. D6-E721
Project No. E-AP78BDI
Project Officer
Gregory J. D'Alessio
Office of Energy, Minerals and Industry
U.S. Environmental Protection Agency
Washington, B.C. 20460
OFFICE OF ENERGY, MINERALS AND INDUSTRY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20U60
-------
DISCLAIMER
This report was prepared by the Tennessee Valley Authority
and has been reviewed by the Office of Energy, Minerals, and
Industry, U.S. Environmental Protection Agency, and approved
for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the
Tennessee Valley Authority or the U.S. Environmental
Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommendation
for use.
11
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ABSTRACT
The use of ALPHA-M, a least-squares computer program tor
analyzing NaI(T£) gamma spectra of environmental samples, is
evaluated. Included is a comprehensive set of program
instructions, listings, and flowcharts. Two other programs,
GEN 4 and SIMSPEC, are also described. GEN4 is used to
create standard libraries for ALPHA-M, and SIMSPEC is used
to simulate spectra for ALPHA-M analysis. Tests to evaluate
the standard libraries selected for use in analyzing
environmental samples are provided. An evaluation of the
results of sample analyses is discussed.
This report was submitted by the Tennessee Valley Authority,
Division of Environmental Planning, in partial fulfillment
of Energy Accomplishment Plan number 78 BDI under terms of
Interagency Energy Agreement D6-E721 with the Environmental
Protection Agency. Work was completed as of March 1976.
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CONTENTS
Abstract iii
Figures vii
Tables viii
Acknowledgments ix
1. Introduction 1-1
2. Conclusions 2-1
3. Recommendation 3-1
14. Gamma Spectroscopy 4-1
4.1 General 4-1
4.2 Interactions of gamma rays with matter . . 4-1
4.3 Characteristics of gamma ray spectra . . . 4-3
4.4 The experimental problem—instrumental . . 4-8
4.5 The experimental problem--extraneous
counts 4-10
4.6 Quantitative analysis of gamma spectra . . 4-n
4.7 Least-squares analysis of gamma ray
spectra 4-13
4.8 References 4-15
5. ALPHA-M 5-1
5.1 General 5-1
5.2 Basic features 5-1
5.2.1 Library standards 5_1
5.2.2 Background compensation 5_1
5.2.3 Activity corrections 5_2
5.2.4 Standard error estimates . 5_2
5.2.5 Weighting schemes 5_2
5.2.6 Gain and threshold shift
compensation 5_2
5.2.7 Rejection coefficient 5_2
5.2.8 Analysis of residuals 5_2
5.2.9 Other minor features 5_3
5.2.10 Diagnostics package 5_3
5.2.11 Alpha factors 5_3
5.2.12 Input/output 5.4
5.2.13 Lower level of detection 5_4
5.3 Standards and data for ALPHA-M ...... 5.4
5.4 ALPHA-M input instructions 5_5
5.5 ALPHA-M output 5_15
5.6 References 5-23
6. Evaluation of ALPHA-M ............. 6-1
6.1 General _
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6.2 Program processing options 6-1
6.3 Library standards 6-7
6.4 Sample analyses 6-30
6.5 Use of the rejection procedure 6-30
6.6 References 6-33
Appendices
A. ALPHA-M A-l
B. GEN4 B_l
C. SIMSPEC C_l
D. Test data D_;L
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FIGURES
Number Page
1 Interaction processes 4_2
2 Representative gamma ray spectrum 4_5
3 Gamma ray spectrum with sum peak 4_7
4 Basic loop structure of ALPHA-M 5_H
5 Arrangement of input card deck for the
ALPHA-M program 5-12
6 ALPHA-M output 5_16
7 Energy error vs. photopeak position 6_6
8 58Co activity vs. 5*Mn activity for
background runs 6-15
9 siCr sample results 6_16
10 13*Cs sample results 6-17
A-1 ALPHA-M main program flow diagram A_37
A-2 ALPHA-M subroutine LABEL flow diagram A_41
A-3 ALPHA-M subroutine STDIN flow diagram A_46
A-4 ALPHA-M subroutine RESIDU flow diagram A_47
A-5 ALPHA-M subroutine DIAG flow diagram A_48
B-1 GEN4 flow diagram B-14
C-1 Program-file dependency in SIMALPH c_5
C-2 SIMSPEC flow diagram c_17
VII
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TABLES
Number Page
1 ALPHA-M Input Instructions 5_5
2 Average Percent Error with Different
Processing Options 6-3
3 Photopeak Positions, Errors, and Energies .... 6-5
4 Gain Shift Effects Nuclide Activities
10 pCi/liter 6_8
5 Correlation Coefficients for Standard
Nuclide Library 6-10
6 Occurrences of High Correlations in a Set of
132 Analyses 6-11
7 Analytical Results from Composite Analysis . . . 6-13
8 Experimental Values Divided by Standard Error
for 23 Background Spectra 6-14
9 Information Matrix 6-19
10 Inverse of Information Matrix 6-20
11 Standard Errors and Lower Limits of Detection
(LLD) for the Standards Library in Appendix D . . 6-22
12 ALPHA-M Standard Errors for 10 Analyses of
Routine Background Spectra 6-23
13 Specific Area, Usable Fraction, and Shape
Factor for the Library Standards in Appendix D . 6-25
14 Analytical Results for l37Cs at Low Activity
Levels 6-27
15 Analytical Results for 65Zn at Low Activity
Levels 6-28
16 Effects on Accuracy Caused by Multiple
Components Nuclide Activity 25 pCi/liter .... 6-29
17 Behavior of the Rejection Process 6-32
A-1 Job/Control Language Procedure RUNALPH A_3
B-1 Structure of Standard Nuclide File B_5
B-2 GEN4 Input Instructions B-6
B-3 GEN 4 Update Instructions B_8
C-1 SIMSPEC Input Instructions c_7
D-1 Library Standards D-3
D-2 Library Spectra D_4
D-3 Test Spectra D-ll
V1X1
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ACKNOWLEDGMENTS
The contributions of N. E. Turnage, R. L. Doty, B. B. Hobbs,
E. A. Belvin, and the Radioanalytical Laboratory Staff of
the Division of Environmental Planning, Tennessee Valley
Authority, are greatly appreciated.
IX
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SECTION 1
INTRODUCTION
The emphasis on monitoring the environment for radiological
impact is growing with the increased use of nuclear power.
Increased nuclear power production requires greater
production from all aspects of the uranium cycle, from
mining and milling to spent fuel reprocessing. One of the
most economical and wide-ranging analytical tools for
environmental monitoring is gamma spectroscopy. However,
accurate quantitative information from gamma-ray analysis is
difficult to obtain, and data reduction requires a
sophisticated approach to produce reliable results.
The basic purpose of this report is to evaluate a standard
least-squares computer program for analyzing gamma-ray
spectral data obtained with Nal(T&) scintillation detectors.
A modified version of ALPHA-M (developed by E. Schonfeld)
has been prepared and tested to determine its capabilities
and limitations for environmental monitoring. This program
is presented in Appendix A.
Certain procedures for evaluating the performance of ALPHA-M
in an individual laboratory program, detailed in this
report, should be completed before adopting ALPHA-tM for
routine analytical work.
Since the audience for a report of this nature is generally
quite broad, it is difficult to select the subjects that
should be covered. The material has been written for a
person with at least a B.S. degree in the physical sciences
and a limited amount of experience in the fields of
radiochemistry and gamma spectroscopy. In an attempt to
discuss the full range of the radioanalytical problem, a
section (Section 4) on gamma spectroscopy has been included.
Section U is also an introduction for new personnel to the
problems of gamma spectroscopy and quantitative radionuclide
analysis. The experienced spectroscopist may wish to skip
Section U and turn directly to Section 5, which contains
instructions for using ALPHA-M. Section 6 describes methods
for evaluating the library standards, background
fluctuations, and program processing options. The program
ALPHA-M, its flowcharts, and other related material are
contained in Appendix A.
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SECTION 2
CONCLUSIONS
The least-squares analysis program ALPHA-M can be used
successfully to quantify Nal(T£) spectra of environmental
samples. Many gamma-emitting radionuclides can be
quantified at activity levels of about 10 pico-Curies per
liter (pCi/£) or less, depending on counting time, at a
confidence level of 95 percent. The least-squares analysis
method is an effective environmental monitoring tool, and
program operation is relatively inexpensive in terms of
counting instruments and actual analyst time.
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SECTION 3
RECOMMENDATIONS
Quantitative analysis of complex gamma-ray spectra taken
with Nal (TS,) detectors should be performed with a weighted
least-squares fitting program such as ALPHA-M. The user of
such a program should study carefully the theoretical model
(including weighting scheme, standards compatibility, and
background interferences) before he uses the program for
routine analyses. The user should also provide for
continuous performance testing and evaluation during routine
use of the program to help prevent the production of
erroneous data.
Although ALPHA-M is now a valuable tool in environmental
monitoring, areas for further development could be
investigated: (1) possible modifications to improve the gain
and threshold shift procedure for environmental samples,
where counting statistics are often poor; (2) possible
modifications in the rejection procedure to compensate
better for imprecise determinations of low activity levels
of radionuclides so that possibly valid data is not
discarded; (3) development of techniques to better handle
highly correlated spectra of certain radionuclides (see
Section 6.3); and (4) development of better criteria than
the residuals and chi-square tests to indicate the validity
of the program results.
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SECTION 4
GAMMA SPECTROSCOPY
4.1 GENERAL
Gamma rays are a type of electromagnetic radiation
characterized by zero rest mass and no electrical charge.
They differ from visible light only in having much shorter
wavelengths (i.e., much higher energy). Gamma rays arise
from transitions of nucleons between nuclear energy levels,
just as optical spectra arise from transitions of electrons
between electronic energy levels.1,2 Although energy
adjustments in the atomic nucleus that lead to gamma-ray
emissions usually occur after the emission of alpha or beta
particles, there are some cases in which gamma-ray emission
occurs without an accompanying alpha or beta emission. For
example, 5*Mn and 85Sr emit only gamma rays.
A single radionuclide may emit one or more gamma rays,
depending on the variableness of prior alpha or beta
emission energies. Although the energy of these gamma rays
is characteristic of a particular radionuclide, a particular
radionuclide is not necessarily the only source of a
specific gamma-ray spectral line. For example, 226Ra emits
a gamma ray with an energy of 186,000 electron volts (186
keV), but 235U and several other radionuclides also exhibit
a 186-keV emission. Thus, one difficulty of gamma
spectroscopy is the assignment of gamma-ray lines to
particular radionuclides.
4.2 INTERACTIONS OF GAMMA RAYS WITH MATTER
The practical energy range for gamma spectroscopy is from a
few thousand to a few million electron volts. Within this
energy range, there are basically three processes by which
gamma rays may interact with matter: the photoelectric
effect, the Compton effect, and pair production.1-* The
relative importance of these three modes of interaction to
the absorption process is a function of the atomic number of
the absorber and the energy of the incident gamma ray. This
relationship is shown graphically in figure 1.
The photoelectric effect occurs when a gamma ray transfers
all its energy to a bound orbital electron. The electron
uses a portion of this energy to overcome its binding energy
and assumes the remainder as kinetic energy. This process
cannot occur with a free (unbound) electron because a third
body, the nucleus, is required to conserve momentum.
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4-2
PHOTOELECTRIC
DOMINANT
PAIR
PRODUCTION
DOMINANT
0.01
COMPTON
DOMINANT
O.I 1.0 10
LOG ENERGY, MeV
100
Figure 1. Interaction processes.
Therefore, a more tightly bound electron has a higher
probability of undergoing the photoelectric process. When
the incident photon energy significantly exceeds the K- or
L-shell binding energies, the probability of photoelectric
interaction in the outer shells is negligible. The removal
of an electron from a low-lying orbit leads to higher-energy
electrons dropping down to fill the vacancy. These excited
atoms lose energy by emitting characteristic X-rays when the
electrons drop down to fill lower-lying orbits. 2
For gamma photons having energies much greater than the
electron-binding energies, the photoelectric process is not
favored. Rather, the photons are scattered when they
interact with the electrons as if the electrons were free
and at rest. This process is called the Compton effect, or
Compton scattering, and is the dominant mode of interaction
at energies of about 1 MeV. in the scattering process, the
gamma photon transfers a portion of its energy to an
electron as the photon is deflected from its original
path.2 , *
If the path of a single gamma photon in a scintillation
detector were observed, the photon might be seen to have
several Compton interactions followed by either a
photoelectric interaction or escape of the scattered photon
from the crystal. Since Compton scattering generally
involves the outer electrons of an absorber atom, a
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4-3
significant number of X rays are not produced except in
absorber elements of low atomic number.1
For energies above 1.02 MeV, pair production, the third mode
of interaction of gamma rays with matter, becomes
increasingly more important. In pair production, a gamma
photon passing through the field of a nucleus disappears
with the creation of an electron-positron pair. The kinetic
energy of this pair is equal to the difference between the
incident photon energy and the rest mass energy (1.02 MeV)
of the two particles. The emitted particles rapidly
dissipate their kinetic energy by ionization or radiative
processes. When the kinetic energy has been dissipated, the
positron that has an available electron is annihilated,
producing two annihilation photons, each having 0.51 MeV
energy. These photons, which are emitted at 180 degrees
with respect to each other, can also undergo Compton
scattering and photoelectric interaction to produce a
complex spectrum.2
The entire process of gamma-ray absorption can be described
as an exponential attenuation of the incident beam. That
is, the number of photons remaining in the beam decreases
exponentially with the distance of penetration into the
absorber. This can be written
I = I0e^x, (D
where I0 = incident beam intensity,
I = beam intensity at distance x,
y = linear absorption coefficient of the absorber,
x = distance penetrated.
The linear absorption coefficient, y, sums all the
coefficients for the photoelectric, Compton, and pair-
production processes.* Equation (1) assumes the idealities
of a point source and a "thin11 absorber. Since, in reality
(i.e., in environmental samples), such ideality does not
occur, a proportionality constant must be determined to
relate the ideal case to the observed data. This is done by
preparing a known source in the exact geometry to be used
for sample analysis.
4.3 CHARACTERISTICS OF GAMMA-RAY SPECTRA
Gamma-ray spectra, obtained with a multichannel analyzer and
an Nal scintillation detector, have several possible
characteristic features: (1) photopeaks, (2) Compton area,
(3) escape peaks, (U) annihilation peak, (5) sum peaks, and
(6) nongamma components (such as bremsstrahlung). All six
features can lead to a complicated spectrum for even a
single radionuclide having multiple emissions; thus, spectra
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4-4
of radionuclide mixtures can become very complex. An
experimental Nal (TX.) spectrum is shown in figure 2.
The photopeak, which results from the total absorption of
the energy of the gamma photon in the scintillation
detector, is the most important feature of the spectrum
because its amplitude and intensity are direct measures of
the energy and intensity of the incident monoenergetic gamma
ray beam. The width of the photopeak reflects the energy
resolution of the spectrometer system, and the fraction of
total counts appearing in the photopeak is a function of the
detector volume. This fraction of total-absorption events
is much larger than predicted by theory for photoelectric
interaction because of the high probability of all photon
interaction processes, such as the photoelectric effect and
Compton scattering, occurring during the collection time of
the scintillation detector, producing only one detector
pulse. Therefore, the single detector pulse reflects the
sum of all the successive Compton events and the final
photoelectric process.5>6
The Compton area of the spectrum stretches from essentially
zero energy to a maximum energy value indicated as the
Compton edge in figure 2. This area, known as the Compton
Continuum, arises from scattered gamma photons escaping the
detector before undergoing complete energy transfer to the
crystal.*,5 Because the possible number of different Compton
interactions is quite large, a broad energy spectrum
results. The Compton portion of the spectrum varies with
the energy of the incident photon. However, the Compton
Continuum has a definite upper limit known as the Compton
edge. This limiting energy value occurs when the incident
photon is scattered through an angle of 180 degrees, thereby
imparting the maximum kinetic energy to the ejected
electron.4 The value for the Compton edge increases and the
Compton Continuum broadens as the incident photon energy
increases.
Another characteristic of the Compton area is the back-
scatter peak. This peak results from the 180-degree Compton
backscattering of gamma rays by the surrounding materials
such as the detector shield. The shape and magnitude of
this peak are functions of the geometry of the counting
system. The intensity of this peak varies inversely with
the size of the shield and the atomic number of the shield
material. In other words, a large shield will show a
substantial reduction in the amount of backscattering
because more of the interactions of the gamma ray with the
shield will proceed photoelectrically (figure 1) . This
reduction is achieved because most of the gamma photon
energy is dissipated before striking the shield, therefore
increasing the probability of the photoelectric effect being
dominant.
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4-5
10'
CO
10'
BREMSSTRAHLUNG
BACKSCATTER
0.5IIMeV
ANNIHILATION
RADIATION
0.76MeV
ESCAPE
PEAKS
.27MeV
COMPTON
EDGE
PHOTOPEAK 1.78 MeV
0 200 400 600 800 1000 1200
PULSE HEIGHT, channels
Figure 2. Representative gamma-ray spectrum.
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4-6
Another feature of the gamma-ray spectrum is the appearance
of escape peaks, which are caused by the repeated escape of
a discrete amount of energy from the detector. Therefore,
an escape peak occurs at a discrete value(s) of energy below
the energy of the photopeak (figure 2) . The most common
escape peak arises from pair production and its associated
annihilation radiation. If a positron-electron annihilation
occurs near the detector surface but inside the detector,
there is a reasonable probability that one of the two
annihilation photons, or possibly both, may escape the
crystal.2,4,s when one annihilation photon does escape
repeatedly, a second peak will appear in the spectrum at an
energy 0.51 MeV less than that of the photopeak. If both
annihilation photons escape the detector, another escape
peak will occur at an energy 1.02 MeV less than that of the
photopeak. Other escape peaks can arise from the
photoelectric interactions of gamma rays with the iodine
atoms of the Nal(TJt) detector.
If positron-electron annihilation occurs outside the
detector, an annihilation photon of 0.51 MeV can penetrate
the detector. This behavior can add a small peak, the
annihilation peak, in the gamma-ray spectrum at 0.51 MeV.
There is also a possibility that more than one gamma photon
may enter the detector simultaneously. If this occurs
within the collection time of the detector, the combined
light emission will be seen by the photomultiplier tube as a
single light pulse. Repeated occurrence of this type of
event will lead to a sum peak (figure 3) at higher energy
than that of either individual gamma photon.
The common sources of sum peaks are the summing of (1) two
gamma photons emitted in cascade from one radionuclide, (2)
different gamma photons from a composite sample, and (3) two
0.51-MeV annihilation photons giving rise to a peak at 1.02
MeV. The probability of the appearance of sum peaks is
higher when sample activity is higher and a large volume
detector is used.2
Two other nongamma components that frequently appear in
gamma spectra are bremsstrahlung radiation and X rays.
Bremsstrahlung radiation is emitted when an electron passes
away from the strong, attractive electric field of the
nucleus. This phenomenon occurs when high-energy beta
particles are emitted from the sample or when pair
production has a high probability for a particular gamma ray
since the electron produced in pair production decelerates
while moving away from the nucleus. X-ray contributions to
the gamma spectrum are produced principally by the
photoelectric interaction process.*
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4-7
I02
10'
C/5
IOL
10'
l0.89MeV
PHOTOPEAKS
"SUM PEAK"
2.01 MeV
0 200 400 600 800 1000 1200
PULSE HEIGHT, channels
Figure 3. Gamma-ray spectrum with sum peak.
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In summary, the peaks often seen in a gamma spectrum result
from basic interaction processes. Complications occur when
Compton-scattered or annihilation photons escape from the
crystal or when other photons are scattered into the crystal
from the shielding. This pattern of peaks can become quite
complicated when mixtures of radionuclides, such as those
contained in environmental samples or reactor effluents, are
examined. These spectra can be further influenced by the
source-detector geometry, the count rate input to the
spectrometer, the size and shape of the detector, and the
experimental conditions at the time of analysis.
U.U THE EXPERIMENTAL PROBLEM—INSTRUMENTAL
A basic system for collecting gamma spectroscopy data
consists of a Nal (T£) detector connected to a pulse-height
analyzer. The quality of the data depends primarily on the
components of the spectrometer. For precise analytical
work, standard measurement conditions must be maintained,
especially if computer analysis is planned.
An examination of the experimental problems of gamrna
spectroscopy must begin with the detector. For a reasonable
compromise of efficiency and resolution, most environmental
work is done with either a 3- by 3-in. or a 4- by 4-in.
right-cylinder-shaped NaI(T£) crystal. The crystal is
hermetically sealed in an aluminum casing with an optical
joint connecting the crystal to a photomultiplier tube.7*8
Caution must be exercised when using NaI(T£) crystals to
prevent thermal or mechanical shock that could fracture the
crystal. Such damage could dramatically change the light
transmission properties of the crystal. The detector and
photomultiplier tube are usually purchased as a system, and
both elements contribute to the spectrometer resolution.
Resolution is usually defined as the relative width of the
photopeak generated by a monoenergetic source of gamma rays
(e.g., 137Cs source). Percentage resolution8 can be
calculated by
W = Ah% x 100% , (2)
max
where W^ = the full peak width at half maximum peak
2 height, % (this resolution is valid only
at the energy calculated) ,
Ahj_ = width of photopeak at half maximum peak
2 height, units of energy,
h = energy value of photopeak.
max
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4-9
Some parameters influencing resolution are light production
in the scintillator, light collection by the phototube,
photocathode electron production, and phototube electron
multiplication. Experimental parameters such as
temperature, source-detector geometry, and count rate can
also vary the detector resolution.
The phototube gain shifts with variations in operating
voltage or source count rate. Changes in gain resulting
from operating voltage variations can be minimized by using
well-regulated power supplies. The magnitude of gain shift
with count rate is proportional to the phototube current;
usually, an increase in the count rate causes an increase in
phototube gain. In environmental work, gain shift with
count rate is rarely a problem and would possibly occur only
during the counting of high-activity standards.
To minimize problems with voltage-related gain shift, a
check source such as 137Cs can be used to readjust the gain
between analyses. This calibration can reduce gain
variations to less than 0.5 percent, if other factors such
as temperature are held constant. The gain shift problem
can also be minimized if a source such as 241Am is
introduced into the scintillation crystal. Appropriate
circuitry can then be installed to automatically adjust the
phototube bias to keep the 2*!Am line at a fixed position in
the spectrum.
Once a proper pulse is generated by the detector system, the
pulse must be amplified for use in the pulse-height
analyzer. The linearity and stability of the amplification
system must remain constant with changing experimental
conditions (e.g., temperature fluctuations and variations in
counting rate, gain, etc.).
One important amplifier problem is zero or threshold shift
with count rate. Threshold shift with count rate is caused
by pulse pileup; that is, the count rate is so high that
circuit capacitance does not have time to discharge
completely. Succeeding pulses to the pulse-height analyzer
then appear larger than their actual size. This problem can
be eliminated by using the "double-differentiating" type of
amplifier.7
The pulse-height analyzer can be performance-rated on the
basis of variables such as its integral and differential
linearity, both of which are basically functions of the
analog-to-digital converter (ADC).
The integral linearity is the relationship of the input
pulse amplitude to the channel position in which the pulse
is stored. For example, if the analyzer is calibrated for 5
keV per channel, a 100-keV pulse should appear in channel
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4-10
20. in general, this relationship will not be linear; that
is, there usually will be deviations at very low and very
high energies. The integral linearity curve must be
adjusted each day by using a multiline calibration source to
align the system.7
The differential linearity describes the uniformity of
channel width over the entire analyzer memory. With newer
analyzers, this uniformity is usually better than can be
easily measured in the laboratory, but the analyzer
performance should be periodically checked to ensure that
constant channel width is maintained. This is usually done
with a sliding scale pulser.
In summary, a large number of variables influence the
quality of data obtained from a gamma spectrometry system.
Because these variables have complex interrelationships that
are impossible to compute, a set of standard experimental
conditions must be defined and rigidly controlled to produce
data that can be quantitatively analyzed with accuracy and
precision.
4.5 THE EXPERIMENTAL PROBLEM—EXTRANEOUS COUNTS
The most difficult problem in the radioanalytical laboratory
is extraneous counts, that is, the problem of isolating the
radiation emitted by a specific radionuclide in the sample
from that of all other sources. These extraneous counts can
originate from two different sources—background radiation
or interference from other radionuclides within the
sample.l°
Background radiation usually is determined by measuring a
simulated sample or source that is identical to an actual
sample except for the relative absence of radioactivity.
This technique can simulate counts arising from naturally
occurring radioactivity (e.g., *°K and decay products of the
238U and 232Th series), radioactivity in the detectors,
cosmic rays, electronic noise, etc. However, this technique
assumes that background activity is stable (constant over a
period of time) and that the only fluctuations that occur
are due to the statistics involved in the radioactive decay
process. Actually, background activity often has more
variability than predicted by counting statistics.
To reduce background contributions, shielding is necessary.
Thick, graded shields of selected lead or steel will
measurably reduce background arising from environmental
radioactivity. Further reduction in background can be
achieved by anticoincidence counting.
Background contributions from environmental sources are
exemplified by radon daughters—decay products of the zaejj
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4-11
series such as 2i*Bi and si*Pb. Radon is always present in
the laboratory; it can be found in concrete block walls,
compressed air, water, and the samples. Therefore,
laboratory procedures can only attempt to minimize the
effect of radon. Several measures can help reduce
background contributions resulting from radon: (1) Air can
be exchanged rapidly in the laboratory (five to ten times
per hour) , (2) water can be boiled or aerated, and (3)
compressed air can be supplied from cylinders that are
filled more than 30 days before use in the laboratory.
Interference can be caused by other radioisotopes in the
sample that are either present originally or that are
introduced during sample processing. Errors encountered
from contamination during sample processing may be reduced
by carrying a "blank sample," a sample having no known
activity, through the total analysis scheme. However, in a
situation in which more than one radionuclide in the sample
is of interest, the multiple components may interfere with
each other or may have decay products that interfere and
cannot be eliminated. How the ALPHA-M technique handles
this problem is discussed in Section 6.3. If the
interferents are different elements, chemical separation is
possible; if they are the same element, the interferents may
be distinguishable by a physical technique, such as a half-
life determination.
Overall, extraneous counts generated by interfering radio-
activity limit the accuracy attainable in any analysis.
Corrections depend on the degree of separation possible and
the reproducibility of the separation. Nevertheless, the
statistical fluctuations from the interferent will cause
errors in the final result just as background variations do.
4.6 QUANTITATIVE ANALYSIS OF GAMMA SPECTRA
To obtain quantitative information from gamma-ray spectral
data, the spectral analysis method must attempt to account
for several types of problems:*
1. Compton interference of higher-energy gamma rays
with the photopeaks of lower-energy photons.
2. A multiplicity of photopeaks from different radio-
nuclides present in the sample. These photopeaks
may overlap one another.
3. interference from secondary peaks such as escape,
annihilation, and sum peaks.
4. Wide variations in the relative activities of the
nuclides present.
-------
4-12
5. Variations in the detection efficiency for
different energy photons.
6. Estimation of errors.
Many techniques for resolving gamma-ray spectra are
available, but none can completely meet all these criteria.
One simple approach to quantifying spectral information is
the use of a graphical technique, in which a graph of the
spectrum is searched for an identifiable, unobstructed
photopeak of good intensity. Once found, the same number of
channels on either side of the peak are totaled. The
baseline is subtracted by extrapolating the baseline from
one side of the peak to the other. This method results in
an accuracy of only 10 to 30 percent and is limited to
levels above 20 to 50 pCi/2,. The method cannot readily
handle complex spectra or account for small peaks that are
hidden by the Compton Continuum of higher-energy
radionuclides. Such limitations make the graphical
technique almost useless in environmental work.*
A second method that is used commonly is spectrum stripping.
The basic assumption in spectrum stripping is that a
composite spectrum will be the channel-by-channel summation
of the spectra of the individual components of the mixture.
Therefore, if the individual components are known, a
channel-by-channel subtraction can be performed to strip out
each contributor one at a time.
In spectrum stripping, the highest energy photopeak is
selected, and its source is identified. A spectrum
multiplier is determined by computing the ratio of the area
of the sample photopeak to the photopeak area of a standard
spectrum for that nuclide. This multiplier is then applied
to each channel of the standard spectrum. The resulting
spectrum is subtracted from the sample spectrum. The
highest energy photopeak remaining is selected, and the
process is repeated until all components are identified,
stripped, and quantified.
Spectrum stripping is a reasonably accurate, but very
tedious, procedure. Errors do creep into the results
through the subtraction process because the shape of a
standard spectrum can differ from that of a sample spectrum.
Also, the error from counting statistics is propagated to
the yet-to-be-stripped nuclides by the subtraction process.
The principal reason for this shape difference is gain or
threshold shifting of the photopeaks. Additionally,
overlapping photopeaks can be a problem in both
identification and quantification. For environmental work,
photopeaks for radionuclides present at very low activity
levels are difficult to identify.
-------
4-13
A third method of analyzing gamma spectra is by simultaneous
equations, which is very similar to methods used for
simultaneous determinations of two or more components in
spectrophotometric analysis. In this method, all nuclides
in a sample must be identified,, and each nuclide must
possess an unobstructed photopeak. Again, this technique
assumes that the contribution of each radionuclide to the
sample spectrum is additive. The contribution of each
radionuclide to the photopeak region of every other nuclide
is determined from standard spectra. These are called
interference factors. A set of simultaneous equations can
then be written for all nuclides:
AA = CA * FBACB * FCACC * FDA CD * ••- ' <3>
where A = ccants in photopeak region of
nuclide A,
C , C , etCo = counts due to nuclide A, B, etc.,
A B
F , F , etc. = interference factors for nuclides
BA CA B, C, etc., in the A photopeak region.
These simultaneous equations can then be solved by using
matrix techniques to find C a C' f etc,
A B
The primary advantage of the simultaneous equations
technique is its computer adaptability. The primary
disadvantage is that the presence of an unidentified
radionuclide in the sample invalidates all results. A large
number of radionuclides cannot be handled without computer
calculation. Also, complex, overlapping spectra are
difficult to analyze^, and the magnitude of errors increases
with the number of nuclides in the sample. However, the
error is very difficult to estimate at all.
The fourth method for resolving multicomponent gamma-ray
spectra is linear regression analysis using the method of
least squares. Least-squares analysis uses all data in all
channels for estimating nuclide concentrations and can
produce an error estimate for each nuclide concentration.
In theory, this method produces the most accurate estimates
for samples containing several nuclides.
4.7 LEAST-SQUARES ANALYSIS OF GAMMA-RAY SPECTRA
The resolution of a gamma spectrum into the concentrations
of its component radioneciides can be treated as d cuive-
fitting problem by using least-squares techniques. The
basic assumption is that the sample spectrum can be
described by a linear combination of the gamma spectra of
-------
4-14
each component obtained separately. This discussion is
intended to present the least-squares approach in non-
mathematical terms. *, s, 11 ,12
The linear least-squares method assumes that the pulse-
height spectrum to be analyzed consists of the summed
contributions of n nuclides, each of which is represented as
a pulse-height spectrum of k channels. This method requires
standard spectra, representing the response of the detector
to gamma rays of the nuclides of interest, for comparison.
The count rate in a sample spectrum due to standard j
(j = 1...n) in channel i (i = 1...k) will be C. . , and the total
count rate in channel i will be X. . The expression,
n
/ \
X— .I. j_
— f • n T p . ~ T f.-,
i \uil Ui2 ^i3 i • ^
accounts for all contributions to channel i.
To obtain quantitative results from resolving a spectrum,
the quantity of nuclide j must be expressed in terms of the
standard for nuclide j. Therefore, a normalization factor
M ., the ratio of the activity of nuclide j in the unknown to
tne value of nuclide j in the standard, must be included:
n
X = / v M. S. . + R. (5)
3 ij i '
where R± represents the random error in the channel i counts
and Si* is the count rate of the standard j in channel i.
Cj_s is simply the product of Mj, the normalization factor,
and S j_ A , the standard count rate.
If the only error in this calculation is the random error of
the counts in a channel, RI, then the least-squares
technique can be used. This method estimates the parameters
that minimize the weighted sum of the squared difference
between two sets of values. The usual case has one set of
values as observed data (X.^) and another set of computed
values:
n
M. S.
-------
4-15
n
This translates to
Minimize X. - ) M S.. W. , (6)
m ij I i
where W^^ is the weighting factor chosen to estimate the
variance of the counts in a channel. The use of weighting
is important because it allows the more important spectral
features, such as photopeaks, to be more highly emphasized
in the calculation. If the variance is estimated for each
channel, the result is a set of linear simultaneous
equations (one for each nuclide of interest) that may be
solved for the values of M,. This solution is most easily
derived by using matrix techniques on a computer.
Again, the least-squares method is theoretically the most
accurate method for determining the activity of a composite
sample. This technique uses all data in all channels to
estimate the nuclide concentrations. In addition, the error
in the calculation for each nuclide concentration is
available from an intermediate step of the linear least-
squares computation.13 Once established, this type of
computer program can be used to process large volumes of
spectral data.
Disadvantages of the least-squares method are the initial
adaptation of the computer program to available processing
equipment and the initial evaluation of the computer program
analytical results. Procedures for both operations are
discussed in the following sections. Ill-conditioned
equations, those equations whose solutions are sensitive to
very small alterations in coefficient values, can cause the
program to produce invalid results. Certain combinations of
nuclides having similar spectral shapes or overlapping peaks
can cause such a problem. These instances must be examined
individually. These problems will be discussed further in
Section 6.
In summary, a properly applied least-squares technique can
yield superior results, as compared with any other method of
analyzing NaI(T£) complex gamma-ray spectra. However, the
installation of such a computer program requires that the
user be aware of the programming and statistical obligations
that must be fulfilled to create useful and sound results.
4.8 REFERENCES
1. Siegbahn, K., Ed. Beta- and Gamma-Ray Spectroscopy,
North-Holland Pub. Co., Amsterdam, 1955, Chapter 2.
(Other eds. 1965, 1974.)
-------
4-16
2. Crouthamel, C. E. , Ed. Applied Gamma-Ray Spectrometry,
Pergamon Press, New York, 1960, Chapter 1. (Another
ed. 1970.)
3. Evans, R. D. The Atomic Nucleus, McGraw-Hill Book Co.,
New York, 1955, Chapter 23.
4. Radionuclide Analysis by Gamma Spectroscopy, U.S.
Department of Health, Education, and Welfare, Public
Health Service, Rockville, Maryland. (Good general
reference.)
5. Heath, R. L. Computer Techniques for the Analyses of
Gamma-Ray Spectra Obtained with Nal and Lithium-Ion
Drifted Germanium Detectors, Nucl. Instrum. Methods,
43: 209-229, 1966.
6. Heath, R. L. Scintillation Spectrometry Gamma-Ray
Spectrum Catalogue, vol. 1, 2nd ed. AEC Research and
Development Report IDO-16880-1, Idaho Falls, Idaho,
August 1964, pp. 4-39.
7. Crouch, D. F., and R. L. Heath, Routine Testing and
Calibration Procedures for Multi-Channel Pulse Analyzers
and Gamma-Ray Spectrometers, AEC Research and Development
Report IDO-16923, Idaho Falls, Idaho, 1963. 42 pp.
8. Price, W. J. Nuclear Radiation Detection, 2nd ed. McGraw-
Hill Book Co., New York, 1964, p. 202.
9. Heath, R. L. Scintillation Spectrometry - The Experi-
mental Problem, In: Applications of Computers to Nuclear
and Radiochemistry, National Academy of Sciences -
National Research Council publication NAS-NS 3107,
Washington, D.C., 1962.
10. Measurement of Low-Level Radioactivity, ICRU Report 22,
International Commission on Radiation Units and
Measurements, Washington, D.C., June 1, 1972.
11. Salmon, L. Computer Analysis of Gamma-Ray Spectra
from Mixtures of Known Nuclides by the Method of Least-
Squares, In: Applications of Computers to Nuclear and
Radiochemistry, National Academy of Sciences - National
Research Council Publication NAS-NS 3107, Washington, D.C.,
1962.
12. Pasternack, B. S. Linear Estimation in the Analysis of
Pulse Height Spectra, Technometrics, 4: 565-571, 1962.
13. Trombka, J. I. Least-Squares Analysis of Gamma-Ray
Pulse-Height Spectra, In: Applications of Computers to
Nuclear and Radiochemistry, National Academy of
-------
4-17
Sciences - National Research Council Publication NAS-NS
3107, Washington, B.C., 1962.
14. Stevenson, P- C. Processing of Counting Data, National
Academy of Sciences - National Research council
Publication NAS-NS 3119, Washington, D.C., May 1966.
-------
SECTION 5
ALPHA-M
5.1 GENERAL
The multicomponent gamma-ray spectrum analysis program
ALPHA-M was developed by E. Schonfeld in 1965*, 2 and
modified for this study by S. Seale (TVA) in 1975. ALPHA-M
determines the activities of radioisotopes by a weighted
least-squares resolution of their gamma-ray spectra. The
application of the least-squares method to gamma spectral
data yields superior quantitative results as compared with
any other commonly used technique. There are several
immediate advantages of this technique:
1. Rapid data processing is possible.
2. Spectra with large statistical variations in count-
ing can be handled.
3. The total spectrum, rather than just the photopeak
regions, is used.
4. Spectra with superimposed peaks can be analyzed.
5. The standard error of the nuclide activity can be
estimated.
5. 2 BASIC FEATURES
5.2.1 Library Standards
The 1975 version of ALPHA-M allows the input of up to 20
library standards of 256 channels each for one to four
detectors. Simple modifications (see Appendix A) allow
further expansion of the library. ALPHA-M can select for a
particular analysis any combination of library members, as
requested, ranging from a single radionuclide standard to a
composite of all members of the library.
5.2.2 Background Compensation
ALPHA-M can accept samples whose background component has
been subtracted in the multichannel analyzer. The program
will convert meg complements (i.e., a number such as 999887)
that arise from statistical counting variations to their
correct negative values. ALPHA-M can also subtract a
background spectrum from sample spectra. Background
-------
5-2
compensation may also be achieved by including the
background as a library standard, and a background spectrum
may be entered to replace the library background spectrum
for special data processing. This last option does not
change the actual stored standard library, but only the one
being used by the program for the particular analysis.
5.2.3 Activity Corrections
The program can take into account corrections for counting
time, decay time, analytical sample size, and concentration
of the sample before analysis, thus allowing the user to
receive corrected results in the desired units (e.g., pCi/£,
pCi/g).
5.2.H Standard Error Estimates
ALPHA-M produces a standard error for each radionuclide
determined in the least-squares process. The standard
errors may be used to erect statistical confidence intervals
or to test statistical hypotheses about the determined
activities.
5.2.5 Weighting Schemes
Several weighting methods are available to the program user.
Sample spectra can be weighted by the observed channel
contents, calculated channel contents, unity, or variance of
the observed or calculated channel contents.
Recommendations for routine weighting options are made in
Section 6.
5.2.6 Gain and Threshold Shift Compensation
ALPHA-M is able to compensate automatically for the gain and
threshold shifts that may occur during sample counting; both
shifts are included as elements of the least-squares
process.
5.2.7 Rejection Coefficient
If the concentration of a radionuclide (or radionuclides) is
negative or less than a predetermined fraction of the
standard error, ALPHA-M can repeat the entire analysis and
omit the standards for the rejected radionuclides. This may
improve the accuracy and sensitivity while reducing the
standard errors of the remaining radionuclides.
5.2.8 Analyses of Residuals
The modified version of ALPHA-M includes a new option for
allowing a more detailed analysis of the residuals obtained
-------
5-3
from the fitting process.3-5 To describe the distribution
of the standardized residuals, the program outputs the mean,
standard deviation, skevmess, and kurtosis of the residuals.
The program also prints the percentage of the residuals
within one, two, and three standard deviations of the
residual mean. A plot of the normalized residuals vs.
channel number can be requested. The program identifies as
"suspicious" those channels lying outside a ±3 standard
deviation band surrounding the residual mean.
5.2.9 Other Minor Features
A calculation of the coefficient of variance (or variation)
has been added to ALPHA-M. This coefficient provides a
measure of comparison of the relative precision of estimates
whose magnitudes vary over a wide range. A program option
has been added to calculate and print out the intervariable
correlations after the terminal cycle of least-squares
refinement. This correlation shows the degree to which any
two variables are interrelated in the calculations.6?7 The
subroutine INVERT has been modified to execute in double
precision.
5.2.10 Diagnostics Package
A series of diagnostics has been included to warn users of
errors or possibly unwise combinations of option selections.
In general, these diagnostics will stop sample processing
and give a diagnostic message. However, certain diagnostxcs
do not stop sample processing, but do provide a warning if
data from a particular determination are questionable. For
example, the matrix inversion subroutine has been rewritten
to test for pivots smaller than 1.0 X 10~io and to change
them, if found, to 1.0. This "fixup" not only prevents the
occurrence of a floating-point divide check, which would
stop processing, but also prints the warning that a singular
matrix has been encountered. This diagnostic informs the
user that the results of the particular analysis are
meaningless.
5.2.11 Alpha Factors
The alpha factor expresses the ratio of the variance of an
estimate to the sum of the variances of all other variables
in the determination. This quantity is roughly proportional
to the weight of a specified variable in the determination.
The alpha factors are independent of the sample spectrum and
are descriptive of the standard nuclide library. Therefore,
alpha factors can be used to monitor the quality of new sets
of standards prepared for ALPHA-M.
-------
5-4
5.2.12 Input/Output
The modified version of ALPHA-M has an entirely new input
and output structure. All input instructions, input data,
analytical results, and performance indicators are now
clearly displayed and labeled on the resulting printouts.
5.2.13 Lower Level of Detection
This version of ALPHA-M also provides an estimate of the
lower limit of detection (LLD) for a particular
determination. This LLD value is calculated from the
technique developed by Altshuler and Pasternack8 and
Pasternack and Harley9 and is illustrated in HASL-300.i°
5.3 STANDARDS AND DATA FOR ALPHA-M
The basic assumption of the least-squares approach to gamma-
ray spectrum analysis is that the experimental conditions
for the standard and sample spectra are identical. The most
important consideration is the maintenance of a constant
energy scale for all data collection, which requires a daily
calibration procedure with a specified set of radionuclide
sources. This calibration procedure must be duplicated
exactly on every occasion to ensure constant spectrometer
performance. In addition to this major daily calibration,
the user should make fine gain adjustments between samples
to account for intraday gain variations. This can be done
by recentering the 662-keV peak of »37Cs to the correct
scale position by adjusting the amplifier fine gain between
sample runs.
Another requirement for the standard library is that the
variability in the library standards must be less than that
in the sample spectra. For example, if a routine sample is
expected to have an average activity of 100 disintegrations
per minute (dpm), then the standards in the library should
have activity levels of 1000 to 10,000 dpm. An alternative
method is to use standards with lower activity levels and to
count them for ten times as long as the samples will be
counted. The latter approach avoids the problems of summing
and gain shift due to high count rate; however, gain
variations resulting from bias and temperature fluctuations
do become important with longer count times.
If background spectra are to be used with ALPHA-M, they must
be determined under conditions identical to those used for
the library standards and sample spectra. Heavy shielding
should be used for environmental work, to reduce
fluctuations of background activity during sample analysis.
A program called GEN4 (Appendix B) may be used to generate
the standard library spectra for ALPHA-M. The program
-------
5-5
assumes that the average user will store the standard
libraries on a computer-accessible mass storage medium
rather than read the standards from cards for each
processing run.
The reference library may be constructed with up to 20
standard spectra (of 256 channels each) for one to four
detector geometries. A standard background spectrum may be
included in the library by submitting to the program a
number of daily background spectra, which are then averaged.
Reference spectra may be supplied to GEN4 with the sample
background previously subtracted by the analyzer, or the
standard background may be averaged by the program and
subtracted from all input spectra. The library produced by
GEN4 contains all data regarding names, half-lives, counting
times, and activities of the standard nuclides.
Operating in the update mode, the program can replace any
library standard spectrum and its identifying header.
Because GENU assumes that such changes will be made to the
background standard only, there is no provision to modify
the appropriate information record (activity, name, half-
life, etc.) for the specified standard. In other words, a
library standard with an activity different from the
original library member cannot be added to the library
without recreating the entire library.
Printed output from GEN4 includes all information recorded
on the information records as well as tabulated values for
all standard spectra input. The sum of all channel counts
for each library spectrum is also displayed.
Specific information for using GEN4 is included in Appendix
B. All ALPHA-M code statements relating to input or storage
of standards, or their use in calculations, have been
restructured or rewritten to conform with the standards
library created with GEN4. Both GEN4 and ALPHA-M can be
easily modified to provide for completely different detector
libraries; instructions for the changes that must be made
are included in Appendix B.
5. 4 ALPHA-M INPUT INSTRUCTIONS
Certain control cards are necessary to operate ALPHA-M.
Table 1 lists each control variable, its position on the
control or option card, and its correct format. Figure 4
illustrates the basic loop structure of ALPHA-M, and figure
5 shows the arrangement of the input card deck for ALPHA-M.
The general control card controls (1) the overall program
input-output and (2) the computational limits that apply to
all samples to be processed. The usual values for the
general control card variables are
-------
5-6
TABLE 1. ALPHA-M INPUT INSTRUCTIONS
(General Control Card - 1114, 8A4)
Variable
M
NIT
NBA
NZ
MF
NTS
NTM
MU
NH
IAUX
IOPT
FM
Columns
1-4
5-8
9-12
13-16
17-20
21-24
25-28
29-32
33-36
37-40
41-44
45-76
Format
14
14
14
14
14
14
14
14
14
14
14
8A4
Description
Number of channels in spectra.
Maximum number of iterations in
least-squares refinement process.
1 = To print library standards.
0 = Not to print library standards.
Initial channel for computation.
Final channel for computation.
Fortran logical unit on which the
standard nuclide library resides.
Fortran logical unit on which the
sample spectra and background
reside.
Fortran logical unit for print-
plots.
1 = To print correlation coeffi-
cients.
0 = Not to print coefficients.
If IAUX greater than zero, auxili-
ary data will be output on
Fortran logical unit IAUX for
further processing.
If IOPT greater than zero, analyti-
cal results will be output on
Fortran logical unit IOPT for
further processing.
This is the format (enclosed in
parentheses) under which all
sample spectra and backgrounds
will be read.
-------
5-7
TABLE 1 (cont.
(Sample Control Card - A8, 413, 5F9.4,
One Card Per Sample)
Variable
XIDT
NOPT
NER
NBS
IABP
MS
TB
ISA
VRED
Columns
1-8
9-11
12-14
15-17
18-20
21-23
24-32
33-41
42-50
Format
A8
13
13
13
13
13
F9.4
F9.4
F9.4
Description
Eight character sample identifica-
tion.
Number of processing options (also
the number of option cards to
read) .
0 = Do not read background for this
sample.
1 = Read a background spectrum for
this sample; also use this back-
ground for all subsequent samples
until another is read in.
1 = To subtract background perman-
ently for this sample (applies
to all processing options) .
0 = Do not permanently subtract the
background for this sample (the
background may still be subtract-
ed for specified options) .
1,2,3, or 4 for detector A,B,C. or D.
If greater than zero, the last back-
ground spectrum input will be ex-
changed with the nuclide standard
MS for the purposes of computation.
(Actual spectrum in library remains
unchanged.) This change is per-
manent for duration of the job or
until another substitution is made
on a subsequent sample.
Counting time (in minutes) for back-
ground spectrum.
Counting time (in minutes) for sample
spectrum.
Volume Reduction Factor (calculated
sample activity is divided by this
factor) .
-------
5-1
:i 1 (cont.)
(Sample Control Card, Cont.)
Variable
DAY
VM
Columns
51-59
60-68
Format
F9.4
F9.4
Description
Decay time in days between sample
acquisition date and counting date.
Volume multiplication factor (cal-
culated sample activity is multi-
plied by this factor) .
(Background Spectrum Cards)
A set of cards or card images residing on the logical unit
specified on the General Control Card and consisting of
1. A 20A4 identifying header card.
2. As many cards or images as required by the format
specified on the Format Control Card.
(Sample Spectrum Cards)
A set of cards or card images residing on the logical unit
specified on the General Control Card and consisting of
1. A 20AU identifying header card.
2. As many cards or images as required by the format
specified on the Format Control Card.
Sample Option Card - 613,3F6 . 2 (2212) ,
a Set of NOPT Cards]
Variable
N
MB
Columns
1-3
4-6
Format
13
13
Description
The number of standard nuclides to
use from the library.
1 = To subtract background from sam-
ple for this processing option.
0 = Do not subtract the background.
-------
5-9
TABLE 1 (cont.)
(Sample Option Card, Cont.)
Variable
NW
KT
IRD
IPRINT
Qti
Columns
7-9
10-12
13-15
16-18
19-24
Format
13
13
13
13
F6.2
Description
1 = For weights based on reciprocal
of the calculated counts/channel.
2 - For weights based on the recip-
rocal of the variance of the cal-
culated counts/ channel (requires
that a sample background be
present) .
3 = For unit weights.
- 1 = For weights based on the
reciprocal of the observed counts/
channel.
-2 = For weights based on the
reciprocal of the variance of the
observed counts/channel (requires
background) .
2 = For automatic gain and energy
threshold shift compensation.
1 = For automatic gain shift com-
pensation only.
0 = For no compensation.
- 1 = For manual compensation -
requires input values of gain and
threshold shifts on a card immedi-
ately following this option card.
-2 = To base the values of gain and
energy threshold shift on the
results calculated from a previous
sample (The value of Qh on this
card must be set to a negative
value) .
0 = For no print- plots.
1 = For print-plots of residuals.
2 = For print- plots of residuals,
calculated and observed spectrum.
1 = To print matrices for each
cycle.
0 = For no matrices for each cycle.
Energy offset, in channels or
fractions of a channel, between
the spectra in the standards
library and the sample spectrum.
Leave blank if unknown.
-------
5-10
TABLE 1 (cont.
(Sample Option Card, Cont.)
Variable
Q
XMOD
IS(1)
IS (2)
1S(3)
IS(N)
Columns
25-30
31-36
37-38
39-40
41-42
Format
F6.2
F6.2
12
12
12
--
Description
0 = For no rejection cycle.
n. m = To apply a rejection ratio
of n.m. (Refer to 5.4.)
Modifier for weighting scheme.
(Refer to 5.4.)
The numbers of the "N" library
standards selected for analysis.
(Manual Shift Card - 2F10.4, This
Card Required Only if KT = -1)
Variable
FTT
SHCI
Columns
1-10
11-20
Format
F10.4
F10.4
Description
Value of gain factor to apply.
Value (in channels) of the energy
threshold shift to apply.
-------
5-11
CALCULATE
&
OUTPUT
RESULTS
Figure k. Basic loop structure of ALPilA-M.
-------
5-12
ETC.
ETC.
ETC.
SAMPLE OPTION CARD #1
SAMPLE SPECTRUM CARDS
SAMPLE #2 CONTROL CARD
ETC.
SAMPLE OPTION CARD #2
SAMPLE OPTION CARD #1
[SAMPLE SPECTRUM CARDS
BACKGROUND SPECTRUM CARDS
SAMPLE#1 CONTROL CARD
GENERAL CONTROL CARD
Figure 5. Arrangement of input card deck for the ALPHA-M program.
-------
5-13
M NIT NBA NZ MF NTS NTM MU NH IAUX IOPT FM
256 5 0 10 181 11 5 900 1 (10F7.0).
Since ALPHA-M is set up to use 256 channels of data, the
parameter M never changes. Experience has shown that five
iterations (NIT) are sufficient to resolve most spectra.
ALPHA-M will terminate the run after less than five
iterations if the chi-square per degree of freedom (CHDF)
falls low enough (<1.2) or if the iterations are diverging
rather than converging. The library standards (NBA) are not
usually printed because of the large volume of print
required. The selection of the initial channel (NZ) for
calculations is arbitrary. Our laboratory selects channel
10 as the first calculation channel—the first nine analyzer
channels are empty because pulse discrimination is used to
remove the influence of the lead X rays and bremsstrahlung
that arise at low energies. Our laboratory selects channel
181 as the final channel for computation (MF) because no
radionuclide for which we are analyzing has a gamma ray with
an energy above 1.7 MeV. This channel selection option
saves CPU time in the calculations, but the limits will vary
with the user. Correlations (NH) are not normally requested
for routine operation because of the extra print
requirements. All data entered into ALPHA-M by our
laboratory are punched or stored in the same 10F7.0 format
(FM) . Other users may wish to change this format
The variables NTS, NTM, MU, IAUX, and IOPT all identify
Fortran logical units from which or to which the program
reads or writes information; they are defined by the system
control cards required to execute the program. An ex-
ample of this setup for an IBM system is given in Appendix A.
For routine processing, the optional printed outputs such as
correlation coefficients, library standards, and residual
plots are not requested because of the large amount of
required print. If a sample analysis appears to be
unsatisfactory, these options could be selected on a rerun
of the sample to determine the source of the poor
performance.
The next card in the control file is the sample control
card. This card contains specific information used to
properly identify and correct the final calculated
activities for the particular sample being analyzed. For a
10-day-old, 3.5-liter water sample that was counted for 4000
seconds to yield a final answer in pCi/l corrected to the
actual time of collection, the sample control card might
look like:
XIDT NOPT NBR NBS IABP MS TB TSA VRED DAY VM
TEST1 100 20 66.67 66.67 3.5 10.0 0 .
-------
5-14
For routine processing, the preferred method of accounting
for the background is to use a background library standard
(Section 6). Therefore, no background is read by ALPHA-M
unless overridden by this card using variable NBR (NBR > 0).
To enter an individual background for a particular sample,
the best method of processing (NBS) is to not subtract the
background permanently. Of course, if only one processing
option is to be run, permanent subtraction is permissible.
However, once a background is permanently subtracted, the
original sample spectrum cannot be restored for analysis by
another processing option requiring the nonstripped
spectrum.
If a "background read" is requested, the background data
follows the sample control card in the control file. These
data cards consist of a header card identifying the
background followed by the background spectrum in the 10F7.0
format. The sample spectrum raw-data cards are the next
cards of the control file read by ALPHA-M. These cards have
the same arrangement and format as the preceding background
data.
After the raw-data cards have been read, ALPHA-M reads the
sample option card. ALPHA-M expects as many sample option
cards as were specified by variable NOPT on the sample
control card. A typical sample card has the following form:
N NB NW KT IRD IPRINT QH Q XMOD IS(1) IS (2) . . .
30120 0 01.00 1 2...
ALPHA-M allows the user to specify how many and which
nuclide standards to use for a particular processing option
with the variables N and IS(1), IS(2), IS(3), etc. If the
user is reasonably certain of which nuclides are present,
those specific nuclides can be called. If the user does not
have any information about the nuclides that are present,
the entire library can be invoked. By using the rejection
coefficient, Q, the program will make two passes on the
data—the first using all requested nuclides and the second
eliminating the library standards for those nuclides that
had negative activities or error terms larger than the
activity found. This rejection technique can achieve the
same effect as using a reduced library. The use of the
rejection coefficient is further discussed in Section 6. If
rejection is not required, then a value of 0.0 is entered
for variable Q.
The energy offset between library standards and the sample
spectrum (QH) is very difficult to determine. Therefore,
this variable should be left as zero except for test
operations.
-------
5-15
Data from this study and from Schonfeld's work1, 2 show that
selection of automatic gain and threshold shift, KT=2,
yields the most accurate results (see Section 6). selection
of the reciprocal of the calculated counts per channel,
NW=1, appears to be the most stable weighting scheme. The
various weighting options are also fully discussed in
Section 6.
If IAUX on the general control card is set for greater than
zero, the user can select which, if any, options to write
out for residual analysis with the variable IRD on the
sample option card. IPRINT allows examination of the
calculation matrices for samples that yield poor results or
that have received a singular matrix warning on a previous
run.
It is strongly suggested that the user select a zero value
for XMOD. All analyses in this report were performed for
XMOD=0.0. Any suggested change should be made only after an
extensive investigation of its effects on the refinement
process. XMOD appears in the weighting expression (Y +1.5
+ XMOD)-i and therefore could have a marked effect on the
analytical results.
If the variable KT on the sample option card has been set at
-2, a manual shift card must follow the sample option card.
The manual shift card tells ALPHA-M the values of gain and
threshold shift to apply to the sample spectrum.
5.5 ALPHA-M OUTPUT
The output from ALPHA-M is shown in figure 6. The first
page of output reflects the information received by ALPHA-M
from the general control card. The information records for
the library standards requested are also printed on this
page, thus allowing the user to see that the proper
standards were indeed selected.
Page two of the ALPHA-M output reflects the information on
the sample control card. The sample number heading on this
and following pages indicates the location of the sample in
the stream of samples submitted for analysis. If a
background spectrum is entered, it appears on page two
before the sample spectrum. The sum of all observed channel
counts is calculated and printed for both the background and
sample spectra. This can serve as a check for bad data
transmittal, if these values are determined in the analyzer
before submittal to ALPHA-M.
The fourth page of output reflects the input information
from the sample option card. The first results listed from
the ALPHA-M calculations are the CHDF, threshold shift, and
gain shift values for each iteration, followed by the
-------
ALPHA-H VERSION 2 LEVEL 3
RADIOANALYT1CAL LABORATORY
DATE: os/zi/76
TIHE:15531S08
GENERAL CONTROL INFORMATION
DATA FORKAT IS ( 10F8 .1 I
NUMBER OF CHANNELS IN ANALYZER 15 256
MAXIMUM NU^BEK OF ITERATIONS IS 5
IMT1AL CHANNEL FOR COMPUTATION IS 10
FINAL CHAfiNEL FOR COMPUTATION IS Ifll
STANDARD SPECTRA ON FORTRAN LOGICAL UNIT 3
SAMPLE SPECTRA ON FORTRAN LOGICAL ONIT 5
LIBRARY STANDARD SPECTRA MLL NUT BE PRINTED
CORRELATIONS BETWEEN VARIABLES KILL BE PRINTED
AUXILIARY DATA OOTPUT UN FORTRAN LTG1CAL ONIT 4
ANALYTICAL RESULTS OUTPUT ON FORTRAN LOGICAL UNIT 2
FORTRAN LOGICAL UNIT FDR PRINT-PLOTS (IF REOUESTED) IS
FILE CONTAINS DATA FDR GEOMETRY TYPE 3.5L WATER
NUCLIOE
BACKGRND
144CE-PR
51CR
1311
137CS
95ZR-NB
56CO
54KN
65ZN
60CO
40K
14C3A-LA
RADON
HALF-LI FE (DAYS) CNT-TIMF(MINS 1 ACT-DET-A
285 .0
27.7
8 .1
369 .0
767.0
11100 .0
65.0
70.8
313.0
245.0
1920.0
12.8
66.66667
66.66667
66 .66667
66 .66667
66 .66667
66 .66667
66 .66667
66 .66667
66.66667
66.66667
66 .66667
£6. 66667
66 .66667
66.66667
66.66667
NUMBER OF STOS IS 15
ACT-DET-B
ACT-DET-C
NUMBER OF DETECTORS IS
ACT-DET-D
350.0
3217.0
4903. 0
4525.0
4151.0
6941.0
3803.0
14540.0
7193.0
6316.0
2538.0
4630.0
22Z50.0
5950.0
350.0
350.0
3217.0
49D3.0
4525.0
4151.0
69il.O
38D3.0
14540.0
7193.0
6318.0
2538.0
4630.0
22250.0
5933.0
350.0
350.0
3217.0
4903.0
4452 .0
4151 .0
6941.0
3803 .0
14540.0
7264.0
6318 .0
2538 .0
4630 .0
22293.0
6011.0
350.0
350.0
3217.0
4903.0
4452.0
4151.0
6941.0
3f03.0
14540-0
7264.0
6318.0
2538.0
4630.0
22250.0
5994.0
350.0
Figure 6. ALPHA-M output.
-------
CONTROL INFORMATION SAMPLE NUMBER 1
SAMPLE ID IS: 1-131-50
NUMbER OF PROCESSING OPTIONS IS 1
COUNTING TIME (MINS.) FOR PKGND IS 66.67
CCUNTIf.G TIME (MINS.) FOR SAMPLE IS 66.67
DECAY TIME (DAYS) IS 0.0
VOLUME REDUCTION FACTOR IS 3.500
VOLUKE MULTIPLICATION FACTOR IS 1.000
SAMPLE TIKE/BKGND TIME = F5 = 1.000
VALUE OF FS»»2 = FX - 1.000
SAMPLE BACKGROUND WILL BE INPUT AND USED IF SUBTRACTION RECUESTED
PERMANENT EACKGROUND SUBTRACTION NOT RECUESTED
DETECTOR A STANDARDS SELECTED
TEST fACKGROUND IS LIBRARY
4000 .0
719.2
705.2
555.1
337.9
350 .7
265 .9
174.5
146 .7
1?4.7
11C .7
107 .6
83.2
74.6
94.9
46.2
45 .3
50 .7
28 .5
25.6
23 .8
32.1
22.5
16.8
18 .4
0.0
0.0
675.6
702.2
516.9
332.6
353.1
267.1
164.7
141.7
124.1
105.8
99.8
60.0
74.8
93.9
4£.2
46.2
47.4
27.6
24.1
26.6
31.8
19.2
It. 7
16.3
0.0
STANDARD NUMBER DNF
0.0
704.7
668 .0
4«5 .5
333.9
317.1
244.0
161 .2
141 .2
1 ? 5 . 1
103.6
101 .3
79 .9
80. 3
85 .9
45 .7
45.3
45 .9
31 .2
25.4
25.8
28 .3
17.9
17.1
18 .6
0.0
0 .0
732 .6
706 .5
491 .4
311 .5
290 .4
221 .2
168 .1
142 .3
128 .5
105 .1
91 .2
72 .0
80 .1
75 .4
45 .3
48 .5
45 .0
28 .0
24 .7
26 .8
27 .3
17.5
16.6
7 .3
0 J3
0.0
779.0
713.2
510.3
309.7
276.8
206.0
151 .8
136.7
114 .7
106.6
93.9
79.9
90.3
73.3
46.9
49.9
39.3
32 .1
23.7
27.8
28.4
17.4
16.3
0.2
0.0
D .3
781 .6
66< .8
53^.9
316 .2
24'i .9
197 .6
15B .8
134 .2
112 .3
102 .5
91 .1
73 .3
93 .6
6!. .9
45 .0
4B .3
35 .7
23 .3
2'-, .0
33 .1
27 .8
17.2
16 .8
3 .1
0 .0
190.9
773.7
614.0
494.9
324.7
249.1
178 .0
157.1
138.1
112.5
104.8
87.6
72.6
98 .3
57.5
42 .7
51 .7
31 .5
26.9
22 .9
26.3
26.6
17.5
15.8
0.0
638 .1
748 .9
581 .2
435 .2
329 .8
259 .5
179 .9
148 .4
135 .0
115 .2
106 .1
87 .3
75 .9
95 .3
52 .7
45 .8
53 .0
37 .4
27.6
24 .8
27.9
25 .8
16.8
16 .7
0 .0
751 .2
728 .0
583 .4
387 .6
333 .2
254 .7
179 .8
152 .4
132 .8
109 .5
110.8
82 .8
70.3
99 .6
51 .5
44 .3
56.3
31 .3
24.0
25.8
28 .7
23.4
15.3
17.2
0 .0
777.5
736.0
579.1
358 .0
343 .4
272 .9
175 .1
155.3
124 .9
110.5
108 .7
86 .6
76 .6
93.4
48 .9
45 .6
49 .6
32.5
26.9
24.3
31.5
20.7
17.7
17.7
0.0
Figure 6. ALPHA-M output (cont.)
-------
SAMPLE CCKSISTS OF 50 PCI/LITEF 1-131 +
1 .0
792 .7
89b .3
602.0
392 .3
335 .2
2 fr c . 1
174 .8
112 .2
137 .8
107 .8
9V .1
9S .5
77 .0
103.1
43 .6
3e .0
56 .1
36 .B
IS .u
24 .6
25.8
9.7
11.1
17.7
2.1
BACK&D SUK-
0.0
669.5
739.8
55-. 2
357.3
35t . 2
320.6
171.2
117.6
134.5
121.1
93.7
81.7
86.3
67.0
52.2
37.8
54.7
24.0
20.9
20.9
3b.C
15.5
ia.6
9.b
1.8
37563.
0 .0
7«1 .8
699 .6
527 .6
293 .7
2°9 .1
2 6 F .2
170.4
134 .8
123.5
86.7
105 .7
63 .0
71 .5
62 .5
62 .8
32 .0
40 .0
27.0
22 .8
21 .1
31.5
7.5
9.5
18.7
0.8
SAMPLE SUK=
BACKCR CUND
0 .0
771 .4
791 .4
524 .3
304 .7
314 .9
207 .6
189 .1
146 .0
143 .0
104 .9
79 .2
75 .3
81 .4
63 .4
45 .7
58 .3
41 .8
20 .8
35 .6
32 .5
26 .2
12 .0
20 .3
6.9
0 .4
40698 .
0.0
791 .8
695.1
693.7
332.7
300-7
252 .8
142.0
120.8
10ft .1
122 .9
95 .1
61 .4
76.1
76.4
53.1
53.6
45 .6
22.4
34 .2
42 .1
34 .1
14.8
16.2
1.5
0.2
3 .3
91b .3
713 .5
f.76 .0
309 .7
236 .8
207 .6
125 .0
153 .3
83 .5
103 .3
101 .6
53 .3
88 .2
57 .3
39 .3
52 .3
33 .2
27 .(,
18 .£>
33 .7
38 .6
!<. .1
19.4
-1 .1
0.7
178 .2
945.2
709.7
829 .6
297 .4
297 .4
190.8
140.0
129.8
128 .8
127.1
78 .6
65.8
86.8
59.6
39.6
46.2
40.0
30.6
27.8
26.8
20 .2
13.4
5.5
0.3
667 .3
91fc .8
634 .6
798 .8
366 .3
229 .7
171 .3
141 .7
160 .2
101 .1
117 .2
7a .2
89 .6
91 .2
48 .1
40 .8
41 .3
22 .6
27 .6
27 .9
31 .1
26.0
20 .9
17.8
-2 .0
772 .9
7P9 .2
596 .3
605 .6
331 .6
253 .4
170.8
137.3
113 .9
107 .9
90 .0
94.3
71 .2
107 .1
62 .3
60 .1
52 .4
36 .0
28 .1
26 .1
27.7
27.8
22 .2
14.0
2.5
853 .1
845 .0
669.0
460 .2
346.1
304.7
166.9
133 .9
144.5
103 .5
95.0
93.9
59 .3
92 .4
77.2
51 .9
54.7
26.0
33 .5
30 .1
36.0
33 .4
13.5
9.0
-0.7
I
I—'
00
Figure 6. ALPHA-M output (cont.)
-------
SAMPLE NUHPER i
ID NO. 1-131-50 PROCESSING OPTION NUMBER
BACKGROUND WILL NOT BE SUBTRACTED THIS OPTION
WEIGHTS TU BE fASED ON CALCULATED SAMPLE SPECTRUM
WEIGHTS PKCPORT10NAL TO RECIPKCCAL COUNTS/CHANNEL
REJECTION COEFFICIENT OF 1.00 WILL BE APPLIED
AUTOMATIC COMPENSATION. RECU1RFD FOR GAIN AND THRESHOLD SHIFT
NUWBEK OF ISOTOPES USED FRPM LIBRARY IS 15
THRESHOLD CHANNEL SHIFT BETWEEN 5TDS AND SAMPLE IS 0.0
LIBRARY STP. NUMBERS, IN ORDER OF DESIRED OUTPUT ARE 123
NORMALIZED RESIDUALS WILL BE PLOTTED
OBSERVED AND CALCULATED SPECTRA WILL BE PLOTTED
KATRU INFORMATION KILL NOT BE PRINTED
7 8 9 10 11 12 13 14 15
CKDF = 0.97 THR SHIFT =
CHDF = C.90 THR SHIFT =
CHDF = 0.86 THR SHIFT =
CHDF - 0.63 THR SHIFT -
CHDF - 0.82 THR SHIFT =
0
0
0
0
0
.0568
.0991
.1196
.1309
.1364
GAIN
GAIN
GAIN
CAIN
GAIN
SHI
SHI
SHI
SHI
SHI
FT
FT
FT
FT
FT
Si
=
=.
=
=
0
0
0
0
0
.9996
.9991
.9986
.9966
.9985
CORRELATIONS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1 .000
-0.191
0.036
0 .055
-C1 .291
0 .044
-C .314
-0.291
0.052
-0.150
-C .127
-0 .437
-0.592
-0 .631
-0 .529
0 .126
-0.112
1 .000
0.016
-0.025
-0.072
0.148
0.026
-O.C25
-0.051
o.oia
0.063
0.1 51
0.095
0.131
-0.092
-0.175
0.246
1 .000
-0 .001
-0 .041
0 .203
-G .029
-0 .063
-C .Of 7
0 .027
0 .057
0 .090
-0 .004
-0 .104
-0 .350
-0 .031
0 .109
1 .000
0 .013
0.341
-r .ou4
-0 .057
-C .1 B2
C .050
0 .134
0.135
0 .032
0 .056
-0 .557
C .207
-0.317
1 .COO
-0.102
-0 .082
n .236
-0.265
0.3-34
-C .056
0.176
0.203
-0.081
0.051
0.065
-0.067
1.000
-0.049
-C.276
-0.468
0.096
0.1 13
0.065
-0.026
C.128
-0.546
0.057
-0.071
1 .000
0 .049
0 .070
-0 .032
0 .044
0 .125
0 .200
0 .229
0 .092
-0.022
-0.040
1 .030
-0.233
0.338
-0.012
0.077
0.179
0.120
0.198
-0.024
0.008
1.000
-0.794
-0.059
-0.077
-0.032
-0.179
0.291
-0.037
0.032
1.000
-0.007
O.OB4
0.065
0.062
-0.049
0.032
-0.001
1 .000
-0.187
0.035
0.105
-0.136
-0.015
-0.002
1.000
0.141
0.163
0.031
0.017
0.011
1
0
0
-0
0
.000
.327
.213
.143
.114
1
0
-0
0
.000
.182
.116
.116
1.000
-0.138
0.192
1.000
-0.822
Ul
I
Figure 6. ALPHA-M output (cont.)
-------
LIBRARY NUCL1DE
NUMBER NAP. F
1 EACKGRtiD
2 144CE-PR
3 51C*
4 1311
5 1 0 6 R U
6 134CS
7 137CS
8 95ZR-N8
9 5bC3
10 54CM
11 6SZN
12 60 CD
13 40K
14 140C-A-LA
15 RADPN
NORKALI
C
2
0
-1
-0
-0
1
1
-u
c
.0
.4
.9
.0
.6
.2
.2
.0
.9
.8
PECAY UKCORRFCTED
ACTIVITY STD . ERR.
99.2208 3.6255
-29.4729 12.7227
-16.1977 24.5637
55 .7074 4 .4788
B .34£ 1 12.6111
2 .5U2 4.1426
-0.2911 2.9736
-1.7G11 3.2C02
-I't.'.S'S 6.2361
3.9251 4.7fc04
-1.2014 5.9745
-1.5538 2.6811
-46.5003 39.3006
5.0339 3.2990
2.6242 4.5061
ZED RESIDUALS PER
O.C
-0.7
0.7
1 .0
-0.3
1 .1
0.1
-0.2
-1 .0
0 .0
-0.8
-1 .5
0 .0
0.3
-1.1
-1 .3
-1 .3
-1 .2
0.0
0.4
-0.3
-1.6
0.4
0.1
0.2
-0.6
0.9
DECAY CORRECT ED
ACTIVITY ST3 . E '. R.
99.2208 3.6255
-29 .4729 12 .7227
-lfa.1977 2\ .3637
55.7074 !>.47B8
8 .3461 12 .311 1
2 .5162 t, .1426
-0 .2911 2 .9736
-1 .7011 3 .2032
-14.4353 S.23M
3.9251 'i.7634
-1.2014 5.97^5
-1.5538 2.6811
-46.5003 3J.3036
5.0339 3.2990
2.6242 '-..50S1
COEFFICIENT ALPHA
OF VARIANCE FACTOR
3.65 5.1268
43.17 0.5990
151.65 0.9160
8.04 1.1009
153.50 1.3733
164.64 1.6750
(,(,»«(.£. 0 .6 184
188.12 0.7197
43.20 1.682J
121.28 1.0568
497.28 0.8121
172.55 1.0776
84.52 0.6725
65.53 1.9222
171.72 3.4124
LLO
11.9278
41.8578
80.6147
14.7352
42.1486
13.6292
9.7831
10.5286
20.5167
15.6blb
19.6562
8.8207
129.2989
10.8536
14.8252
CHANNEL
0 .0
-1 .7
0.7
1 .'<.
-0.9
1 .1
-1 .5
0 .4
0.3
0.0
-0 .0
-0 .3
0.0
0 .8
0.1
-1 .3
-0 .4
0 .3
0.0
1 .2
-1 .2
0.5
-0.6
1 .6
-0.4
0.2
-0.7
0 .0
0 .3
1 .2
-0 .5
1 .4
0 .7
1 .2
-0 .4
-1 .2
0.0
-1.5
-0.1
-0.4
-0.8
-1.3
0.2
1 .1
-0.3
0 .2
0 .2
-0.2
-0.4
1.2
-0.8
-1.2
2.2
0.4
0 .9
-0 .i
-0 .7
0.1
0 .9
-0 .5
0 .<.
-0 .5
0 .3
-1 .4
-3 .t.
0 .1
3 .5
3 .6
-3 .3
1 .3
0 .1
0 .5
-0.3
-0.3
-0.5
0.7
-0.1
0 .3
-0.6
1 .0
-0.7
-0.5
-0.6
1.0
1 .2
0.9
-0.7
0.2
-0.4
-0.5
-0.3
2 .1
1 .0
-0 .2
-0 .3
0.3
-0.8
-0.1
0.5
1 .3
-1 .7
-0.3
-1 .4
-1 .5
0 .9
-0.3
-1 .2
-0 .3
1 .3
0.4
1 .7
-0.4
1.2
-Q .5
-0.7
-O.B
0.7
1 .0
0.7
-1 .4
0.5
-0.8
-0.5
0.1
-0.8
-l.fr
-1 .3
-1 .1
-0.5
0.3
-0.1
0.9
0.8
1.2
0.4
-0.1
0 .2
0 .6
0.4
-0.1
0.6
0.3
0 .4
-0.7
AVERAGE =-0.0076 5TD. DEV. = 0.8610 SKEkNESS = 0.1509 KURTOSIS « 2.5276
PERCENT CF RESIDUALS UNDER 1 SIGMA = 65.1 2 SIGMA = 97.1 3 SliMA -100.0
SAMPLE/OPTION WRITTEN TO 10PT AT 05/21/76 15:3U18
I
KJ
O
Figure 6. ALPHA-M output (cont.)
-------
SUBPLE NUKPER 1
ID NO. 1-131-50 ... PROCESSING OPTION NUMBER I
BACKGROUND HILL NOT BE SUBTRACTED THIS OPTION
WEIGHTS TO BE BASED DM CALCULATED SAMPLE SPECTRUM
WEIGHTS PROPORTIONAL TO RECIPROCAL COUNTS/CHANNEL
REJECTION COEFFICIENT OF i.00 HAS SEEN APPLIED
AUTOMATIC COMPENSATION REQUIRED FOR GAIN AND THRESHOLD SHIFT
NUMBER OF 1SPTCPES USED FROM LIBRARY IS 3
THRESHCLD CHANNEL SHIFT BETWEEN STCS AND SAMPLE IS 0.0
LIBRARY STD. NUMBERS, IN ORDER OF DESIRED OUTPUT ARE 1 4 14
NORMALIZED RESIDUALS WILL BE PLOTTED
OBSERVED AND CALCULATED SPECTRA WILL BE PLOTTED
MATRIX INFORMATION WILL NOT BE PRINTED
CHDF
CHDF
CHDF
CHDF
CHDF
B
X
3
=
I
1.01
0.96
0.95
0.94
0.93
THR
THR
THR
THR
THR
SHIFT
SHI
SHI
SHI
SHI
FT
FT
FT
FT
0
0
0
0
0
.0155
.0290
.0358
.0395
.0420
GAIN
GAIN
GAIN
GAIN
GAIN
SHIFT
SHIFT
SHIFT
SHIFT
SHIFT
K
B
I
V
m
1-0030
0.9999
0.9997
0.9997
0.9996
CORRELATIONS
1 1.000
2 -0.425 1.000
3 -0.816 0.120 1.000
4 -0.006 0.140 -0.043 1.000
5 -0.031 -0.211 0.055 -0.811 1.000
LIBRARY NUCLIDE DECAY UNCORRECTED DECAY CORRECTED
NUMBER NAME ACTIVITY STD. ERR. ACTIVITY STD. E*R.
1 BACK&RND 96.9487 1.5517 96.9487 1.5517
4 1311 57.3890 3.5928 57.3890 3.5928
14 140BA-LA 3.6308 2.8904 3.6308 2.8934
NORMALIZED RESIDUALS PER CHANNEL
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2.7 -0.9 -0.8 0.7 -1.7 0.1 1.3 0.3 -1.4
0.8 0.8 -1.5 -0.3 0.9 -0.2 -1.1 1.4 -0.1
-0.3 1.9 0.6 -1.2 1.6 0.1 0.5 -0.5 -0.4
-2.0 -1.5 -0.4 0.2 -0.9 1.0 -0.4 1.6 -0.7
-0.0 1.2 -1.0 0.1 1.3 0.2 1.6 0.9 -1.2
1.3 0.2 -1.1 0.2 -1.3 -1.4 -0.4 1.2 0.2
0.7 -0.4 -1.5 -0.8 0.3 -0.5 0.2 -0.4 1.1
-0.7 -0.9 -1.2 1.0 0.5 0.5 -0.5 -I J3 -0.2
1.1
AVERAGE = 0.0129 STD. OEV . = 0.9547
PERCENT OF RESIDUALS UNDER 1 SIGMA * 66.9 2 SIGMA
SAMPLE/OPTION WRITTEN TO IOPT AT os/21/76 15:31:22
0.2
0.4
-0.1
-0.4
1 .3
-0.8
-1.2
2.6
0.6
SKEWNESS
•95.9
0.3
-0.*
-0.7
0.3
0 .9
-0.4
0.3
-0.3
0 .6
.
3
-2.0
-0.4
0.0
D .4
D .8
-0.3
1 .0
D .3
0.8
0.3874
SIGMA
COEFFICIENT ALPHA
OF VARIANCE FACTOR
1.60 1.9363
6.26 0.7793
79.61 1.4861
-0.3
-0.5
-0.7
0.5
0.0
0.4
-0.6
1.4
-0.5
-1.2
-0.7
0.9
1.1
1.0
-0.7
0.2
-0.2
-0.2
-1.7
2.5
1.0
-0.6
-0.3
0.2
-0.9
0.2
0.7
0.9
-1 .4
-0.3
-1 .7
-1 .4
0.9
-0.3
-0.9
-0.2
KURTOS1S -
-100.0
1.4
0.9
2.2
-0.9
1.2
-0.5
-0.7
-0.6
1.0
2.6775
LLD
5.1051
11.8203
9.5094
1.2
0.7
-1.2
-0.4
-0.7
-0.5
-0.1
-0.7
-1.5
-1.3
-1.4
-0.0
-0.8
0.0
1.0
0.6
1.5
0.6
0.2
0.0
1.3
-0.9
0.0
0.6
0.1
0.6
-0.6
L/l
I
NJ
Figure 6. ALPHA-M output (cont.)
-------
5-22
correlation coefficients. The values of the correlation
coefficients reflect the interactions of the nuclides in the
matrix inversion calculations. This correlation table is
read by the row-column method used for determinants. The
correlation between nuclides 6 and 10 is given in row 10,
column 6. Correlation values consistently greater than 0.6
indicate that the two nuclides in question may interfere
with each other in the analysis and therefore may weaken the
least-squares model used by ALPHA-M. A discussion of this
problem and possible solutions are included in Section 6.
The next results printed are the actual analytical results
determined by ALPHA-M. The library number of the particular
nuclide is written in the first column and the nuclide name
is written in column 2. The two columns designated as DECAY
UNCORRECTED contain the nuclide activity and standard error
not corrected for decay. This uncorrected activity value is
important for those radionuclides having short half-lives.
If a sample was collected more than four half-lives before
analysis, the uncorrected activity may show a value below
the lower limit of detection for that nuclide. In such a
case, the uncorrected activity value will indicate that the
large results created by decay corrections are meaningless.
In addition, the DECAY UNCORRECTED results should always be
used in any statistical evaluation of program performance.
This situation also is reflected in the LLD values found in
the last column of results; these LLD values are corrected
for decay.
The next double column is labeled DECAY CORRECTED and
contains those nuclide activities and standard errors which
have been corrected for decay. The coefficient of variance
for a particular nuclide appears in column 5. This quantity
is calculated by dividing the standard error of a particular
nuclide by its calculated activity and multiplying by 100;
this quantity will reflect the relative precision of the
analysis.
After the analytical results, ALPHA-M prints out the
standardized residuals. These residuals are the channel-by-
channel difference between the observed and calculated
values divided by the Poisson standard deviation of the
observed value for a specified channel.5 ALPHA-M provides
some descriptive statistics for these residuals. The
average value of the residual should be zero in the ideal
case and close to zero in all cases. The standard deviation
should approximate the CHDF value, and the skewness should
fall between -0.464 and +0.464 for 150 data points. The
value of kurtosis should range between 3.65 and 2.45 for 150
data points. The suspicious channels tabulated at the end
of the printout are those channels lying outside a three-
standard-deviation band surrounding the residual mean.
These suspicious channels should be observed closely over a
-------
5-23
period of time to test the frequency with which certain
channels appear. The recurrence of particular channels
could indicate the presence of a nuclide in the samples for
which there is no standard in the library.
For the printout in figure 6, ALPHA-M was requested to apply
a rejection coefficient of 1.0 to the analysis results
obtained by using the full set of library standards. Those
library members selected for the second pass had
contributions with standard errors that were smaller than
the calculated activity on the first pass. The output for
the second pass follows the same format as the first. The
data from this second analysis should be an improvement in
the analytical results for those nuclides used for the
second determination since the number of library members is
reduced. However, some very imprecise but real measurements
may be rejected by this process. This is discussed more
fully in Section 6.
5.6 REFERENCES
1. Schonfeld, E. ALPHA - A Computer Program for the Deter-
mination of Radioisotopes by Least-Squares Resolution
of the Gamma-Ray Spectra, Nucl. Instrum. Methods, 42:
213-218, 1966.
2. Schonfeld, E. ALPHA-M - An Improved Computer Program
for Determining Radioisotopes by Least-Squares Resolu-
tion of the Gamma-Ray Spectra, Nucl. Instrum. Methods,
52: 177, 1967-
3. Anscombe, F. J., and J. W. Tukey, The Examination and
Analysis of Residuals, Technometrics, 5: 141-160, 1963.
4. Wooding, W. M. The Computation and Use of Residuals in
the Analysis of Experimental Data, J. Qual. Tech., 1:
175-188, 1969.
5. Pasternack, E., and A. Luizzi, Patterns in Residuals:
A Test for Regression Model Adequacy in Radionuclide
Assay, Technometrics, 7: 603, 1965.
6. Scheffe, H. The Analysis of Variance, John Wiley and
Sons, Inc., New York, 1959, Chapter 4.
7. Bennett, C. A., and H. L. Franklin, Statistical Analysis
in Chemistry and the Chemical Industry, John Wiley
and Sons, Inc., New York, 1954, Chapter 6.
8. Altshuler, B., and B. Pasternack, Statistical Measures
of the Lower Limit of Detection of a Radioactivity
Counter, Health Phys., 9: 293-298, 1963.
-------
5-24
9. Pasternack, B., and N. H. Barley, Detection Limits
for Radionuclides in the Analysis of Multicomponent
Gamma-Ray Spectrometer Data. Nucl. Instrum. Methods,
91: 533-540, 1971.
10. U.S. Atomic Energy Commission, HASL-300 Procedures
Manual, Health and Safety Laboratory, New York, 1972.
-------
SECTION 6
EVALUATION OF ALPHA-M
6.1 GENERAL
The performance of ALPHA-M depends on the properties of the
standard spectra, the properties of the sample spectra, and
the program processing options chosen. Summarizing this
performance and resolving anomalous results during initial
program installation and later operation require both some
radiochemical and statistical expertise.
This section provides results to guide ALPHA-M users in
their selection of program processing options. Methods also
are presented for examining the standard libraries to
determine their performance capabilities and for monitoring
actual analytical results to test for anomalous values.
6.2 PROGRAM PROCESSING OPTIONS
ALPHA-M offers a large variety of options for sample
analysis. The following decisions must be made before
processing:
1. Whether background is to be (a) stripped (either by
the analyzer or the program) from sample spectra or
(b) included as a library standard.
2. Whether (a) both gain and threshold shift, (b) gain
shift alone, or (c) no shift is to be applied to the
sample spectra.
3. Whether the weighting scheme to be applied in the
refinement process should be (a) reciprocal of the observed
counts, Yo1, (b) reciprocal of the calculated counts,
Y-1, (c) reciprocal of the observed counts plus back-
ground, DY-1, (d) reciprocal of the calculated counts
plus background, DY-1, or (e) unity weights.
These choices lead to 30 different methods for analyzing
sample spectra. The number of options can be reduced by
eliminating the obviously poorer and theoretically unsound
weighting schemes. Theory suggests that the weights should
equal the reciprocals of the variances of the data being
fitted.i
All weights based on observed counts should be disregarded
for environmental work because of the large relative
variability of counting statistics at low counting rates.
-------
6-2
Also, unity weights should not be selected because unity in
no way represents the variance of the data being fitted.
Elimination of these weighting schemes reduces the possible
processing options to 12.
If the sample spectra are stripped of background, simple
weighting by Y-1 does not properly estimate the variance of
the data point's. Similarly, using DY"1 without stripping
adds an extra background to the weights so that again the
theoretical variance is not estimated.
Therefore, we are left with the choice of using (1)
background stripping and the DY^1 weighting scheme or (2)
background as a library standard and the Y"1 weighting
scheme. These options are the only two weighting schemes
that are compatible with theory. Of course, the shifting
options have not been considered. To determine superiority
among the remaining options, the program SIMSPEC (Appendix
C) was used to simulate sample spectra for each of 12
different nuclides. Six spectra were created for each
nuclide at an activity level of 50 pCi/£ and were analyzed
using the remaining options. The average absolute percent
error for each nuclide appears in table 2. These values are
all somewhat high because the variances of the simulated
spectra are not equal to the mean counts, but rather to
twice the mean counts.
There is little difference between the two weighting
options. However, in 9 of 12 cases, compensating for
background by using a library standard gave a slightly
smaller error. Treating the background as a library
standard has the advantage that overall changes in
background level are better compensated for in the
processing.
Gain shifting is generally defined as the situation in which
the energy zero intercept remains unchanged while the rest
of the spectrum channel contents are shifted up or down in
energy in a multiplicative fashion. Threshold shifting,
however, is the translation of the entire spectrum along the
energy axis in an additive fashion. For Nal scintillation
spectra, normal gain shifts are usually cited as being less
than 3 percent and threshold shifts are usually less than
1.5 channels. Note that the factors known as gain and
threshold shifts are often merely components of a single
effect produced by the variability of the detector-
electronics package.
The gain and threshold shift procedure in ALPHA-M is based
on an estimate of the derivative of the true spectrum
obtained by differencing the observed spectrum.2 This
estimate, scaled in two different ways, is used to create
two additional independent variables in the regression
-------
TABLE 2. AVERAGE PERCENT ERROR WITH DIFFERENT PROCESSING OPTIONS0
Option
Strip DY-i
Gain- threshold
shift
Strip DY-1
Gain shift only
Library BKG Y~*
Gain- threshold
snif t
Library BKG Y~4
Gain shift only
Nuclide (50 pCi/ e.)
144Ce
17.5
27.4
15.7
24.2
slCr
24.7
33.4
3t,6
28.5
1312
7.5
7. 1
6.4
7. 1
106Ru
30.7
28.8
24.8
27.9
5aCo
17.4
19.2
14.6
14.4
134CS
6.3
6.2
6.5
6.7
1 37Cs
4.1
4.3
5.7
b.3
9SZr
12.8
12.7
11.9
11.3
5*Mn
6.3
3.6
5.0
3.2
65Zn
7.6
6.9
6.9
6.8
60CO
5.3
5.3
i.8
6. 1
i *OBa
10.4
10.4
11.3
10.6
°SError =
Known-Found
Known
x 100
-------
6-4
equation. Because this estimate is subject to the counting
fluctuations in the observed spectrum, these new independent
variables may not match the effects of the gain and
threshold shift very well.
Schonfeld tested the gain and threshold shift algorithms.
on samples having activities well above environmental levels
and showed that dramatic improvements in analytical results
were obtained. Samples with environmental levels of
activity were not tested.
Before evaluating any translational effect, such as
threshold shifting in environmental spectra, one must
determine the degree of accuracy with which the position of
any peak can be determined. For a photopeak such as the
795. 8-keV peak of *• 34Cs (see the standards library in
Appendix D) , one may apply a least-squares Gaussian fitting
process using the channel numbers and contents describing
the peak to determine its position quite accurately-3
If (1) the contents of the photopeak channel and the
contents of the two or three channels immediately below it
are reduced by twice the square root of their contents, (2)
the contents of the two or three channels above the
photopeak are increased similarly, and (3) these values are
then refit to a Gaussian, the exact position of the peak is
shifted upfield by a small amount. If the process is
reversed, the photopeak will be shifted downfield by a small
amount. Thus, a small uncertainty in the position of any
peak will exist because of counting statistics alone. This
effect will be much more pronounced at environmental levels
of activity than at levels such as those used by Schonfeld
because the peaks are not as well defined.l
Table 3 illustrates the peak position error obtained by the
above process for various photopeaks in the standards
library. The average positional error is quite small (about
0.24 channel), but the errors range from 0.09 to 0.47
channel. Obviously, any threshold shift less than 0.50
channel will be difficult to detect.
If the channel and energy data in table 3 are fitted to a
straight line, the estimated gain is 11.32 kev per channel.
The energy error associated with the photopeaks in table 3
is shown in figure 7. Arguments similar to the above may be
used to indicate that system gain is uncertain to a degree
roughly equal to the expected gain shifts.
Shifts due to counting statistics or detector-electronics
effects do occur, and thus the question of whether ALPHA-M
can compensate for these shifts must be considered. To
determine this, sample spectra consisting of a standard
background plus nine nuclides, each at an activity level of
-------
6-5
TABLE 3. PHOTOPEAK POSITIONS, ERRORS, AND ENERGIES
Nuclide
106Ru
S8CO
»3*CS
6°CO
i40fia
40R
«5Zn
s*Mn
9«Zr
137CS
sicr
131J
Energy
(keV)
511.8
622. 1
511.0
810.6
604.7
795.8
1173.0
1332.0
487.0
815.8
1596.0
1460.8
1115.5
834.8
756.7
661.6
320.1
364.5
Peak
Channel
53.15
63.35
52.89
80.09
61,25
77-74
112.22
125.92
50.94
80.81
148.20
136.25
107.02
82.49
75.69
66.88
34.34
38.90
Error Range
(Chnls)
0.15
0.32
0.33
0.24
0. 19
0.29
0.32
0.47
0.09
0.23
0.25
0.44
0.27
0.15
0.18
0. 11
0. 13
0.12
-------
30
20 •
»
10
cc
o
i
LU
CD
-20
-30
40
50
60 70
80
90 100 110 120 130 140
150
CHANNEL NUMBER
Figure 7. Energy error vs. photopeak position.
-------
6-7
10 pCi/£, were generated and randomized six separate times
using SIMSPEC. The replicates were subjected to an ALPHA-M
analysis with no shifting, after being shifted upfield by
1.5 percent and then after being shifted downfield by 1.5
percent. The results are shown in table 4. Because of the
very high percent error at this low activity level and
because of the number of components, any systematic effects
are hopelessly masked. However, a gain shift of 1.5
percent, which corresponds to a positional shift of about
1.0 channel for the i^Cs standard, does not move the
average percent error outside the range observed with no
shift.
Most threshold and gain shifts, as reported by ALPHA-M, are
less than the calculated average error in photopeak
positioning. For example, in a set of 400 spectra made by
SIMSPEC with no shifts imposed, the average gain factor
(1.000) and threshold shift (-0.23) are very close to ideal
values determined earlier. This result indicates no
inherent instability in the gain or threshold shift
algorithm. Any apparent increase in analytical accuracy
deriving from the application of automatic shifting may be
due less to the actual shifting than to the use of this
translational degree of freedom in accounting for the slight
variations caused by counting statistics.
Since there is no evidence that it is detrimental to the
final analytical results, use of the gain and threshold
shift option may be worthwhile. The activity levels at
which gain and threshold shifts can yield marked
improvements in results have not been determined, but the
routine use of shifting may have shifting invoked when these
levels are indeed present in a sample.
Therefore, a summary of processing options can be
recommended for routine use:
1. Compensate for background with a background library
standard.
2. Use Y-i as the weighting scheme.
3. Allow automatic compensation for gain and threshold
shifts.
6.3 LIBRARY STANDARDS
After the program processing options are fixed, the
performance of ALPHA-M will depend primarily on the library
standards created for use with the least-squares process in
spectra fitting. The primary consideration in creating a
library of standards for use over a relatively long period
of time is the stability of the spectrometer system. As far
-------
6-8
TABLE h. GAIN SHIFT EFFECTS
NUCLIDE ACTIVITIES 10 pCi/LITER
Nuclide
1311
134QS
137CS
5*Mn
60CO
58CO
*«°Ba
106Ru
'szr
131J
13«CS
137CS
5*Mn
*°CO
58CO
i*oBa
106RU
95Zr
-1.5% Shift
No Shift
+1.5% Shift
Weights based on (Yc)-1
%E°
89.0
54.9
60.4
68.7
87.6
146.0
77.0
153.0
140.0
%E
70.0
66,0
57.2
53.0
60.0
83,7
85.7
105.0
138,0
%E
68. 1
68.7
57.3
64.6
58.0
69.2
82.9
1^8.0
133.0
Weights based on (DYC)-4
88.3
53.7
61.0
62.7
54.2
148.0
75.0
151-0
140.0
70,0
66,0
57,2
53.0
60,0
83.7
85,7
105.0
138.0
73.6
67.8
55.3
63.7
55.6
88.3
88.9
144.0
129.0
%E - % Error =
Known-Found
Known
X100
-------
6-9
as possible, all standards and sample spectra must be
determined under an identical set of experimental
conditions.
Factors such as system gain, linearity, and counting
geometry must be maintained through rigorous quality control
procedures. Changes in the counting system require
restandardization followed by a reevaluation of the library.
The selection of members for the standard library for a
particular analysis has a great deal to do with the
performance of ALPHA-M. Therefore, after the library is
created, the relationships among members must be determined.
The first step in this process is to analyze a background
spectrum using the full library. When the run is made, the
correlation coefficients should be printed out as in table
5. These correlations reflect the interference or
interaction of nuclides in the least-squares calculations.
These coefficients are calculated from the inverted matrix
from ALPHA-M and are equal to
- -
(A.. > (A. . )
where A. represents the matrix elements.
In least-squares analysis, the independent variables ideally
should be mutually orthogonal; where this is not the case,
the least-squares model will be weakened by interference in
the process of refinement and greater inaccuracies will be
included in the final results.
A survey of the correlation coefficients will indicate
possible interfering pairs by showing values of greater than
0.6. High correlations may occur occasionally because of
large fluctuations in counting statistics; but in general,
the correlation matrix from a background sample will present
a definite pattern. The analyses shown in table 6 were made
during the course of this study using the standard library
included in Appendix D. Examination of the correlation
matrix will indicate possible sources of poor analytical
performance among the selected standards.
These studies should be followed by analysis of gamma-ray
spectra of composite samples containing combinations of the
standard library radionuclides in known amounts.
Satisfactory analytical results are a function of the
criteria used by the analyst. One set of criteria for water
samples has been set up by the Environmental Protection
Agency in its gamma-in-water crosscheck program.5 The one
-------
TABLE 5. CORRELATION COEFFICIENTS FOR STANDARD NUCLIDE LIBRARY
Background
""•Ce
51Cr
'"I
">'Ru
13 "Cs
»37Cs
'5Zr
*»Co
5*Mn
ESZn
6 "Co
*°K
"•°Ba
Radon
Cain
Threshold
Background
1.000
-0.191
0.036
0.055
-0.291
0.044
-0.314
-0.291
0.052
-0.150
-0.127
-0.437
-0.592
-0.631
-0.529
0.126
-0.172
""-Ce
1.000
0.016
-0.025
-0.072
0.148
0.026
-0.025
-0.051
0.018
0.083
0.151
0.095
0.131
-0.092
-0.175
0.246
5!0
1.000
-0.001
-0.041
0.203
-0.029
-0.063
-0.087
0.027
0.057
0.090
-0.004
-0.104
-0.350
-0.031
0.109
131I
1.000
0.013
0.341
-0.004
-0.057
-0.182
0.050
0.134
0.135
0.032
0.056
-0.557
0.207
-0.317
106Ru
1.000
-0.102
-0.082
0.236
-0.265
0.334
-0.056
0.176
0.203
-0.081
0.051
0.065
-0.067
13 "C6
1.000
-0.049
-0.276
-0.468
0.096
0.113
0.065
-0.026
0.128
-0.546
0.057
-0.071
137Cs
1.000
0.049
0.070
-0.032
0.044
0.125
0.200
0.229
0.092
-0.022
-0.040
9SZr
1.000
-0.283
0.338
-0.012
0.077
0.179
0.120
0.198
-0.024
0.008
5 "Co
1.000
-0.794
-0.059
-0.077
-0.032
-0.179
0.291
-0.037
0.032
5*Mn
1.000
-0.007
0.084
0.085
0.062
-0.049
0.032
-0.001
65Zn
1.000
-0.187
0.035
0.105
-0.136
-0.015
-0.002
6°Co
1.000
0.141
0.163
0.031
0.017
0.011
"°K
1.000
0.327
0.213
-0.143
0.114
"°Ba
1.000
0.182
-0.116
0.116
Radon
1.000
-0.138
0.192
Gain
1.000
-0.822
Threshold
1.000
I
I—'
o
-------
6-11
TABLE 6. OCCURRENCES OF HIGH CORRELATIONS IN A SET
OF 132 ANALYSESa
Correlated Pair
s*Mn-58Co
i3*Cs-95Zr-Nb
saco-1 06Ru
58Co-95Zr-Nb
i 3ij-5 iQr
i06Ru-5*Mn
40K-60CO
i3*Cs-106Ru
134CS-58CO
137CS-1 06RU
^szr-Nbio^Ru
65Zn-60Co
No. of Occurrences
131
30
9
2
2
2
2
1
1
1
1
1
% of Total
99.2
22.7
6.8
1.5
1.5
1.5
1.5
0.8
0.8
0.8
0.8
0.8
QCorrelations between certain nuclides can be increased to
importance on occasion, if large fluctuations in back-
ground or counting statistics occur.
-------
6-12
standard deviation limit is 5 pCi/jj, , if the activity is less
than 100 pCi/£, or 5 percent, if the activity is greater
than 100 pCi/£. It is true that these limits are
established only for the case of a single nuclide; however,
cases in which several nuclides are present are so complex
that these values are used as a reasonable approximation.
Analytical results for a composite are given in table 7;
these results correspond very closely to the known values.
Selected single nuclide spectra can be analyzed for those
nuclides having interference problems or those nuclides
quantified inadequately in the composite samples such as the
io6RU value for detector D in table 7. Poor performance
with the individual nuclide spectra indicates possible
problems with particular standard spectra. After all
analytical problems are solved using known samples, the
standards may be more fully evaluated for the type of
analytical performance that may be expected in routine
operation of the program.
The next step in testing the standard library is to examine
the analytical results from the analysis of a large number
of background spectra. Statistical fluctuations of the
background counting rate should lead to a distribution of
analytical results for each radionuclide in the standard
library. Table 8 shows the distributions resulting from the
analysis of 23 such background spectra. The library used
with ALPHA-M to determine these values is not the one listed
in Appendix D.
Ideally, all the radionuclides in the library should show a
distribution with a mean value not significantly different
from zero. A departure from zero could have several
possible causes such as contamination of the shield,
insufficient spectrometer stability, or uncompensated radon
fluctuations in the counting room. All these factors could
result in a larger background variability than that allowed
from counting statistics only.
Overall, the agreement is good except for the isotopes
134Cs, 58Co, and 5*Mn. What nonideal properties of real
data cause these discrepancies is an important question. An
obvious contributor to the 58Co-5*Mn anomalies is the
correlation shown in table 6. Figure 8 better illustrates
this correlation in action with the real analytical results.
The anomalous 13*Cs, 58Co, and 5*Mn results may also be
related to the fact that these isotopes have, as shown later
in this section, the lowest usable fractions in the library.
Radon and its daughter products present the most difficult
problems in the ALPHA-M data analysis technique. Figures 9
and 10 illustrate the improvement that can be made in
analytical results by including a simple radon standard
-------
6-13
TABLE 7. ANALYTICAL RESULTS FROM COMPOSITE ANALYSIS
Nuclide
1311
1 03—1 06RU
13*CS
137CS
»52r-Nb
s*Mn
6szn
«oco
**°Ba-La
Known
(pCi/£)°
67±15
92±15
95±15
130±20
269±40
37±15
83±15
102±15
76 + 15
Found (pCi/Mb
Det A
6 9 ±7
97±26
106±8
1 13±7
249+9
50±7
65±12
97±15
69±6
Det B
66 ±6
110±24
105+6
110+6
263±8
34±6
67±11
95±5
72±5
Det C
61 +6
89±25
101 ±7
113 ±7
251±8
40±6
70±12
96±5
66±5
Det D
65±6
140 ±24
95 ±7
125 ±7
242±8
38±10
74±11
91±5
73 ±5
aAmount added to the composite with the 3-sigma error as
allowed by the criteria: <100 pCi/x, activity = 1o = 5 pCi/
>100 pCi/£ activity = 1 a = 5%
bResult reported by ALPHA-M with the program standard error.
-------
TABLE
EXPERIMENTAL VALUES DIVIDED BY STANDARD ERROR FOR 23 BACKGROUND SPECTRA
l«*ce
-7*°
-6*
-5*
-4*
-3*
-2*0
-1*0116
-0*13567
0*112333155679
1*6
2*
3*
4*
5*
6*
7*
137CS
-7*
-6*
-5*
-a*
-3*
-2*346
-1*023559
-0*12358
0*1266
1*05673
2*
3*
4*
5*
6*
7*
s»Cr
*
*
*
*
*
*00
*3
*1355789
*26678
*122
*11346
*
*
*
*
*
•»5Zr-Nb
*
*
*
*
*
*42
*017
*045
*012355677
*012348
*
*
*
*
*
*
1311
*
*
*
*
*4
*367
*134
*2579
*03589
*69
*026
*7
*
*
*1
*
s*Mn
*
*
*
*
*
*
*01278
*35
*02223357
*134
*358
*29
*
*
*
*
1 06Ru
A
*
*
*
*6
*
*12568
*3679
*012346
*0123
*02
*8
*
*
*
*
<-5Zn
*
*
*
*
*
*4
*1335
*57
*124799
*05557
*01124
*
*
*
*
*
seCo
*
*
*
*15
*7
*1113
*239
*235
*57889
*0111
*7
*
*
*
*
*
60CO
*
*
*
*
*
*68
*033
*11246669
*12368
*1358
*0
*
*
*
*
*
13*CS
*
*
*1
*9
*6
*2367
*5
*366
*59
*189
*
*
*
*68
*
*13
40K
*
*
*
*
*
*0015
*6
*013789
*2334579
*1258
*5
*
*
¥
*
*
i*°Ba
+
4
*
*
*
*1
*025
*0133679
*0112445689
*38
*
#
4
*
*
*
I
I—'
-D--
°The values are represented by two digits, the integer part and the first decimal.
The digit to the left of the asterisk, shown only in the leftmost column, gives
the integer part. Each digit on the right of the asterisk is the decimal part of
one of the values. For example, entries for seco on the -1 row are -1.2, -1.3,
and -1.9.
-------
20.
6-15
p. _
0
O O
o
O
O
00
m
0 O
Q O
0 O ©
-20
-20
54
Mn,pCi/!
i
20
Figure 8. seco activity vs. **Mn activity for background runs.
-------
6-16
A. NO RADON STANDARD IN LIBRARY
10 9 8 76543 21 0-0-1-2-3
(Decade)
B. RADON STANDARD IN LIBRARY
6 5 43 2 1 0 -0 -1 -2 -3 -4
(Decade)
Figure 9. Cr sample results (pCi/£)
-------
6-17
A. NO RADON STANDARD IN LIBRARY
I I
22-25 18-21 14-17 10-13 6-9 2-5 1-1 2-5 6-9 10-13
(pCi/A)
B. RADON STANDARD IN LIBRARY
-T
22-25 18-21 14-17 10-13 6-9 2-5
(pCi/A)
1-1 2-5
6-9 10-13
Figure 10.
sample results (pCi/2.).
-------
6-18
(radium in equilibrium with its short-lived decay products)
in the library. In the set of library standards included in
Appendix D, radon can interfere with the analysis of sicr,
131J, i3*CSr and
A single radon standard that has been allowed to reach
equilibrium cannot completely account for all the radon
daughter interferences that may be present in a sample. If
the interference is not in equilibrium, then a standard in
equilibrium will improve some radionuclide results and bias
others. A possible solution for this problem is to make two
library standards, one for 2t*pb and one for 21*3!. These
standards can then allow ALPHA-M to compensate for
variations in the radon equilibrium.
After the standard library has been properly prepared and
tested and is performing satisfactorily, the ultimate
capability of the analysis system can be evaluated by using
the standard errors calculated by ALPHA-M. These standard
errors are obtained from the inverse of the ALPHA-M
information matrix. The diagonal elements of the inverse
matrix are the variances of each respective component, and
the standard error of a component is simply the square root
of its variance.6
For the Y-1 weighting option, the standard errors for any
situation can be calculated after the nuclide and background
levels have been specified. Let the count in channel i for
standard j be given by X, . . Let W. be the weight chosen for
channel i. Then the (i,j) element of the information matrix
is given by
X.. W. X..
11 1 1
If a laboratory attempts to minimize background
fluctuations, the only component necessary for consideration
with environmental samples, where essentially no nuclide is
presented, is the background library standard. Thus, an
evaluation of ALPHA-M can be derived from the information
matrix using weights given by the inverse of the background
standard.
The library background spectrum is submitted to ALPHA-M for
analysis. The full library, including the background
standard itself, is used in analyzing the spectrum; no gain
or threshold compensation is applied. Printouts of all
matrix information should be requested. Tables 9 and 10
provide the resulting information matrix and inverse matrix
respectively.
-------
TABLE 9. INFORMATION MATRIX
(Multiply Values by 106)
»««Ce
stCr
131I
S06RU
"CO
i«Cs
t37Cs
*szr-Nb
s«Mn
6»2n
e>oco
« OK
looBa
Bkgd .
2. tO
0.19
0.35
0,57
0.
-------
TABLE 10. INVERSE OF INFORMATION MATRIX
(Multiply Values by 1CT6)
i««Ce
siCr
I31J
106RU
seco
»3«CS
137CS
»s£r-Nb
s«Mn
652n
toco
«OK
»«°Ba
Bkgd.
0.55
-0.15
0.02
-0.02
-0. 11
0.08
0.01
-0.02
0.03
0.03
0.04
0.06
0.02
-4.26
-0. 15
9.25
-0.18
0.36
-0. 13
G.18
0.07
0.01
0.09
0. 10
0.19
0.32
-0.02
-15.02
0.02
-0.148
4.20
-0.01
-0.34
0.19
0.04
-0.07
0.10
0.13
0. 18
0.42
0.07
-19.21
-0.02
0.36
-0.01
2.88
-1.20
-0.08
-0.13
0.29
0.38
-0.05
0. 15
0.26
-0.02
-11.21
-0.14
-0.13
-0.34
-1.20
5.79
-0.92
0.07
-0.25
-1.30
-0.08
-0.15
-0.25
-0.10
15.38
0.08
0.18
0.19
-0.08
-0.92
0.80
0.00
-0.41
0.05
0.05
0.05
0. 11
0.04
-7.97
0.01
0.07
0.04
-0. 13
0.07
0.00
0. 25
0.00
-0.01
0.02
0.02
0.06
0.02
-2.99
-0.02
0.01
-0.07
0.29
-0.25
-0.41
0.00
0.65
0. 15
-0.02
0.01
0.02
-0.01
0.06
0.03
0.09
0. 10
0.38
-1.30
0.05
-0.01
0.15
0.54
0.00
0.04
0.06
0.01
-3.78
0.03
0.10
0. 13
-0.05
-0.08
0.05
0.02
-0.02
0.00
0.57
-0.07
0.02
0.01
03.33
0.04
0.19
0.18
0. 15
-0.15
0.05
0.02
0.01
0.04
-0.07
0.20
0.04
0.01
04.65
0.06
0.32
0.42
0. 26
-0.25
0. 11
0.06
0.02
0.08
0.02
0.04
0.90
0.04
-11.03
0.02
-0.02
0.07
-0.02
-0. 10
0.04
0.02
-0.01
0.01
0.01
0.01
0.04
0.02
-2.13
-4.26
-15.02
-19.21
-11.21
15.38
-7.97
-2.99
0.06
-3.78
-3.33
-4. 65
-11.03
-2.13
479.93
I
ho
o
-------
6-21
The standard errors are the square roots of the diagonal
elements of the inverse matrix multiplied by (1) the
activities of the standard spectra and (2) a volume
reduction factor of 1/3.5 (3.5 liters of water are normally
counted). No correction is made for counting time since the
sample and standards are counted for the same time period.
No decay corrections are applied. Table 11 contains the
resulting standard errors. (These are the standard errors
used to compute table 8.)
The error estimates given by the ALPHA-M output (uncorrected
for decay) differ in only two ways from the standard errors
obtained above: (1) The information matrix used for the
error estimates is the result of the ALPHA-M iteration; (2)
the error estimate contains an additional factor equal to
the square root of the CHDF. If the fit is good, CHDF
approximates unity. Thus, except for high-activity samples,
the measure of fit and standard errors such as those in
table 11 provide the same information as the routine error
estimates produced by ALPHA-M. To illustrate the close
correspondence of the routine values to those obtained
theoretically, table 12 contains the ALPHA-M error estimates
for ten background spectra taken over a two-week period.
Closer examination of the standard error term shows that it
can be expressed as the product of four factors: (1) the
reciprocal of the specific area; (2) the reciprocal of the
shape factor; (3) the reciprocal of the square root of the
usable fraction; and (4) scale factors such as the volume
adjustments, time adjustments, and decay factor. The
specific area is the total counts (the sum over all
channels) for the standard divided by the activity of the
standard in pico-Curies. This factor measures the number of
disintegrations that result in counts and thus reflects such
things as sample geometry and detector efficiency. The
shape factor is the square root of the diagonal element of
the information matrix divided by the total counts and is
proportional to the standard error that would apply if no
other nuclides were being sought in the analysis and if the
true background spectrum were subtracted from the sample
before analysis. The shape factor measures the sharpness
and number of the photopeaks and their relation to the
background spectrum. For example, the shape factor accounts
for the fact that a nuclide with all its counts in one
channel would be easier to detect than a nuclide with the
same number of counts but with a spectrum more like the
background spectrum. The usable fraction measures the way
that the nonorthogonality of the standard spectra affects
the standard error.7 If the standards were orthogonal, the
usable fractions would be equal to one. Other things being
equal, the lower the usable fraction, the higher the
standard error. The usable fraction can be computed from
the information matrix and its inverse. For the jth
-------
6-22
TABLE 11. STANDARD ERRORS AND LOWER LIMITS
OF DETECTION (LLD) FOR THE STANDARDS LIBRARY IN APPENDIX D
Nuclide
144Ce
51Cr
1 31J
106Ru
S8CO
134CS
137CS
9szr-Nb
5*Mn
^szn
6°CO
*OK
J*OBa-La
Standard Error
10.08
17.97
2.31
8.69
3.95
2.45
2.31
2.90
3.00
3.53
1.93
30. 18
3.09
LLD
33. 16
59.12
7.60
28.59
13.00
8.06
7.60
9.54
9.87
11.61
6.35
99.29
10. 17
-------
TABLE 12. ALPHA-M STANDARD ERRORS FOR 10 ANALYSES OF
ROUTINE BACKGROUND SPECTRA
Nuclide
i**Ce
sicr
131J
106Ru
13*CS
137CS
95Zr-Nb
seco
s*Mn
*5Zn
*°CO
*OK
i*OBa-La
Standard Error
1
9.64
18.32
2.78
10.05
3.14
2.31
2.59
5.06
3.84
4.56
2. 12
31.77
2.51
2
9.45
18.88
2.81
9.96
2.88
2. 11
2.49
4.12
2.94
4.56
2. 12
33.09
2.36
3
8.40
15.65
2.36
8.75
2.75
1.97
2. 17
4.29
3.27
3.99
1.80
27.22
2.09
4
8.80
16.82
2.69
9.54
2.95
2.20
2.36
4.48
3.41
4.17
1.81
26.46
2.00
5
9.14
18.33
2.72
9.42
2.82
2.04
2.41
3.98
2.78
4.18
2.02
31.61
2.22
6
8.47
16.02
2.77
9.46
2.83
1.92
2. 14
4.40
3.39
4.04
1.78
29. 11
2.09
7
9.04
16.90
2.64
9.46
2.94
2.09
2.33
4.65
3.54
4.44
1.94
29.05
2.32
8
10.27
19.68
3.21
10.88
3.44
2.50
2.68
5. 12
3.82
4.69
2.07
30.29
2. 36
9
8.17
16.98
2.48
8.81
2.56
1 .90
2.20
3.65
2.58
3.86
1.85
28.79
2.09
10
10.37
17.50
3. 15
10.89
3.46
2. 38
2.76
4.63
3. 15
5. 12
2. 37
34.99
2.53
I
K>
U>
-------
6-24
nuclide, the usable fraction is given by the reciprocal of
the product of element (j, j) of the information matrix and
the element (j, j) of the inverse of the information matrix.
Table 13 gives values for the shape factors, usable
fraction, and specific area of the standard library in
Appendix D.
An analysis similar to that given in table 13 can impart
direct information to the user on the results to be expected
in routine analysis. Nuclides with low specific areas or
low usable fractions will be much more difficult to detect
at very low levels. In addition, low values for these
parameters could possibly lead to erratic results at near-
zero activity levels. The analyst can also improve his work
by selectively choosing his library members. Unfortunately,
what the analyst must analyze for is not always a matter of
choice.
The standard errors in table 11 have two important uses: (1)
to determine a threshold level high enough that a reported
activity above this level has little chance of being the
result of a zero-activity sample; (2) to determine a lower
limit of detection (LLD) at a sufficiently high value of the
true activity that detecting that quantity of the nuclide
has a high probability.8-10 A discussion of the difference
between these two uses is worth a brief discussion. The
determination of a threshold is concerned with whether a
measurement has significant activity; for instance, to hold
the chance of mistaking a zero-activity sample for one
containing the nuclide to a 5 percent level, a threshold of
1.645 times the standard error is used. Determination of an
LLD is concerned with whether a sample containing the
nuclide will register enough counts to exceed the threshold.
During the counting period, an abnormally low number of
disintegrations may occur, thus resulting in a determination
that does not exceed the threshold. To hold a 5 percent
chance that the sample containing the nuclide will result in
a measurement that exceeds the threshold, the sample must
have a true activity of at least 3.290 times the standard
error. Table 11 gives the LLD values derived for the
standards in Appendix D; these values are calculated by
ALPHA-M for each nuclide in each sample. Samples with true
activities at the LLD value have a 95 percent probability of
producing a measurement higher than the threshold set to
hold the chance of the threshold being exceeded by a zero-
activity sample to 5 percent. This criterion is used in
this version of ALPHA-M.
This 95 percent confidence criterion is very rigorous. A
more liberal criterion would be to allow a 25 percent chance
of erroneously reporting" activity when none is actually
present and to keep the 5 percent requirement for missing
activity when it is actually present. This criterion would
-------
6-25
TABLE 13. SPECIFIC AREA, USABLE FRACTION, AND
SHAPE FACTOR FOR THE LIBRARY STANDARDS IN APPENDIX D
Nuclide
i44Ce
sicr
131J
106RU
58CO
134CS
137CS
s*Mn
«5zr-Nb
ftszn
60CO
40K
i^OBa-La
Specific Area
3.24
2. 13
22.62
8.82
24.39
44.37
15.21
18.53
17.89
11.15
31.28
1.76
35.88
Usable Fraction
0.7527
0.6837
0.5228
0.3327
0.1488
0.1549
0.6779
0.2739
0.3527
0.6404
0.4283
0.4938
0.1985
Shape Factor
0.0102
0.0091
0.0076
0.0065
0.0077
0.0067
0.0099
0.0098
0.0093
0.0091
0.0072
0.0076
0.0058
-------
6-26
result in the LLD being 2.32 times as great as the standard
error.
Actual results of ALPHA-M performance at environmental
activity levels are presented in tables 14 and 15. The
analyst must decide what degree of imprecision is
satisfactory before setting limits on data reporting.
Further study was conducted to determine how the presence of
more than one component in the sample spectrum could affect
accuracy; the simulation program SIMSPEC was used for this
work. Sample spectra, containing a standard background plus
three, five, seven, or nine different nuclides, were
generated. These four samples were each randomized six
separate times and analyzed (vs. the complete library) by
the Y=1 weighting scheme. Nuclide concentrations were 25
pCi/£ for each nuclide. The other processing options used
are defined in Appendix D. The average absolute percent
error (for each set of six replicates) for each nuclide was
determined in each sample.
As more components are introduced into the sample spectrum,
the relative accuracy decreases (table 16), thus agreeing
with theoretical prediction.9 However, the effect is
minimal and the program is still performing adequately.
Also shown in table 16 are the values for single nuclide
spectra prepared and analyzed in the same manner as were the
multicomponent spectra. All the spectra in this study were
randomized to a level greater than predicted by three
standard deviations in counting statistics to ensure
representation of the worst case of counting statistics.
The minimal rise in percent error with increasing number of
nuclides in the spectra does not imply that high
concentrations of certain nuclides would not cause very
large changes in these percent error values. These results
are meaningful only when all nuclides are present at
environmental levels.
ALPHA-M is a weighted least-squares routine modified to
compensate for gain and threshold shifts and to allow the
weights to depend on those isotopes that are actually
present. A detailed description of ALPHA-M requires
consideration of the consequences of these modifications.
The efficient method of evaluation first determines (1) how
ALPHA-M would behave if it were a weighted least-squares
routine and (2) how the modifications make the behavior
differ from that of weighted least squares. This two-step
approach is efficient because the first step can be handled
by theory whereas the second step requires only enough
simulation to compare ALPHA-M with weighted least squares.
The comparison should require relatively little simulation
because the iterative process for finding the proper shifts
-------
6-27
TABLE lit. ANALYTICAL RESULTS FOR i37Qs AT LOW ACTIVITY LEVELS
Added
(pCi/£)
2.81
5.61
14. 12
21.20
42.22
Found (pCi/£) ± s.E.a
No Rejection Applied
(%Error)
1.85±1.95
0.62±2.03
1.62±1.71
3.46±2.36
1.70±1.82
Average 1.85 (-34.2%)
4.3011.86
6.43±2.03
2. 14H.94
9.51+2.09
5. 14±2.04
3.09±2.08
Average 5.10 (-9.1%)
14.61+1.58
17.54±2.41
14.0611,75
14.60±2.24
13.67±1.82
14.34 + 2.07
Average 14.80 (4.8%)
19.07±2.27
20.84±2.38
24.26±2.54
14.25±2.02
15.4 1±2.27
22.81+1.84
Average 19.44 (-8.3%)
36.86±2.51
38.20±2.47
38.39±2.31
38.98±2.61
42.47+2.86
Average 38.98 (-7.7*)
Rejection Applied13
( ;* Error)
4.02±2.36
— i \
( i
4.97±1.74
5.82±1.92
2.33±1.89
9.86±2.09
5.97±1 .96
1.32±2.06
5.05 (-10.0%)
14.08±1.48
17.20±2.20
14.60±1.72
15. 0512.05
13.54±1.77
15. 23±1.95
14.97 (6.0%)
19.46±2.20
19.3412.62
25.22±2.39
14.24+1.90
17.48±2.27
22.24+1.93
19.66 (-7.3%)
36.9112.35
39,15+2.36
40.62+2.28
39. 5912. 54
41. 7512.48
39.60 (-6.2%)
aS,E. = ALPHA-M standard error.
bl3Tcs was rejected after the first ALPHA-M pass because the determined
concentrations were less than the standard error-
-------
6-28
TABLE 15. ANALYTICAL RESULTS FOR «5Zn AT LOW ACTIVITY LEVELS
Added
(pCi/X.)
3.01
6.59
16.55
24. 80
49.40
Found (pCi/£)
No Rejection Applied
(*Error)
1.7514.04
10.09±5.13
-1.55±4.81
-2.38±3.80
8. 17±4.49
11.65±3.82
T\ ,, ..-.v- -j ,-. ,-, /I £L 9 / £ Q C^/ (Oo . ~>?b)
8. 11±4.00
4.43±4.33
8.59±3.58
5.75±4.02
14.7813. 41
9.6214.54
Average 8.55 (29.7%)
25.23+4.95
20.5314.31
15.7613.71
20.75+4.27
14. 6413.47
20.5914.25
Average 19.58 (18.3%)
22.99+4.71
25.2114.81
31.4514.39
22.2514.12
25.7514.40
Average 25.53 (2.9%)
54. 1414.75
51.9H5.35
50. 95+5.03
40. 46+4. 86
50.93+3.76
46.24+4.90
Average 49.11 (0.6%)
1 S.E.a
Rejection Applied
(%£rror)
_ _ _
9.2214.60
6.4414.33
10. 3113. 71
(_ \
)
7.22+3.83
3.36±4.31
8.9813.39
4.0513.80
13.69+3.30
9.0014.46
7.72 (17.25b)
23. 0714.65
19. 66 ±4. 26
14. 93i3.45
19.32±4.03
15.16±3.34
20.57±4. 15
18.79 (13.5%)
23.84+4.63
25.14+4.56
29. 6414.44
22.3413.93
25.23+4.04
25.24 (1.8*)
53. 7014. 84
51. 89 ±5. 13
51. 36 15. 22
41. 5714.78
49. 85 13.74
46.04+4.74
49.07 (0.7%)
. = ALPHA-M standard error.
was rejected after the first ALPHA-i*, pass because the determined
concentrations were less than the standard error.
-------
TABLE 16. EFFECTS UPON ACCURACY CAUSED BY MULTIPLE COMPONENTS
NUCLIDE ACTIVITY 25 pCi/£
Sample
(Obtained for Single
Component Spectra)
1
2
3
4
Nuclide (XError0)
131J
26. 2
26.7
28.3
32.4
35.7
134CS
26.4
27.7
29.1
29. 1
29.1
137CS
23.7
24.5
24.6
24.9
25.7
s*Mn
20.6
—
21.8
28.3
28.8
60CO
24.3
--
25.1
24.5
24.8
58CO
42.7
__
—
54.4
58. 1
i*°Ba
35.5
__
__
39.1
40.0
106Ru
50.4
--
—
—
59.8
95Zr
54.3
--
--
__
61.6
I
to
'% Error =
Known-Found
Known
x 100
-------
6-30
and weights is designed to make ALPHA-M approximate weighted
least squares.
6.4 SAMPLE ANALYSES
The main tool that the ALPHA-M user has for evaluating the
analytical results produced by the program is the fit
information provided in the program output. The CHDF value
and the descriptive statistics for the residuals indicate
the quality of the fit. ALPHA-M is designed for Poisson
distribution of the counts in the sample, with means given
by some linear combination of the library standards. The
program is not designed to handle the variations in the
sample that arise from variations in the radon level or from
isotopes not included in the library. The residuals and the
CHDF statistic may not handle such variations adequately.
That the CHDF statistic sometimes indicates that the
residuals are non-normal is not surprising, nor is it an
indication that the analytical results are invalid.
To better estimate the analytical results on a continuing
basis, the user should take several approaches. First,
duplicate sample analysis on a daily basis can provide a
good idea of the precision that the program is capable of
obtaining. Frequent analysis of samples having known
activity coupled with a crosscheck program involving other
laboratories can serve as a check on the routine accuracy of
the analytical results from ALPHA-M and the whole analysis
system.
Samples yielding anomalous results should be recounted and
resubmitted to ALPHA-M if abnormal background fluctuations
are suspected. Careful scrutiny of results and the
maintenance of distribution charts (table 8) for all
nuclides will also assist in isolating unusual values. In
addition, records should be kept for suspicious channels as
identified by ALPHA-M. These data may point to the presence
of previously unsuspected nuclides for which no library
standard is available.
6.5 USE OF THE REJECTION PROCEDURE
ALPHA-M provides the option of specifying that a "rejection"
process be used in its analysis. If this option is selected
(via program input), the analysis is first performed in the
normal manner with the specified number of refinement
cycles. Then, those nuclides whose standard error is
related to the absolute value of their determined activity
in a specified manner are removed from consideration, and
the analysis is repeated.
If a nuclide's standard error equals or exceeds the absolute
value of its determined activity, it is removed from the
-------
6-31
reanalysis. This corresponds to the point at which the
activity of the nuclide is not significantly different (at
one standard deviation) from zero. The actual criterion by
which a nuclide will be rejected from reanalysis may be
adjusted via program input.
About 1350 analyses of SIMSPEC-generated spectra were
performed using the rejection criterion. The results
obtained before and after rejection were compared for
accuracy to determine the effectiveness of the rejection
scheme.
Because of the wide variation in accuracy over the entire
body of analyses, the results were segmented into accuracy
percentile decades, and the effect produced by rejection was
determined for each decade. Table 17 shows the number of
cases and the benefit derived from rejection for each
percentile decade. For example, there were 126 analyses for
which the error in the determination was between 50 and 60
percent; of this group, the standard rejection procedure
improved the accuracy of the determination in 40 percent of
the analyses.
Because the levels of activity commonly found in radio-
chemical analyses of environmental samples usually fall into
the region in which greater than 70 percent error is common,
the small percentage of cases in which the accuracy of the
determination will be improved may reduce the advantages
that can be produced by a rejection and reanalysis procedure
using the standard criterion.
The expectation of an improvement in accuracy as a result of
rejection and reanalysis is based primarily on the
assumption that the reduced library size will introduce
fewer errors due to unnecessary terms in the matrix of
simultaneous equations. This conclusion is shown to be
correct by the improvement noticed in samples exhibiting
high accuracy and precision. In such cases, the rejection-
reanalysis process serves as a further refinement cycle and
is reminiscent of automatic stepwise-regression algorithms.
Difficulties arise in applying this process to analyses with
a relatively low accuracy. In these cases it is common for
a nuclide to be rejected on the basis of an imprecise
determination.
On first analysis, this possible rejection of valid data
might be prevented by allowing the rejection of a nuclide
only if its standard error is at a different level (i.e.,
equal to or greater than twice the magnitude of its
determined activity). This criterion would decrease the
occurrence of situations in which an existing nuclide is
rejected because of poor precision, but would also result in
-------
6-32
TABLE IT. BEHAVIOR OF THE REJECTION PROCESS
Accuracy Percentile
Decade Range of
% Error Observed
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
>100
Number
of Cases
in Decade
270
324
252
36
90
126
36
18
18
54
126
Percentage of Cases
Improved by Reana lysis
after Standard Re-jection
67
58
56
36
40
40
14
11
28
15
23
-------
6-33
a smaller decrease in library size. These two effects would
tend to cancel each other.
However, there are also strong arguments for the use of a
rejection procedure. One advantage of this procedure is
illustrated by the case of 54Mn_5eco discussed earlier.
These two nuclides are highly correlated and, as shown in
figure 8, actual cases of a large activity for one nuclide
and negative activity for the other occur. When the nuclide
with negative activity is rejected and ALPHA-M makes a
second pass, the result for the remaining nuclide is lowered
substantially.
Another factor to consider is the inability to know what
activity levels to expect in a sample. If a sample has an
activity sufficient to achieve reasonable accuracy (<40
percent error), the rejection procedure will lead to
improvement in the processing. Another approach is to use
rejection, but to keep both the before- and after-rejection
activities in a data base to be statistically studied at a
later time.
6.6 REFERENCES
1. Quittner, P. Gamma-Ray Spectroscopy, Halsted Press,
New York, 1972, p. 62.
2. Schonfeld, E., A. H. Kibbey, and W. Davis, Determination
of Nuclide Concentrations in Solutions Containing Low
Levels of Radioactivity by Least-Squares Resolution of
the Gamma-Ray Spectra, Oak Ridge National Laboratory,
Oak Ridge, TN, January 1965, 57 pp.
3. Mukoyama, T. Fitting of Gaussian Peaks by Non-Iterative
Method, Nucl. Instrum. Methods. 125: 289-291, 1975.
4. Crouch, D. F., and R. L. Health, Routine Testing and
Calibration Procedures for Multichannel Pulse Analyzers
and Gamma-Ray Spectrometers, Research and Development
Report IDC 16923, Atomic Energy Commission, Idaho
Falls, Idaho, 1963, 42 pp.
5. Environmental Radioactivity Laboratory Intercomparison
Studies Program, 1973-74, Environmental Protection Agency,
Las Vegas, Nevada, 1974, 12 pp.
6. Stevenson, P- C. Processing of Counting Data, National
Academy of Sciences - National Research Council
Publication NAS-NS 3119, Washington, D.C., May 1966,
p. 87.
7. Beaton, A. E., and J. W. Tukey, The Fitting of Power
Series, Meaning Polynomials, Illustrated on Band
-------
6-34
Spectroscopic Data, Techometrics, 147-192, 1974.
8. Altshuler, B., and B. Pasternack, Statistical
Measures of the Lower Limit of Detection of a Radio-
activity Counter, Health Phys. 9: 293-298, 1963.
9. Pasternack, B. B., and N. H. Harley, Detection
Limits for Radionuclides in the Analysis of Multi-
component Gamma-Ray Spectrometer Data, Nucl. Instrum.
Methods. 91: 533-540, 1971.
10. Fisenne, I. M., A. O'Toole, and R. Cutler, Least-
Squares Analysis and Minimum Detection Levels
Applied to Multicomponent Alpha Emitting Samples,
Radiochem. Radioanal. Lett. 16: 5-16, 1973.
-------
APPENDIX A
ALPHA-M
-------
A-2
A.1 GENERAL
This modified version of ALPHA-M has been prepared for exe-
cution on an IBM 370-165. An effort has been made to
eliminate program features that depend on an IBM
installation. The only installation feature in the program
is a time-of-day clock used for writing the analytical
results to the Fortran logical unit designated by TOPT.
Users should consult the computer staff at their laboratory
before using the example Job Control Language given in this
appendix (table A-1).
At installations that have computing equipment other than
IBM, changes may be necessary in the ALPHA-M program.
Computing center staff should be consulted regarding program
revision and information about which Systems Control
Language to use. To increase the nuclide standards in each
library to more than 20, to increase the number of detectors
to more than 4, or to increase the number of data channels
to more than 256 requires certain modifications to ALPHA-M.
To modify ALPHA-M to use more than 20 library standards,
subscripted variables dimensioned by NS must be changed to
the proper size; the subscripted variables and their
dimensions are given in Section A. 3. Also, if standard
libraries are created with GEN4, then appropriate changes
must be made in GEN4; these changes are discussed in
Appendix B.
To modify ALPHA-M to accept standard libraries having more
than four detectors, subscripted variables dimensioned by
NDETS must be changed appropriately- Again, GEN4 must be
modified to create the proper libraries.
To modify ALPHA-M to analyze data with more than 256
channels, subscripted variables dimensioned by M must be
changed. The use of the value 256 in program operations
such as DO LOOP indices has been removed; instead, the
indices are limited by the input value of M. Those
parameters in GENU that are subscripted by M must also be
modified.
A.2 ALPHA-M FILES
According to the input or processing options selected,
ALPHA-M may require use of the following files.
-------
TABLE A-l. JOB CONTROL LANGUAGE PROCEDURE RUNALPH
//RUNALPH
//ALPHA
//STEPLIB
//
//FT02F001
//FT03F001
//
//FT04F001
//
//fT05F001
//FT06F001
//
//FT09F001
//ANALYZE
//STEPLIB
//
//FT02F001
//FT06F001
//
//RUNALPH
PROC
EXEC PGM=ALPHAM,REGION=17J0K,TIME=2
DD DSN=ENV20. RADLAB.SS622030.TLXB,DISP=SHR,UNIT=3330
VOL=SER=SYSU£»4
DD UNJT=SYSPL,DISP= (NEW, DELETE, DELETE) ,SPACE=(TRK, (10,5) )
DD DSN=ENV20. RADLAB. SS62203J3. STDH20, DISP=SHRrUNIT=3330
VOL=SER=SYSU04 '
DD DSN=&6RESID,UNIT=SYSPL,DISP-(NEW,PASS/DELETE) ,
SPACE=(TRK/ (10,1)RLSE) , DCB= (RECFM=VBS,LRECL=780,BLKSI2iE=31 24)
DD DDNAME=SYSIN
DD SYSOUT=A,DCB= (RECFM=FBA,LRECL=133,BLKSIZE=3059) ,
SPACE= (CYL, (1,1) ,kLSE)
DD SYSOUT=A,DCB=*.FTer6F001,SPACE=(CYL, (1,1) ,RLSE)
EXEC PGM=ANALYZE,REGION=100K
DD DSN=ENV20.RADLAB.SS622030.TLIB,DISP=SHR,UNIT=3330,
VOL=SER=SYSU04
DD DSN=&&RESID,DISP= (OLD,DELETE,DELETE) ,UNIT=SYSPL
DD SYSOUT=A,DCB= (RECFM=FBA/LRECL=133,BLKSIZE=3J059) ,
SPACE= (CYL, (1,1) ,RLSE)
PEND
>
-------
A-4
A.2.1 Standard Nuclide Library
This input file is always required. Refer to documentation
regarding program GEN4 (Appendix B) .
A.2.2 Auxiliary Output File
An output file is required if the ALPHA-M input variable
IAUX is greater than zero. If this option is selected, a
binary unformatted record is written on Fortran logical unit
IAUX at the completion of each processing option. This
record contains the ALPHA-M variables XIDT, R, YC, and YOBS.
XIDT is the sample identification (eight bytes, alpha-
numeric) , and R, YC, and YOBS are vectors (each dimensioned
at 256) containing, respectively, the normalized residuals,
the calculated spectrum derived by ALPHA-M, and the original
sample spectrum. This information may be made available to
other software for further analysis of the residuals, for
plotting purposes, or for any other record keeping of pro-
cessing functions. If this sequential file is stored on a
3330-type device with a
DCB=(RECFM=VBS,LRECL=780,BLKSIZE=3124) ,
each 3330 track may contain about 16 records.
A.2.3 Analytical Results File
An output file is required if the ALPHA-M input variable
IOPT is greater than zero. if this option is selected, a
binary unformatted record is written to Fortran logical unit
IOPT at the end of each processing option. This record is
written according to the following list:
TNAME, XIDT, IMAGE, ABATE, ANOUN, NT, (TISO (IT (J) ) , ZT (IT (J) ) ,
STDT(IT(J) ) ,J=1,NT) .
TNAME is the sample header card; XIDT is the sample
identification (eight bytes, alphanumeric); ADATE is the
date of numerical analysis (eight bytes, alphanumeric in the
form MM/DD/YY, month/day/year); ANOUN is the time of
numerical analysis (eight bytes, alphanumeric in the form
HH/MM/SS, hour/minute/second); TISO is a vector containing
standard nuclide names; NT is the number of nuclides for
which the analysis was performed; IT is a vector containing
the library standard numbers for those NT nuclides; and ZT
and STDT are vectors containing the determined activities
and standard errors respectively. IMAGE is a five-digit
number that reflects the processing options used for the
sample analysis. Each digit denotes a different option.
This is determined in the following manner: 10000*IABP +
1000*NB + 100*(NW+2) + 10*(KT+2) + 1*Q. For example, an
IMAGE value of 21340 indicates that the sample was analyzed
-------
A-5
in the following fashion: (1) detector 2 standards were
used, (2) background was subtracted, (3) the weighting
scheme was the reciprocal of the calculated counts, (4)
automatic gain and threshold shift was used, and (5) no
rejection coefficient was applied.
The file created from these records is intended to be a
temporary storage facility for information that will be
transferred, after editing, to a permanent data base. As
described above, each record will have a length of 28+NT*12
bytes, or a maximum length of 196 bytes. If this file is
written to a 3330-type device with a
DCB=(RECFM=VBS,LRECL=200, BLKSIZE=3004)
providing 15 records of information per block, each 3330
track will contain a minimum of 60 records.
A.2.4 Alternate Printer File
An output file is required if the user requests print-plots
of either the normalized residuals or the observed and
calculated spectra. Subroutine RESIDU produces these plots
with printer formatted write statements directed to Fortran
logical unit 9. A DD card describing this unit as a
SYSOUT=A data set should be included if either of these
plots is requested.
-------
A-6
A.3 GLOSSARY OF IMPORTANT ALPHA-M VARIABLES
A.3.1 Unsubscripted Variables
Variable Definition
CH
CHDF
-VY
> 0.
1
-y V/l
c .
1 \
Y + 0.1 + XMOD
c .
i
+ BA. *FX\
l
/
CH/DN
DN
DAY*
F
FM*
FP
FTT
FS
FD
FX
FTT*
FAT
IAUX*
IABP*
IOPT*
Degrees of Freedom = MF - NZ - N + 1
Decay time in days
Gain shift (multiplicative factor) per cycle
of refinement
Format under which all sample and background
spectra will be read
Accumulated gain factor
Input value of gain factor
Ratio of sample counting time/background
counting time
Decay factor, e~^t
FS2
Value of gain shift input manually
Ratio of standard counting time/sample count-
ing time
Fortran logical unit for auxiliary data output
Integer to control which detector set is used
Fortran logical unit for analytical data
output
*These variables appear on the ALPHA-M control cards. Refer
to Section 5.0 for additional information.
-------
A-7
Variable
IRD*
IPRINT*
IS*
KT*
M*
MF*
MS*
MU*
N*
Definition
NIT*
NBA*
NZ*
NTS*
NTM*
NH*
NDETS
NOPT*
Flag to control print-plotting of residuals
and spectra
Flag to control printing of matrix information
The numbers of the "N" library standards
selected for analysis
rnlay to control compensation technique to be
used
Number of channels in spectrum
Final channel to be used in computations
See page 5-7 for definition
Fortran logical unit for print-plots
Number of nuclide standards from library to
use in analysis. (This value is incremented
and decremented during processing to serve as
a pointer for the gain and threshold variables,
if used.)
Maximum number of cycles of least-squares
refinement
Plag to control printing of library standards
First channel to be used for computations
Fortran logical unit for standard library
spectra
Fortran logical unit for sample spectra and
background
Flag to control printing of correlation
coefficients
Number of detector sets in liorary
Number of option cards (processing options)
*These variables appear on the ALPHA-M control cards. Refer
to Section 5.0 for additional information.
-------
A-8
Variable
Definition
NBS*
NB*
WW*
NS
Q*
QH*
RE
RT
SH
SHC
SHCT*
SMSHC
SI
SB
TB*
TSA*
T
Flag to control reading of background spectrum
Flag to control background subtraction
Flag to control background subtraction for a
given option
Flag to control weighting scheme application
Number of library standards
Ratio upon which to base rejection, and flag
to control whether to use previously cal-
culated values of gain and threshold shift
Energy offset (in channels) between sample
and standards
- Y
the residual
YCi + 0.1 H
XMOD
standardized residual
BAi *FX
Accumulated energy zero channel per cycle of
refinement
Energy threshold shift per cycle of refinement
Value of threshold shift input manually
Accumulated energy threshold shift
The sum of the sample spectrum channel counts
The sum of the background spectrum channel
counts
The background counting time
The sample counting time
*These variables appear on the ALPHA-M control cards. Refer
to Section 5.0 for additional information.
-------
A-9
Variable
TMO
TMP
TE
Description
+ 0.1 + XMOD
Y +0.1+ X1VIOD
\-> •
BA.j_*FX
TT
VU
VY
VW
VM*
VRLD*
XLD
XIDT*
XMOD*
i
/ wi (Yo. - Yc.\ 2: at end of each GYcle' VY = VY/DN
- - —i j \ I \
•c .
+ 0. 1 + XMOD
BA^FX
Volume multiplicative factor; calculated
activity and standard error are multiplied by
this factor to give results corrected for
sample concentration before analysis
Volume reduction factor; calculated activity
and standard error are divided by this factor
to give values corrected for analytical
sample size
Lower limit of detection
Sample identification
Modifier for weighting scheme
*These variables appear on the ALPHA-M control cards. Refer
to Section 5.0 for additional information.
-------
A-10
A. 3. 2 Subscripted Variables
Variable
(Dimensions)
Description
MF
A(NS+2,NS+2) Information matrix where A,
Skij*S£ij Wi
AC(NS,NDETS)
AT(NS+2)
B(NS+2)
BA(M)
CC(NS+2)
DA(NS+2,NS + 2)
DER(M)
FM(20)
HA(NS)
IS(NS*2)
IT(NS+2)
R(M)
i=NZ
where j = constant value for a particular
analysis
Matrix of standard nuclide activities
Vector of alpha factors
MF
Observation vector where
'kij'
i=NZ
where J = constant value for a particular
analysis
Background spectrum vector
Vector of correlation coefficients
Matrix in which A is stored prior to inversion
so that identity matrix may be calculated
Vector of derivatives (dCounts/dChannel)
Format under which sample is to be read
Vector of standard nuclide half-lives
The numbers of, or positional flags for
variables selected, depending on location in
program
Normalized residuals, R .
i
Y - Y /Y + BA
o . c . c .
S(NS,M,NDETS) Matrix containing all standard nuclide spectra
SS(NS,NDETS) Squares of the sum of channels NZ to MF for all
standard nuclides
STD(NS+2)
STDT (NS+2)
Contains standard errors for calculated para-
meters
Report vector for standard errors
-------
A-ll
Variable
(Dimensions)
TST(NS)
TISO(NS+2)
TISOT(NS + 2)
TNAME(20)
W(M)
XI(NS+2,NS-f-2)
XPE(NS)
XPET (NS)
Y(M+1)
YC(M)
YT(M)
YOBS(M)
Z (NS+2)
Description
ZT(NS+2)
ZUC(NS-»-2)
ZTUC (NS+2)
Vector of counting times for standard nuclides
Vector of names for standard nuclides, ordered
as in calculations
Vector of standard nuclide names
Contains identification header
Channel weights
Calculated identity matrix AA~», or DA A"1
Work vector for coefficients of variance
Report vector for coefficients of variance
Input vector for sample spectrum
Y , vector for calculated sample spectrum
\^r
Holding vector for corrected sample spectrum
Y , holding vector for corrected sample
spectrum
Vector of calculated coefficients,
MF
i=NZ
Report vector for final activities
Working vector for uncorrected activities
Report vector for uncorrected activities
-------
A-12
A, H IMPORTANT FORMULAE
CHDF
/Y - Y \
( °i CJ
Y + BA. + 0.1
c . l
DN
Activity
of
Nuclide.:
Zj_ * FAT * AC.i_ *FD * VM/VRED
Std. Error
of
Nuclide.
_1 2
A. * EWdY
--
* FAT * AC. * FD * VM/VRED
Alpha-factor
of
Nuclide.
A.1 *
ss.
SdY'
C.V. of
Nuclide
= TOO X Std. Error Nuclide./(Activity Nuclide
Correlation
Coefficient
of Nuclide
with Nuclide
-1
-
A. *
-------
A-13
A. 5 ALPHA-M PROGRAM
The following is a computer printout of the program ALPHA-M.
-------
A-14
ALPHA-M PROGRAM
-------
A-15
ALPHA-M MULTI-COMPONENT GAMMA-RAY SPECTRUM ANALYSIS
BASED ON THE PROGRAM WRITTEN BY EARNEST SCHCENFIELD, ORNL, 19S5
CURRENT VERSION 2, LEVEL 3, MAY 1976, TENNESSEE VALLEY AUTHORITY
DIVISION OF ENVIRONMENTAL PLANNING, RADIOLOGICAL HYGIENE BRANCH
RIVER OAKS BUILDING, MUSCLE SHOALS, ALABAMA 35660
00000020
00000030
00000040
00000045
00000050
00000055
00000056
00000060
00000070
00000090
REAL * 8 TISOT,TISO,X1DT,ADATE,ANOUN,D 00000100
INTEGER * 4 FM.TNAME 00000110
DIMENSION YZ(25fc},A122,221,Y1257 1 ,Z(22),CC(22 I ,STD(22),B»22> , 00000120
$ R(2561,W(256I,DER(256>,YT1256).IR(256J,BA1256»,FH{8I, 00000130
* SS(20,4),AC(20»4),HA(20),1S(22J,TST(22},HAT122),ATC22J, 00000140
* STDTI22),TNAME(20J,TISOT(22),TISD(22>,IT(22),ZT«22), 00000150
$ S(20,256,4),XPE120).XPETC20) ,YC(256) ,XI(22,22), 00000160
$ DA122.22),ZUC<22),ZTUC(22),YOBS(256),STDUC(22). 00000170
i STTUC(22),XLD(20),XLDT(20J 00000180
COMMON/STUFF/XIDT,T1SOT,NS,M,NIT,NBA,NZ,KF,NH ,KK,NTS,NTM,NQ,Q,FX, 00000190
* M5,N5AMP,NDPTrIPRlNT,NBR,NBS,lABP,TBrISA,VRED,DAY,VM, 00000200
$ NBN,Nb,NW,N,KTILW,YOBS,K230,QH ,NDET ,1S ,MD,NRED,IN,FS, 00000210
$ NBR1 ,FM,S,SS,AC,NDETS,hA,TST,Y,tC,10PT,IAUX,R,XMOD,I.ID,MU00000220
00000230
IBM EXTENDED ERROR MESSAGE HANDLING FACILITY 00000240
TERMINATE JOB UPON SINGLE OCCURRENCE OF DEC-CHAR CONVERSION 00000250
00000260
00000270
00000280
00000290
00000300
00000310
00000320
00000330
00000340
00000350
00000360
00000370
00000380
00000390
00000400
00000410
00000420
00000430
00000440
00000450
00000460
00000470
00000480
00000490
00000500
00000510
00000520
00000530
00000540
00000550
00000560
00000570
NRED=0
NBR1 =
HI =5
H0=6
00 1 I
Ycm
Rl I) =
BA(I)
0
=1,256
0.0
0 .0
0.0
CALL DATE IADATE,ANOUN)
SUBROUTINE DATE IS T.V.A.
WRITE(MD, 9901)A DATE, ANDUN
INSTALLATION DEPENDENT
READ CONTROL CARD AND DATA FORMAT
READtMI.52)
CALL LABEL
CALL OIAG
M,NIT,NBA,Ni,MF,NTS,NTM.MU,NH,IAUX,10PT,FM
READ STANDARDS INFORMATION
CALL STDIM
READ SAMPLE INFORMATION CARD
17 RE AD(MI,65,END=180) XIDT,NOPT ,NBR ,NBS , IABP ,MS ,TB,TSA.VRED,DAY.VH
IF (NBR.EO.l) NBR1 = 1
DEFINE CONSTANTS VM,VRED,FS ,FX
-------
A-16
261
262
263
C
c
C
31
C
C
C
18 IF CVM! 19,19,20
19 VH=1.0
20 IF IVRED) 21,21,22
21 VRED=1.0
22 IF ITBJ 23,23,24
23 FS=0.0
GO TO 25
24 FS=TSA/TB
25 FX FS**2
CALL LABEL!
CALL DIAGl
IF(NBR) 27,27,26
READ BACKGROUND IDENTIFICATION
26 PEAD(NTH,67!TNAME
WRlTEfHC,68) TNAME
READ BACKGROUND SPECTRUH
KEAD(NTM,FH) BA
WRITE(MO,61J BA
WRI1E(MO,64J
SWAP BKGND FOR LIBRARY STANDARD IF REQUESTED
IF (HS.EQ.OJ GO TO 27
DO 261 1=1,H
SCKS ,1 ,1ABP) = BA CI)
DO 263 J=1.NS
SSIJ.IABP) 0.0
DO 262 I=NZ,MF
SSCJ,lAfaP) SS(J,IABPJ + S(J,F,!ABP}
SS(J.IABP) = SSU.IABP) * SS(J,IABP»
READ SAMPLE IDENTIFICATION
WRITE (HO ,64 J
27 READJNTH.67) TNAHE
WRITE(MOt68J TNAHE
NRED=NRED+1
READ SAMPLE SPECTRUH
READ(NTM,FH) (Y(I)»I=1(H)
CORRECT FOR NEGATIVE COUNTS
DO 28 1=1,H
28 IF (Y( I ) .GT .900000.0) Yd) = Yd) - 1000000.0
IF (NBS) 37,37,35
SUBTRACT BACKGROUND PERMANENTLY IF REQUIRED
35 DC 36 1=1 ,H
36 Y(I)=Yd)-BAd)»FS
00000580
00000590
00000600
00000610
00000620
00000630
00000640
00000650
00000660
00000670
00000680
00000690
00000700
00000710
00000720
00000730
00000740
00000750
00000760
00000770
00000780
00000790
00000800
00000810
00000820
00000830
00000840
00000850
00000860
00000870
00000880
00000890
00000900
00000910
00000920
00000930
00000940
00000950
00000960
00000970
00000980
00000990
00001000
00001010
00001020
00001030
00001040
00001050
00001060
00001070
00001080
00001090
00001100
00001110
00001120
00001130
00001140
00001150
00001160
00001170
-------
A-17
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
-------
A-18
c
c
c
c
c
c
c
r
L
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
50
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
YQBSU) = V|J)
FP =1.0
SMSHOO.O
KT1 - KT * 1
IF (KT1) 93,91,94
IF (KKJ 92,92,93
FOR MANUAL COMPENSATION, ENTER GAIN AND THR SHIFT VALUES
READ(MI,56) FTT.SHCT
WRITE(HQ,56l FTT,SHCT
CALL SHIFT (Y.M.SH, FTT.SHCT)
FP=FTT
SMSHC=SHCT
CALCULATE POINTERS FOR GAIN AND THR SHIFTS
!StN*l> NS * I
IS
-------
A-19
C
C
C
106
107
108
109
110
111
c
c
c
112
1=M-1
N5=IS(N)
SETUP GAIN SHIFT VARIABLE
DO 109 J=2,I
C = J
IF(Y(J+ll-1.0 ) 108,108,106
IF(Y( J-D-1.0 ) 108,108,107
DEM J) = (Y{ J+ll-YU-1) )/2.0
GO TO 109
DEK(J)=0.0
S(N5,J,IABP) -DERU) * {C*SH)/100.0
N5=IS
-------
A-20
1001
c
c
c
1500
C
c
c
c
1003
1004
C
C
C
1005
1006
C
c
c
2000
118
119
C
C
c
120
C
c
c
c
c
c
DD 1001 J=l ,N
DA( 1 , J ) = A(I»J)
INVERT MATRIX A
CALL INVERT (A,N,OJ
IF (IPRINT.EO.O) GO TO 2000
PRINT INVERSE AND IDENTITY HATR1X If REQUESTED
WRITECM0.82J
DO 1003 1=1, N
KRITEIM0.63) ( A ( I , J J , J = l , N )
DO 1004 1=1, N
DO 1004 J=1,N
XI U , J ) 0.0
CALCULATE IDENTITY MATRIX
DO 1005 1=1 ,N
DO 1005 J=1,N
DD 1005 K=l »N
XHI,J| - XI(I,J| •» A( I,K i*OA(K,J)
HRITECMO,86»
DD 1006 1=1, N
HR1TEIMO,63) UlC I ,J) ,J = 1 ,N>
CALCULATE VECTOR 1 1NV A * B
DO 119 J=1,N
SUH=0 .
DO 118 1=1, N
SUM=SUM*A« J, I) »8CI »
CONTINUE
Z( Ji=SUH
CH=0 .0
VY=0.
CHS =0.0
VU=0 .0
vvv=o .0
BEGIN LOOP TO CALCULATE ERROR SUMS, RESIDUALS, AND NEW HEIGHTS
DO 128 J=NZ,MF
SV 0 .
DD 120 1=1, N
N5 I S( I)
SV SV * S(N5,J, IABP) * Zf IJ
YC IS CALCULATED SPECTRUM
YC(J» SV
CALCULATE RESIDUAL RE
RE=Y J JI-SV
T =RE **2
VY=VY*W (J) *T
VU=VU+T
00002980
00002990
00003000
00003010
00003020
00003030
00003040
00003050
00003060
00003070
00003080
00003090
00003100
00003110
00003120
00003130
00003140
00003150
00003160
00003170
00003180
00003190
00003200
00003210
00003220
00003230
00003240
00003250
00003260
00003270
00003280
00003290
00003300
00003310
00003320
00003330
00003340
00003350
00003360
00003370
00003380
00003390
00003400
00003410
00003420
00003430
00003440
00003450
00003460
00003470
00003480
00003490
00003500
00003510
00003520
00003530
00003540
00003550
00003560
00003570
-------
A-21
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
164
183
186
185
121
122
123
124
128
129
130
132
THD - A&S(SV •» 0.1 + XMDD J
I F{TMO)183,184,183
TMO = 1.0
CONTINUE
CALCULATE VARIANCE DF CALCULATED COUNTS/ CHANN EL
TMP=TMQ+BA (J)»FX
IF UMP )185,186,185
TMP - 1.0
CONTINUE
VVV=VVV+TMP
IF (NW) 124,124,121
IF WEIGHTING SCHEME BASED ON CALC'D COUNTS, ASSIGN NEW HEIGHTS
IF (Nk-2) 123,122,124
FOR HEIGHTS BASED ON RECIPROCAL VARIANCE (YCALCJ
W( J) =1 .0/TMP
GO TO 124
FOR WEIGHTS BASED ON RECIPROCAL YCALC
W( J)=l ,0/TMO
RT=T/THP
CH=CH+RT
TMP=SQRT(TMP>
CALCULATE VECTOR OF NORMALIZED RESIDUALS
R(J )=RE/TMP
CONTINUE
END LOOP FOR ERRORS, RESIDUALS, AND WEIGHTS
CALCULATE DEGREES OF FREEDOM AND FIT FACTORS
DN = HF-N-NZ+1
CHDF - CH/DN
VY = VY/DN
CALCULATE STD DEV OF PARAMETERS
DO 129 1=1, N
E=AU ,1 J*VY
STDU )- E
CONTINUE
IF (KT-1) 130,133,132
WRITE(MO,73) CHDF
IF
-------
A-22
CD TO 134
133 NU=N
$HCr 0.0
134 F=l .0-Z(NU)/100.0
p p cFP*F
SMSHC=SHSHC+5HC
KR1TE
DO 9190 I = 1,N
DO 9189 J = 1,N
9189 CCU» - AU,J)/(SQRT(ABS(A(J.jmeSQRT(ABS(A(l,I)m
9190 HRITE(MG,9902)I,(CCIK),K=1,I>
C
C CALCULATE ALPHA FACTORS
C
145 DO 143 1=1 ,NT
K5=IS«I»
N6=IT(1 J
IF(VU) 190, 191, 190
191 All, I ) =0.0
AT!K6) = 0 .0
GO TO 143
190 CONTINUE
All, I! SSIN5.1ABPJ » All, II «• VY/VU
AT (N6) SORT
-------
A-23
XLD(I) = STO(l) » 3.29
ZUCU! - ZUJ * FAT * AC(N5,1ABP) » VH/VREO
ZtlJ Z(I) » FAT * ACCN5.IABP) * FD » VM/VREO
XPEU) = ABS( im 1)-CZU I-STDU ) J)/Z(I)) *100.)
144 CONTINUE
146 DO 147 J=1,NT
N5 = ITU)
ZT(N5) Z(JJ
ZTUC1N5) ZUC(J)
STTUCIN5) = STDUCU)
XPETJN5) - XPEU)
XLDTCN5) = XLD(J)
STDT(N5) = 5TDCJ)
OUTPUT RESULTS
CMC,75)
WRITE
DO 1147 J=l,NT
N5 = ITU)
1147 WRITE I HO,76) N5,TISD(N5),ZTUC(N5 I ,STTUC(N5),ZT(N5).STDTCN5)•
$ XPET(N5»,AT(N5),XLDT(N5)
CALL RESIOU
IMAGE 10000*(IABP) + 1000*(NB) -» 100*JNW+2) + 10*CKT+2> + KK
WRITE AUX. OUTPUT AS REQUESTED
IF (IAUX.GT.O) WRITEUAUX) X I DT , IMAGE ,R , YC ,YOBS
WRITE DATA BASE OUTPUT AS REQUESTED
IF (IOPT.EQ.O) GO TO 1148
CALL DATE (ADATE,ANOUN )
KRITE(HD.9904) ADATE,ANOUN
WRITE(IOPT) TNA^E.XIDT,IMAGE,AD ATE, ANOUN ,NT,
$ ITISOUTUn.ZTUTUn ,STDT( IT U)),J=l,NT»
: RE-ORDER ARRAYS IF REJECTION PROCEDURE UTILIZED
r-
1148 IF (Q) 156,169,148
148 KK=KK+1
IF (KK-2) 149,169,169
149 DO 151 1=1,NT
IF lzm/STD(I) - ABS(QI) 150,150,151
IS(I)=0
CONTINUE
KR=0
DO 153 J = 1,NT
IF USUM 153,153,152
KR=KR*1
ISIKR)=IS(J)
IT(KR)=J
153 CONTINUE
IF
-------
A-24
c
C HEAD BACK TO RECALCULATE WITH REJECTION
C
156 FTT=FP
SHCT=SMSHC
C
169 CONTINUE
C
C END OPTIONS LOOP ------------------------------ — —___»._- — __—_
C
174 GO TO 17
180 KR1TE(6,176»
STOP
C
f &&&&&&&&&&&&&&&&&&.'&&&& &A&AA #&&&$$$&$ #•$$&#$$ ^^^^^^^^^^^^^^^^^^^^OO^^
C
52 FORMATU114,8A4)
56 FORMAT (2F10 .4}
61 FORMAT (1X,IOF12.1 }
63 FORMAT(E14.,6,E14.6,E14.6,E14.6i,E14.6.E14.6,E14.6,E14.6,EI4.b)
64 FORHATUHIJ
65 FORMAT (A8, 513, 5F9 .4}
67 FORMAT120A4)
68 FORMAT { 1 X , 18 A4 ,2 A8 }
69 FGRHATU2H BACK&O SUM= FIO.OB16H SAMPLE SUN= F10 .0 I
70 FORMAT (613, 3F6. 2, (2212! )
73 FORMATC CHDF ',F6.2,» THR SHIFT = »»F7.4,
$ • GA IN SHIFT «,F7.4>
75 FORMAT!/, T3 , 'LIBRARY', T13, 'NUCL I DE • ,T28 , 'DECAY UNCORRECTED ',
i 755, 'DECAY COR RE CTE D • ,T77 , 'COE FF 1C 1 ENT ' ,T9 3, • ALP HA • ,/ ,
$ T3, 'NUhBER ',T13, 'NAME ',T26, 'ACTIVITY STO. ERR.',
t T52, 'ACTIVITY STD. E RR . • ,T 77 , "OF VA RIANC E • ,T93 , "FACTOR' »
$7X, «LLD»»
76 FORMATU6,,6X,A8,4UX,F9.<.!,6X,F6.2,7X,F7.4,5X,F8.«iB
82 FORMAT!/,' INVERSE MATRIX',/}
83 FORMAT!/, • INFORMATION MATRIX', /»
86 FORMAT!/, • IDENTITY MATRIX',/)
9901 FORMAT( 'CALPHA-M VERSION 2 LEVEL 3 RA DIOAN AL YT 1C AL
*• LABORATORY', 12X , 'DATE: ',A8,5X,' TIME :• . AS ,/// I
9902 FORMAT 1 14, 16F8 .3J
9903 FQR«AT(/,' CORRELATIONS ',/)
9904 FORMAT (/.' SA HP LE /OPT 1 CM WRITTEN TO IOPT AT • , A8 , IX ,D8 >
C
C»«*«ft»*9«»»»«»*«*«i>9i>*S»*«aC»«i>i5O«*«**«C»«9C« ««**«»« ft»»«t»»*0»»9»ft»»
C
C TO CHECK FOR SUBSCRIPTS OVERRANGING, RUN UNDER IBM FORTRAN :. G
C REMOVE THE 'C ' FROM THE FOLLOWING 2 CARDS...
C DEBUG SUBCHK
C AT 2
END
SUBROUTINE STDIN
C
C SUBROUTINE TO READ IN LIBRARY STANDARDS AND INFORMATION
C
INTEGER TNAME.FH
REAL*8 X1DT.T1 SO.TISOT
DIMENSION YZI256) ,A(22,2? ! , Y (257 » , Z »22 ! , CCJ 22 ) ,STDf22J ,81221 ,
$ K(256),WC256).DER(256I,YT(256I,IR1256),BA(256),FM(8)
00005460
00005*70
00005480
00005^90
00005500
U0005S10
00005520
«•' ^;or\5530
00005550
00005560
00005570
00005580
00005590
AA o^nnnn^Ann
wv **^uUUUJOUUi
00005610
00005620
00005630
OQOC"5.ft4u
00005650
00005660
00005670
00005680
C0005690
00005700
00005710
00005720
00005730
00005740
00005750
00005760
00005770
00005780
00005790
00005800
oooosaio
00005820
** S 00005830
•. 00005840
00005841
00005860
00005870
00005880
00005890
o*»*00005900
00005910
AND 00005920
00005930
00005940
00005950
00005960
00005970
00005980
00005990
00- 'jij'bQ OS
00006010
00006020
00006030
, 00006040
C221 , 00006050
-------
A-25
10
c
c
c
15
C
C
C
20
C
50
C
100
101
102
103
106
107
» STOT(22 ),TNAME(20),TI50T(22) ,TISO(22 ) .1T(22),ZT<22!,
$ S!2G,256,4»,XPF(20»,XPET(20),YC(256»,L1 C3),YOBS(256»
COMMON/SI UF F/X ! D7 ,T1 SO T.K'S.M.NIT ,IJBA,NZ,HF,NH ,KK,NTS,NTM,NQ, 0,FX
$ Mj,NSAMP,NOPT,IPRINT,NBR,NBS,lAbP,TB,TSA,VRED»DAY,VH,
$ NBN,NB,NH,NtKT,LW,YOBS,K23D,QH,NDET,IS,MO,NRED,IN,FS,
$ NBR1,FM,S,SS,AC,NDETS,HA,TST,Y,YC,IDPT , IAUX ,R ,XMOD,1RD ,
CET DESCRIPTION OF GEOMETRY, ft STDS., W DETECTORS
READJNTS1 Ll.NS.NDETS
KRITE(MU,107> ll»NS8NDETS
CET NUCLIDES NAMESr HALFLIVES, COUNT TIMES, ACTIVITIES
RE AD SHI jJ (TISOTU ),HA(I I ,TSTm,(AC{I ,K»,K=1 ,4),I = 1,NSI
WRUEJMG ,102?
kf f~ ~ •'•• 1.01 J ' T? SOT I I ) ,HAU I ,TST( J ) , ( AC U ,KI » K=l ,^ ) , I =1 ,N SJ
rul. EACH OETECTDR-GEOMETRY SET
DO 50 K = UNDETS
DO 10 I=1,NS
READ SPECTRA FOR ALL NUCLIOES
READ(NTS) TNAME
IF (NBA.EQ.l) HRITE(MO,106) TNAHE
READ(NTS) CS«!.J,K1,J~lBM I
IF (NBA.EQ.l) WR! TE(MO,103J (SC I ,J,X»,J = 1,M )
CONTINUE
CALCULATE NUCLIDE CHANNEL SUMS
DO 15 1=1,NS
SSCI.K) * 0.0
DO 15 J NZ.MF
55(1,K) = SSII.K) + SU.J.KI
CALCULATE NUCLIDE CHANNEL SUM SQUARES
DO 20 I = 1,NS
SMI ,K) = SS(1 ,K)**2
CDMTINUE
FORHAT!A8,6F10 ,2}
FORMAT (1X,A8.5X,F10.1,7X, F10. 5,6X,F10.1,3X,F10.1,3X,F10.1t3XtFli)
$ J
FORM AT ACT-DET-A',^X,»ACT-DET-Bf,'iiX,'ACT-DET-Ct,^X,'ACT-DET-Dt,/J
FORMAT(1X.10F12.1 )
FORMAT(1H1,20A4)
FORMAT I'OFILE CONTAINS DATA FOR GEOMETRY TYPE >,3A4,10Xi
J'NUMBER OF STDS I S • , I 3 ,10X , "NUMBER OF DETECTORS IS',13}
RETURN
END
SUBROUTINE RES1DU
00006060
00006070
00006080
00006090
00006100
MU00006110
00006120
00006130
00006140
00006150
00006160
00006170
00006180
00006190
00006200
00006210
00006220
00006230
00006240
00006250
00006260
00006270
00006280
00006290
00006300
00006310
00006320
00006330
00006340
00006350
00006360
00006370
00006380
00006390
00006400
00006410
00006420
00006430
00006440
00006450
00006460
00006470
00006480
00006490
00006500
00006510
00006520
.100006530
00006540
00006550
00006560
00006570
00006580
00006590
00006600
00006610
00006620
00006630
00006640
00006650
-------
A-26
SUBROUTINE TO PROVIDE ANALYSIS OF RESIDUALS
C
c
C
INTEGER L1NEC101)
INTEGER TNAHE.FM
REAL»8 XIDT.TISO,
DIMENSION YZ(256!
4 R<256),
t 55(20,4
* STDH22
* S(2G,25
i DA(22,2
COMHON/STUFF/XIDT
$ MS.NSAK
$ NBN.NB,
i UBR1.FH,
»NSTAR/«»»/,NBLNK/« •/,NPNT/• .•/.NPLUS/'+'/
TISOT
, A(22,22 ),Y(257J,Z(22),CC(22),STD(22),BI22) ,
W(256),DER(256),YT(256> ,IR(256),BAt256) ,FMt 8) ,
!,AC<20,4),HA(20),1S(22),TST(22J ,HATt22>,AT(22)
),TNAME(2C),TISUT<22),TISQ(22),IT(22),IT122»,
6,4),XPE<20),XPET(201fYC(256).
2),ZUC(22).ZTUC122) ,YOB 5(256)
,TISOT,NS»M,N1T,NPA,NZ ,MF ,NH ,KK ,NTS ,NTH ,NQ,Q,FX
P,HOPT,lPKlNT,NBR,NBSfIABP,TB,TSA,VRED,DAY,V*i
NW,N,KT,LK,YOBS ,K230,OH ,NDET,IS,MO,NRED,IN,FS,
S,SS,AC,NDETS,HA,TSTtY,YC,IOPT,IAUX,RtXMOD,l*Of
OUTPUT NORMALIZED RESIDUALS
WRITE(MO,79)
WRlTElKQ.aO HRUI ,J = 1,WF)
K = 0
SIG3 = 0.
S1G2 - 0.
51G1 = 0.
SUHT - 0.
XRSUM = 0
XSQSUH = 0
XCBSUM = 0
X4TH = 0.
DETERMINE STATISTICS AND SUSPICIOUS CHANNELS FROM RESIDUALS
DO 164 J = NZ.MF
XRSUH - XRSUH •» R (J >
XSQSUM XSQSUH * R(J)«R(J>
XCBSUM = XCBSUM + R(J)*RIJ 1 »R(J )
XNO = MF-NZ + 1
XRSUM/XNO
50RT((l./«XNO-l.))»(XSQSUK!-f(XRSUM»*2)/XND)l»
J NZ.MF
SUHI + ((R(JJ-XAVG1/XS1GJ**3
SUMT + ((R(Jl-XAVG)/XSlG)*»4
5UMI/XNO
XAVG =
XSIG
DO 163
SUMI -
163 SUMT -
XSKEH =
XKURT = SUMT/XNO
PLUS3S = XAVG + 3.0 * XSI&
XMIN3S XAVG - 3 .0 * XSI&
DO 165 J = NZ,MF
IF ( (RU).LT.PLU53SJ.AND.IR{J) .&T.XHIN3S I) GO TO 165
K = K •» 1
JCHNL = J
IF «R(J! .LT.XMIN3SI JCHNL JCHNL * (-11
165 IR(K) = JCHNL
WRITE(MO,84) XAVG.XSIG.XSKEW, XKURT
DO 1655 J=NZ,HF
IF ((R(J).LE.(3.*XSIG)).AND.IR(JJ.GE.(-3.*XSIG!!>SIG3=SIG3+1
IF ((K(J).LE.12.«XSIG)(.AND.CR(J).GE.(-2.»XSIG)J)SIG2=S1G2+1
1655 IF(!R(J).LE.(XSI&)).AND.(R(J) .GE .(-XSIG) MSIG1=SIG1*1.
SIG3 - (51G3/XNO) * 100.
SI&2 =- (S1G2/XNO) » 100.
SI&l = (S1G1/XNO) * 100.
00006660
00006670
00006680
00006690
00006700
00006710
00006720
, 00006730
00006740
00006750
00006760
, 00006770
00006780
00006790
HU00006800
00006810
00006820
00006830
00006840
00006850
00006860
00006870
00006880
00006890
00006895
00006900
00006910
00006920
00006921
00006930
00006940
00006950
00006960
00006970
00006980
00006990
00007000
00007010
00007020
00007022
00007024
00007025
00007026
00007027
00007040
00007050
00007060
00007070
00007080
00007090
00007100
00007110
00007120
00007130
00007140
00007150
00007160
00007170
00007180
00007190
-------
A-27
C
c
C
166
10
C
c
c
15
16
17
20
25
C
79
80
81
82
83
WRME(MD,83) S IG1 , S I G2 ,SIG3
IF CK.EQ.O) GO TO 166
WRITE IM0.81)
WRITE(MG,82) (IR(JI,J = l ,K )
PRODUCE PRINT-PLOT OF NORMALIZED RESIDUALS
IF(IRD.EQ.O) GO TO 1000
WRITE(MU,85) XIDT.1N
WRITE(MU.88 )
N3P = (PLUS3S+10.0)70.2
N3M = (XMJN3S+10.01/0.2
IF (N3P .GT.101) N3P = 101
IF (N3M.LT.1) N3M - 1
DO 10 J NZ,MF
DO 5 K - 1,101
LINE(K) - NBLNK
LINE(N3P) = NPNT
L1NE(N3H ) = NPNT
LlNEtSl) - NPNT
MPOS - (R(J) +• 10 .0)70.2 + 1
IF (NPOS.GT.101) MPOS = 101
IF 1NPOS.LT.1) NPOS = 1
LINE (NPOS) = NSTAR
WR1TE(MU,500) J,R {J ),NSTAR ,L INE .NSTAR
PRODUCE PRINT-PLOT OF OBS'D AND CALC'D SPECTRA
IF (IRD.NE.2) GO TO 1000
YOFSET 0.0
VMIN = l.OE+20
YMAX = -l.OE+20
DO 15 I=NZ,MF
IF IYOBS1 1) .GT.YMAX) YMAX YOB5U)
IF (YC ( 1 ) .GT.YMAX ) YHAX = YC(I>
IF IYOESH ) .LT.YMIN) YMIN = YOBS(I)
IF IYCCn.LT.YHIN> YK1N = YCCI)
IF (YMIN) 16,17,17
YOFSET = ABSIYM1N J
YRAKGE = YMAX - YHIN
YINC = YRANGE7100 .0
WRITE (MU ,86 ) X1DT , IN
WRITE IHU,89)
DO 25 I=NZ,MF
DO 20 J=l,101
LINE tJ) = NBLNK
IF (YhlN.LT.O.) LINE(IF1XCYOFSET/YINC)+lJ = NPNT
NPOS (YOBSf1)-YMIN)/YlNC + 1
LINE(NPOS) - NSTAR
NPOS = (YC(1J-YMIN)7YINC + 1
L I NE (NPOS) = NPLUS
WRITEIKU.87) 1,YDBSCI),YC C I > ,NSTAR ,LINE,NSTAR
FORKAT(/,» NORMALIZED RESIDUALS PER CHANNEL"!
,20F6.1 )
CHANNELS',/)
FORMAT (/,' SUSPICIOUS
FCRHAT (2515)
FORMAT(IX,'PERCENT OF RESIDUALS UNDER
$•2 SIGMA =«,F5.1,5X,'3 SIGMA =',F5.1)
84 FORMAT!/,IX,"AVER AGE = • ,F7 .4 ,10X ,'STD. DEV-
1 SIGMA =',F5.1,5X,
•,F7.
-------
A-28
85
86
87
88
89
500
C
1000
$»SKEWNESS =',F9.4,10X,'KURTDSIS =',F9.4)
FORMAT(1H1,« PLOT OF RESIDUALS VERSUS CHANNEL NUMBER*,10X,
S'SAMPLE ID: •,A8,10X,"OPTION NUMPER •»13,//>
FORMATUH1,' PLOT OF YOBS AKD YCALC'.IOX,
J'SAhPLE IDS ',AS,10X, "OPTION NUMBER • ,I 3,//)
FORMAT(I5.2F10 .2.103A1 I
FORMAT!/,* CHNL R'»
FORMAT!/,• CHNL YOBS YCALC'J
FORHAT(I6,5X,F5.1,5X,A1,101A1,A11
RETURN
END
SUBROUTINE SHIFT (Y,M.SH,F,SHC)
E. 5CHOENFIELD, MARCH 25, 1966
DIMENSION Y!257),YC«257J
Y(l)=0 .0
TE=SHC+SH*|F-1.0)
TO 60 1=1, M
UI = I
DC 40 J=JT,H
41
45
IF (CiI-QJJ 41,45,40
IF f J-l ) 45,45,50
YC(1)=Y(J)/F
GO TO 60
40 CONTINUE
76 FORMAT! 16.6X.A8 ,4 (4X.F9.4 ) ,7X,F6.2,<»X.F9 .
50 YC(I)=(Y{J)-Y(J-1))/F
YC(n=Y(J-l)+YC(l)*{QI-OJ + F)
YC(IJ=YC JIJ/F
60 CONTINUE
DO 80 1=1,M
80 Y( I)=YC( I)
YC(1)=1.0
RETURN
END
SUBROUTINE INVERT (G,N,D)
GAUSS-JORDAN METHOD * VERSION BY
M H L1ETZKE ET AL (ORNL-3430)
DIMENSION A (22 ,22 l,Bl22),C(22),LZt22)
DIMENSION G (22,22>
REAL " 8 A,B,C,W,Y.D.EPS
EPS = l.OD-10
D = 1.000
DO 40 1=1,N
DO 41 J=l,N
A(I ,J)=G(1,J)
41 CONTINUE
40 CONTINUE
DO 10 J=I,N
10 LZ(JJ=J
00007800
00007810
00007820
00007830
00007840
00007850
00007860
00007870
00007880
00007890
00007900
00007910
00007920
00007930
00007940
00007950
00007960
00007970
00007980
00007990
00008000
00008010
00008020
00008030
00008040
00008050
00008060
00008070
00008080
00006090
00008100
00008110
00008120
00008130
00008140
00008150
00008160
00008170
00008180
00008190
00008200
00008210
00008220
00008230
00008240
00008250
00008260
00008270
00008280
00008290
00008300
00008310
00008320
00008330
00008340
00008350
00008360
00008370
00008380
00008390
-------
A-29
DO 20 1=1,N
K = I
Y=A(I,I)
L = I-1
LP=I+1
IF(N-LPJ21,11,11
11 DO 13 J=LP,N
H=A(I,J)
IF (DABS(HJ-DABS(Y) 113,13,12
12 K=J
Y = W
13 CONTINUE
21 IF lOAPS(Y)-EPS) 24,24,25
24 Y =1.0
WRITE (6,9923)
9923 FORMAT (• »»***»** MATRIX IS SINGULAR *»»»*»**•)
25 CONTINUE
14 DO 15 J = 1,N
CCJJ=A(J,K)
A(J,K)=A(J,I)
A( J,I)=-C(J)/Y
A I I , JHA Cl,JJ/Y
15 6
-------
A-30
INTEGER TNAME.FH
REAL*8 XIDT.TISO,
DIMENSION YZI256)
$ R 1256 ) ,
* 55120,4
$ STDT122
t 5(20,25
COMKON/STUFF/XIDT
$ M5.N5AM
$ NBN.NB,
$ NBRliFHt
TISDT
.A122.22 ),Y(257),Z(22),
H1256J,DER(256 ),YT(256)
},AC(20,4),HA120),15(22
) ,TNAHE(20).TI5DT122),T
6,4>,XPF (2C) .XPFT120) ,Y
,T15UT,(.S,H,NIT,NBA,N2,
P,NOPT,lPRIMT,NPk,NBS,l
NW,N,KT,LW,YOBS,K23D,QH
S,S5iAC,MDETS,HA,TST,Yi
CC(22),STD(22),B122) ,
,IR(256),BA1256),FHt8).
).TST(22J ,HAT(22),AT122)
150(22),ITI22),ZT(22),
C1256) .YOBS1256)
K.F.NH ,KK,NTS,NTH ,NQ,Q,FX
ABP,TB,T5A,VRED,DAY,VMt
,NOET,IS,HU,NREO,IN,FS,
YC,10PT,IAUXtRrXMQO,IRD,
LABEL GENERAL CONTROL INFORMATION
WRITE(MO il) FH.HtNIT,NZ,HF,NTS,NTH
IF (NBA.GT.O) GO TO 100
URITE (MO,21
100
110
115
117
118
119
120
121
122
123
C
C
C
GO TO 110
WRITE (MO, 31
IF 1NH.GT.O)
KRITE1MQ.36)
GO TO 117
WRITE(MO,35}
IF (IAUX.EQ.
WRITE(MD,38 )
GO TO 119
WRITE (HO, 39 )
IF (IDPT.EQ.
WRITE (HO.'fO I
GO TO 121
WRITE (HO ,41 J
IF (HS.GT.01
WRITE(HO,43 J
GO TO 123
HRITE(HO,42)
RETURN
LABEL 5AMPLE
GO TO
0) GO
I AUX
0) GO
I OPT
GO TO
HU
115
TO 118
TO 120
122
CONTROL INF!
ENTRY LABEL1
NSHP KREO + I
WRITE(MO,4) NSHP,XIDT,NOPT,TB,T5A,DAY,VREO,VH,FS.FX
130 IF (NBR.GT.O) GO TO 140
WRITEIM0.7)
GO TO 150
140 WRITE(HO,8»
150 IF INBS.G1.0) GO TO 160
WRITE (MO,9)
GO TO 170
160 kRITE(MC,10)
170 GO TO (171,172,173,174),IABP
171 WRITElMO.ll)
CO TO 175
172 KRITE(MOtl2)
GO 10 175
173 WRITE(MO,13)
GO TO 175
174 KR1TE(MO,14)
175 IF (HS.EO.O) GO TO 176
00009000
00009010
00009020
00009030
00009040
. 00009050
00009060
00009070
, 00009080
00009090
00009100
MU00009I10
00009120
00009130
00009140
00009150
00009160
00009170
00009180
00009190
00009200
00009210
00009220
00009230
00009240
00009250
00009260
00009270
00009280
00009290
00009300
00009310
00009320
00009330
00009340
00009350
00009360
00009370
00009380
00009390
00009400
00009410
00009420
00009430
00009440
00009450
00009460
00009470
00009480
00009490
00009500
00009510
00009520
00009530
00009540
00009550
00009560
00009570
00009580
00009590
-------
A-31
176
C
C
C
WRITEJMO
RETURN
44) HS
LABEL SAMPLE OPTION INFORMATION
220
230
240
250
260
270
280
290
300
305
310
320
330
340
350
360
370
380
390
395
400
405
407
408
410
415
NRED ,XIDT,IN
GO TO 220
GO TO 240
260i270,280
TO 300
CD
0
Q
TO 305
ENTRY LA8EL2
WRITE(MCJ,33)
IF (NB.GT.O)
HRITEtMQ.lS)
GD TO 230
WRITEIM0.16)
IF (NW.GT.O)
WRITE(MO,17)
GO TD 250
WRITE(MO,18)
IF UABS(NW)-2)
WRITE(MO tl9)
GD TO 290
WRITE(MG,20)
GO TO 290
WRITE(HOF21)
IF (Q.GT.O) GO
WRITE(MO,22)
GD TO 310
IF (KK.EQ.O)
WRITE(MD,34)
GO TO 310
WRJTE(MG,23 I
NEKT = KT+3
GO TO (320,330 ,340,350 ,350 )t NEKT
WRITE (ML),24)
GD TO 360
WRITE(MO,25)
GO TO 360
WRITE(HO,26)
GO TO 360
WRITE IKO,27
IF (KT.LT.O GO TO 380
IF (KT.EQ.l GO TO 370
WRITEf MO,28
GO TO 380
KRITE(MO,29
WRITE(MO,30
WRITE (MO,31 )
WRITE(MG,32)
IF (XMOD J 390,395
WRITE(HU,45) XMOD
IF (IRD.GT.O) GO TO
WRITE (MO,47)
GO TO 405
WRITE (MO,46)
IF (IRD.EQ.2)
WRITE(MO,50)
GO TO 408
WRITE(MO,51)
IF MPRIMT.EQ.O) GO TO 410
WRITE(KG,49)
GO TO 415
WRITE(MO,48)
WRITE(MO,37»
N
QH
US(
,390
400
GO TO 407
00009600
00009610
00009620
00009630
00009640
00009650
00009660
00009670
00009680
00009690
00009700
00009710
00009720
00009730
00009740
00009750
00009760
00009770
00009780
00009790
00009800
00009310
00009820
00009830
00009840
00009850
00009860
00009870
00009880
00009890
00009900
00009910
00009920
00009930
00009940
00009950
00009960
00009970
00009980
00009990
00010000
00010010
00010020
00010030
00010040
00010050
00010060
00010070
00010080
00010090
00010100
00010110
00010120
00010130
00010140
00010150
00010160
00010170
00010180
00010190
-------
A-32
c
1
2
3
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
32
33
34
35
36
37
38
RETURN
FORMATdHO, 'GENERAL CONTROL INFORMATION •,//.
$ 1X8BDATA FORMAT IS »,8A4,/,
$ IX, 'NUMBER OF CHANNELS I fJ ANALYZER IS',15,/,
$ IXt'HAXIKUM NUMBER OF ITERATIONS IS',I3,/,
$ IX, 'INITIAL CHANNEL FOR COMPUTATION IS1, 14,7,
$ IX, 'FINAL CHANNEL FOR CONFUTATION IS', 14,7,
$ IX, "STANDARD SPECTRA ON FORTRAN LOGICAL UNIT', 13, /,
$ IX, "SAMPLE SPECTRA ON FORTRAN LOGICAL UNIT', 13)
FORMAT (IX, "LI bRARY STANDARD SPECTRA WILL NOT BE PRINTED')
FORMAT (IX, 'LIBRARY STANDARD SPECTRA WILL BE PRINTED'!
FORM AT C 1 Hi s *C ON TR 0 L 1 NFOFM ATION ..... SAMPLE NUM8ER*«I3s
$ 10X, "SAMPLE ID IS: 88A8,/,/,
$ !Xe'NUMBER OF PROCESSING OPTIONS IS',I3,7t
$ IX, 'COUNTING TIME (WINS.) FOR BKGND IS»,F8.2,7,
$ IX, 'COUNT! NG TIKE ( M I N S . ) FOR SAMPLE IS',F8.2(/t
$ IX, 'DECAY TIKE (DAYS) 1S',F7.2,/,
$ 1X,'VDLUME REDUCTION FACTOR IS • ,F 7. 3 ,/ ,
$ IX, 'VOLUME MULTIPLICATION FACTOR IS",F7.3,/,
$ IX, 'SAMPLE T1HE/BKGND TIME = FS = e,F7.3./,
$ IX, 'VALUE OF PS*-?? = FX =%F7.3J
7 FORMAT (1X,8SAHPLE BACKGROUND NOT INPUT; PREVIOUS BKGND WILL BE
$ED IF SUBTRACTION REQUESTED11)
FORMAT (IX, 'SAMPLE BACKGROUND WILL BE INPUT AND USED IF SUBTRACT
JN REQUESTED'!
FORMAT ( IX, 'PERMA NENT BACKGROUND SUBTRACTION NOT REQUESTED')
FORMAT (IX, 'PERMANENT BACKGROUND SUBTRACTION REQUESTED*)
FORMAT (IX, 'DETECTOR A STANDARDS SELECTED9,/}
FORMAT (IX, 'DETECTOR B STANDARDS SELECTED', 7)
FORMAT (IX, "DETECTOR C STANDARDS SELECTED",/!
FORMAT (IX, 'DETECTOR D STANDARDS SELECTED', /I
FORMAT ( IX, 'BACKGROUND HILL NOT PE SUBTRACTED THIS OPTION")
FORMAT 1 IX, "BACKGROUND WILL BE SUBTRACTED THIS OPTION'}
FORMAT SIX, 'WEIGHTS TO BE BASED ON OBSERVED SAMPLE SPECTRUM')
FORMAT (IX, 'WEIGHTS TO BE BASED ON CALCULATED SAMPLE SPECTRUM')
FORMAT!! X, 'WEIGHTS PROPORTIONAL TO RECIPROCAL COUNTS/CHANN EL "1
00010200
00010210
00010220
00010230
00010240
00010250
00010260
00010270
00010280
00010290
00010300
00010310
00010320
00010330
00010340
00010350
00010360
00010370
00010380
00010390
00010400
00010410
US00010420
00010430
1000010440
00010450
00010460
00010470
00010480
00010490
00010500
00010510
00010520
00010530
00010540
00010550
00010560
FGRHAT (IX, 'HEIGHTS PROPORTIONAL TO RECIPROCAL VARIANCE OF COUNTS /C00010570
iHANNPL ')
FORMAT (IX, 'UNIT WEIGHTS ASSUMED'?
FORMAT (1 X, "NO REJECTION COEFFICIENT APPLIED*}
FDRKATUX, 'REJECTION COEFFICIENT OF %F6.2,» WILL BE APPLIED")
FORMAT ( IX, 'COMPENSATION BASED ON PREVIOUSLY CALCULATED VALUES')
FORMATUX, 'MANUAL COMPENSATION REQUIRED"}
FORMAT (IX, 'NO COMPENSATION REQUIRED'}
FOPMATtl X, 'AUTOMATIC COMPENSATION REQUIRED9)
FORMAT J1H+.T34, "FOR GAIN AND THRESHOLD SHIFT'S
FORHAT (IH-t ,T34 , 'FOR GAIN SHIFT ONLY " J
FORHATI1X, 'NUMBER OF ISOTOPES USED FROM LIBRARY IS»,13)
31 FORMAT I IX, 'THRESHOLD CHANNEL SHIFT BETWEEN STDS AND SAMPLE IS'.
$F6.2!
FORMATdX, 'LIBRARY STD . NUMBERS, IN ORDER OF DESIRED OUTPUT ARE'
$ 2013)
FORMAT IIHI.'SAMPLE NUMBER', 13,' ID NO. ',A8B' ... PROCESSING
$PTION NUKBER1, 13, //)
FORHAT (IX, 'REJECTION COEFFICIENT OF ",F6.2,» HAS BEEN APPLIED')
FORMAT « IX, 'CORRELATIONS BETWEEN VARIABLES WILL BE PRINTED'l
FORMAT I1X, 'CORRELATIONS BETWEEN VARIABLES WILL NOT PE PRINTED')
FORMAT t/I
FORMAT (IX, 'AUXILIARY DATA OUTPUT ON FORTRAN LOGICAL UNIT',131
00010580
00010590
00010600
00010610
00010620
00010630
00010640
00010650
00010660
00010670
00010680
00010690
00010700
. 00010710
00010720
000010730
00010740
00010750
00010760
00010770
00010780
00010790
-------
A-33
39
40
41
42
43
44
45
46
47
48
49
50
51
C
c
C
c
c
c
c
c
1
100
2
110
3
120
4
130
5
140
FORMATUX, "AUXILIARY DATA WILL NOT BE OUTPUT")
FORMAT (IX, 'ANALYTICAL RESULTS OUTPUT ON FORTRAN LOGICAL UNIT', 13
FORMATUX, "ANALYTICAL RESULTS WILL NOT BE OUTPUT TO DISK")
FORHATdX, "FORTRAN LOGICAL UNIT FOR PRINT-PLOTS (IF REQUESTED) 1
$", m
FQRMATd X, "FORTRAN LOGICAL UNIT FOR PRINT-PLOTS NOT SUPPLIED"!
FORHATdX, 'LIBRARY STD. NO. ',12," BEING REPLACED WITH BKGfJO'J
FURHAT (1X.30I •»")," WEIGHTING MODIFICATION * , F6 .2 ,3X , 30 8 • *" J I
FORMAT (IX, "NORMAL IZED RESIDUALS WILL BE PLOTTED"*
FJRHAT (1 X, 'NORMAL 1 ZED RESIDUALS WILL NOT BE PLOTTED'l
FORMAT (IX, "MATRIX INFORMATION HILL NOT BE PRINTED")
FORMAT (IX, 'MATRIX INFORMATION WILL BE PRIIMTEO'8
FORKATdX, 'OBSERVED AND CALCULATED SPECTRA HILL NOT BE PLOTTED")
FURHAT (1 X, 'OBSERVED AND CALCULATED SPECTRA WILL BE PLOTTED'l
END
SUBROUTINE DIAG
SUBROUTINE TO PROVIDE DIAGNOSTICS FOR JNPUI PARAMETERS
SETS IEK = 1 FOR TERMINAL ERROR
REAL * 8 TISOT.TI SO ,X I DT , ADATE , ANOUN.D
INTEGER * 4 FM,TNAME
DIMENSION YZ( 256) ,A(22,22) ,Y (257) ,Z»22),CCf 22), STD«22»,B(22) ,
* R«256),W(256),DER(25b),YT(256),IR{256)iBAt256JtFMt8)i
$ SS(20,4),AC(20,4),HA(20),IS(22J,TST(22),HAT(22),AU22)
$ STDU22),TNAfE(20),TISnT(22)fTISO(22),IT(22).ZU22l,
$ S(20,256,4),XPE(20),XPET(20),YC(256J,XH22,22Jt
» DA(22,22),ZUCS22),ZTUC(22)tYOBS(256)
COKMON/STUFF/XIDTfTISOT,NS,M,NIT,NbA,NZ,HF,NH,KK,NTS,NTM,NQ,C,FX
$ MS,NSAMP,NOPT,IPRlNT,NPR,NBS,IABP,TB,TSA,VRED,DAY,V«t
$ NBN,N6,NW,N,KT,LH,YQBS,K23D,QH,NDET,I5,MO,NRED,1N,FS,
$ NBRl,FM,S,SS,AC,NDETS,HA,TST,Y,YC,IOPTtIAUXtR,XHDD,IRD,
INTEGER ERRORC4) /•****".•* ER'.'ROR ",»****•/
DIAGNOSTICS FOR GENERAL CONTROL CARD
IER = 0
IF (M .LE .256) GO TO 100
WRITE(MO.l) ERROR
FORHAT(4A4,5X, "NUMBER OF CHANNELS CM) GREATER THAN 256*1
IER - 1
IF (MF.LE.M) GO TO 110
HRITE(MO»2) ERROR
FORMAT (4A4,5X, "FI NAL CHANNEL (MFJ GREATER THAN VALUE OF H8 I
IER = 1
IF (MF.LE.256) GO TO 120
KRITE(MO,3) ERROR
FORKAT(4A4,5X, 'FI NAL CHANNEL SMFJ GREATER THAN i56B?
IER = 1
IF (NZ.LT.MF) GO TO 130
WRITE(MO,4) ERROR
FORMAT(4A4,5X, "INITIAL CHANNEL JNZ» GREATER THAN FINAL «MF}»!
IER = 1
IF (NZ.CT.O) GO TO 140
WR1TEIHG.5) ERROR
FORMAT(4A4,5X, 'INITIAL CHANNEL (NZ! IS ZERO OR LESS B J
IER = 1
IF (NTS.GT.O) GO TO 150
WRITE(MU,6) ERROR
OC010800
) 00010810
00010820
S 00010830
00010840
00010850
00010860
00010870
00010880
00010890
00010900
00010910
00010920
00010930
00010940
00010950
00010960
00010970
00010980
00010990
00011000
00011010
00011020
00011030
00011040
, 00011050
00011060
00011070
00011080
, 00011090
00011100
00011110
MU00011120
00011130
00011140
00011150
00011160
00011170
00011180
00011190
00011200
00011210
00011220
00011230
00011240
00011250
00011260
00011270
00011280
00011290
00011300
00011310
00011320
00011330
00011340
00011350
00011360
00011370
00011380
00011390
-------
A-34
6
150
7
160
8
C
C
C
170
9
180
10
190
11
200
210
12
212
215
18
220
13
230
240
14
250
260
FORKAT(4A4,5X,«NO FORTRAN UNIT FDR STANDARD LIBRARY SPECTRA'I
i t K 1
IF JNTM.GT.O! GO TO 160
WRITEIM0.7) ERROR
FORMAT(4A4.5X, 'NO FORTRAN UNIT FOR SAMPLE SPECTRA*)
IER = 1
IF (IER.EQ.OI RETURN
WR!TE(MO,8)
FORHATCOJDB TERMINATED FOR ABOVE ERRORCS)')
STOP 5095
DIAGNOSTICS FOR SAMPLE CONTROL CARD
ENTRY DIAGi
IER = 0
IF ((NBS.EQ.l) .AND.((NBR + NBR1).EQ.OII GO TO 170
GO TO ICO
KR1TE(MG,9) ERROR
FORHAT(4A4,5X, "BKGND SUBTRACTION REQUESTED BUT NO BKGND INPUT')
IER 1
IF < IABP.LE.NDET5I GO TO 190
KRITE(HG.IO) ERROR
FORMAT(4A4,5X,'DETECTOR NO. IABP GREATER THAN ANY IN LIBRARY*)
IER = 1
IF (TB.GT.O.) GO TO 200
WRITEtMO.llJ ERROR
FORKAT(4A4,5X, 'SAMPLE COUNT TIME IS ZERO MINUTES')
IER - 1
IF ((TSA.LE.0.).AND.t(NBR+NBR1) .GT.O.) ) GO TO 210
GO TO 212
HRITEtMO,12) ERROR
FDRhAT(4A4,5X, *BKGND COUNT TIME IS ZERO MINUTES'J
IER = 1
IF «MS.GT.O).AND.((NBR+NBR1) .EO.OH 00 TO 215
GO TO 220
MR ITE(MO,18I ERROR
FORMAT(4A4,5X,'LIB. STD. REPLACEMENT REQUESTED BUT NO BKGND',
$• SPECTRUM HAS BEEN INPUT'!
IER 1
IF UER.EQ.O! RETURN
WRITE(HO,8)
STOP 5095
DIAGNOSTICS FOR SAMPLE OPTION CARD
ENTRY DIAG2
IER 0
IF (N .LE .NS) GO TO 230
KRITE(MO,13) ERROR
FORKATI4A4.5X,"NO. NUCLIDES SELECTED IS GREATER THAN NO. IN',
$' MERAftY'J
IER = 1
IF ( (NB.EQ.l J.AND.UNBR + NBR1 KEQ.O) ) GO TO 240
GO TO 250
WRITE (MO,14) ERROR
FORNAT(4A4,5X, 'BKGND SUBTRACTION REQUESTED BUT NO BKGND INPJT')
IER = 1
IF S(1ABS(NW).EQ.2).AND.(INBR^NBRl).EQ.0)) GO TO 260
GO TO 270
WRITEtMQ.lS) ERROR
00011400
00011410
00011420
00011430
00011440
00011450
00011460
00011470
00011480
00011490
00011500
00011510
00011520
00011530
00011540
00011550
00011560
00011570
00011580
00011590
00011600
00011610
00011620
00011630
00011640
00011650
00011660
00011670
00011680
00011690
00011700
00011710
00011720
00011730
00011740
00011750
00011760
00011770
00011780
00011790
00011800
00011810
00011820
00011830
00011840
00011850
00011860
00011870
00011880
00011890
00011900
00011910
00011920
00011930
00011940
00011950
00011960
00011970
0001J980
00011990
-------
A-35
15 FORMAT(4A4.5X,"HEIGHT1N& SCHEME
$ " BUT NONE HAS BEEN INPUT')
IER = 1
Z70 IF (N.GT.NS) GO TO 280
IF1 - 0
00 272 INT = 1,N
IF CIS(IK'T) .LE.O) IF1 = 1
272 IF (1SUNT) .GT.NS) IF1 = 1
IF (1F1.EQ.1) GO TO 275
GO TO 260
275 WRITE1MG.I6) ERROR
16 FORMAT (<+A4t5X,'ONE OR MORE LIB.
$• OF RANGEM
IER = 1
280 NEND = N-l
IF1 = 0
DO 285 I = l.NEND
K = 1 + 1
DO 285 J = K,N
IF (IS(I).EQ.ISIJM IF1 - 1
285 CONTINUE
IF (IF1.EQ.1) GO TO 290
GO TO 295
290 WRITE(HO,17» ERROR
17 FORKATKA4.5X, 'TWO OR MORE LIB.
IER = 1
295 IF UER.EQ.O) RETURN
WRITE(HO,8)
STOP 5095
C
END
SELECTED REQUIRES A BKGNDV
STD. NOS. SELECTED ARE OUT'.
STDS SELECTED ARE REDUNDANT")
00012000
00012010
00012020
00012030
00012040
00012050
00012060
00012070
00012080
00012090
00012100
00012110
00012120
00012130
00012140
00012150
00012160
00012170
00012180
00012190
00012200
00012210
00012220
00012230
00012240
00012250
00012260
00012270
00012280
00012290
00012300
-------
A-36
A. 6 ALPHA-M FLOW DIAGRAMS
The following figures are the flow diagrams for the computer
program ALPHA-M. Figure A-1 (U sheets) is the main program
flow diagram, A-2 (5 sheets) is for the subroutine LABEL,
A-3 is for the subroutine STDIN, A-4 is for the subroutine
RESIDU, and A-5 (2 sheets) is for the subroutine DIAG.
-------
A-37
Figure A-1. ALPHA-M main program flow diagram.
-------
A-38
START
OF
ITERATION
LOOP
Figure A-1. ALPHA-M main program flow diagram (cont.)
-------
A-39
GAIN & THR
END OF
ITERATION--- v ITERA"
LOOP \TIONS.
YES
Figure A-1. ALPHA-M main program flow diagram (cent.)
-------
A-4G
Figure A-1. ALPHA-M main program flow diagram (coirt.)
-------
A-41
PRINT 36
.* — —
PRIN
Figure A-2. ALPHA-M subroutine LABEL flow diagram.
-------
A-42
(ENTRY}
LABEL I J
Figure A-2. ALPHA-M subroutine LABEL flow diagram (cont.)
-------
A-43
L.
ENTRY "*\ _
LABEL 2 J
PRINT:
NRED.
XIDT,
IN
Figure A-2. ALPHA-M subroutine LABEL flow diagram (cont.)
-------
A-44
PRINT 24
*
PRINT 25
PRINT 26
* t
PRIN
<
Figure A-2. ALPHA-M subroutine LABEL flow diagram (cont.)
-------
A-45
395
Figure A-2. ALPHA-M subroutine LABEL flow diagram (cont.)
-------
A-46
Figure A-3. ALPHA-M subroutine STDIN flow diagram.
-------
A-47
c
Figure A-4. ALPHA-M subroutine RESIDU flow diagram.
-------
c
START
A-48
Ef>
FLA
N!
\
10R\ YES
O - I/ *
/NO
WRITE 8
1
NO
YES
WRITE 8
1
( RETURN ) ( STOP J
"D (
STOP
Figure A-5. ALPHA-M subroutine DIAG flow diagram.
-------
A-49
C
Figure A-5. ALPHA-M subroutine DIAG flow diagram (cont.)
-------
APPENDIX B
GEN4
-------
B-2
B.1 INTRODUCTION
Program GEN4 was written to provide a means of easily cre-
ating and updating the standard nuclide library. This
reference library may be constructed to contain up to 20
standard spectra (of 256 channels each) for one to four
detector geometries. A standard background spectrum may be
created by submitting to GEN4 a number of background spectra
that are then averaged. Reference spectra may be supplied
to GEN4 with the sample background previously subtracted by
the analyzer, or a standard background may be calculated by
the program and subtracted from all input spectra. In
addition, the library produced by GEN4 contains all data
regarding names, half-lives, counting times, and activities
of the standard nuclides.
Operating in the update mode, the program can replace any
library standard spectrum and its identifying header. Since
it is assumed that such changes will be made to the
background only, there has been included no provision to
modify the appropriate information record (activity, name,
half-life, etc.) for the specified standard.
Printed output from GEN4 includes all information recorded
on the information records as well as tabulated values for
all standard spectra input. The sum of all channels in each
spectrum is also displayed.
To increase the size of the standard nuclide library to more
than 20 nuclides requires that the following variables be
redimensioned: TST, TISOT, HA, and AC. For more than four
detectors, the variables AC and NDN must be dimensioned
accordingly- In addition, program lines 190-210 must have
the value of K adjusted for the desired number of detectors.
Additional lines of code must be added after line 110 to
name the added detectors. Lines 80-110 name the first 4
detectors (detectors A, B, C, and D) . The values 193, 194,
195, and 196 are the integer equivalents for the alphabetic
characters A, B, C, and D on the IBM-370.
To vary the number of data channels in the standard spectra,
variables SPECT, BKGND, and AVBK must be redimensioned. The
DO LOOP indices on lines 270, 330, 370, 510, 560, 1200,
1270, 1300, and 1400 must be changed.
B.2 STANDARD NUCLIDE LIBRARY
The standard nuclide library is a file of unformatted vari-
able-length blocked records containing the title of the
-------
B-3
library; the number of standards and detector sets it
contains; the names, halflives, counting times, and
activities of all standard nuclides; and a descriptive
header and spectrum for all standard nuclides. The format
and organization of this file are described in the following
paragraphs.
B.2.1 Type 1 Record
The first record in the file contains the variables LIP, NS,
and NDETS. LIB is an integer vector of dimension three and
contains a 12-character description, or title, of the
library. The variables NS and NDETS are 4-byte integer
numbers containing, respectively, the number of standards in
a detector-geometry set, and the number of such sets. This
record is 20 bytes in length. Information on this record is
read by ALPHA-M and is included in its printout to serve as
verification that the user has accessed the proper standard
nuclide library (there may be several).
B.2.2 Type 2 Record
This record contains information regarding all library
standards and is written according to the form
(TISOT (I) ,HA(I) ,TST(I) , (AC(I,K) ,K=1,4) , I = 1,NS)
TISOT is a singly dimensioned, double precision variable
that contains the alphanumeric name of each standard
nuclide. The singly dimensioned variables HA and TST
contain the half-lives (in days) of all the nuclides and the
standard counting times (in minutes) , respectively. The
array AC (dimensioned 20 x 4) contains the activities as
counted by each detector. That is, variable AC(4,2) would
contain the activity of standard nuclide number 4 when
counted by detector number 2. If there were three standard
nuclides for each detector set (i.e., NS=3), this second
type of record would appear as
TISOT (1) ,HA(1) ,TST(1) , AC (1 , 1) , AC (1 , 2) , AC (1 , 3) , AC (1 ,4) ,
TISOT(2) ,HA(2) ,TST (2) , AC (2, 1) ,AC(2,2) ,AC(2,3) ,AC(2,4) ,
TISOT (3) ,HA(3) ,TST (3) , AC (3, 1) , AC (3, 2) , AC (3 , 3) , AC (3, 4) .
The information contained on this record is read by ALPHA-M
and is necessary for the analysis of sample spectra. It is
also on the ALPHA-M printout to provide library verification
for the user. Where there are less than four detector sets,
the unused locations will be padded with zeros. Under an
arrangement of 14 standards, the record is 448 bytes long.
-------
B-4
B.2.3 Type 3 Records
After the first two records, the identifying headers and the
spectra for each of the standard nuclides for each detector-
geometry set will follow. Each header record will consist
of an 80-byte alphanumeric description of the nuclide
spectrum immediately following it. The types of information
usually contained on this header record include the name of
the nuclide, its activity, the detector number, and the time
and date on which the standard was counted. This
information is for the benefit of the user; it is not read
in detail by ALPHA-M or any other existing software. Each
sample spectrum resides on a single 1024-byte record
immediately following its respective header. All channel
contents are written as 4-byte real numbers. The type 3
records are organized sequentially according to detector-
geometry sets; that is, all headers and spectra for nuclides
1 through NS of detector set 1 are followed by all headers
and spectra for nuclides 1 through NS of detector set 2,
etc. The last nuclide spectrum in each detector set (that
is, nuclide number NS) is assumed to be the standard
averaged background prepared by GEN4. For a library
containing three detector sets of four standard nuclides
each, the library file would be organized as shown in table
B-1.
The total length of the type 3 records will be
NDETS*(NS*1104) bytes; therefore, with 14 standards and 2
detectors, the length would be 30,912 bytes.
The standard nuclide file should be created with a record
format of VBS, a record length of 1028 bytes, and a
blocksize of 2060 bytes. According to the functions
specified in the program, this file may be used as output
only or as input and output.
-------
B-5
TABLE B-1. STRUCTURE OF STANDARD NUCLIDE FILE
Type 1 Record, Library definition information
Type 2 Record, Standard nuclide information
Header for Std.
Spectrum for Std.
Header for Std.
Nuclide 1,
Nuclide 1,
Nuclide 2,
Spectrum for Std. Nuclide 2,
Detector
Detector
Detector
Detector
Header for Std.
Spectrum for Std.
Header for Std.
Spectrum for Std.
Header for Std.
Spectrum for Std.
Header for Std.
Spectrum for Std.
Nuclide 3, Detector
Nuclide 3, Detector
Nuclide 4, Detector
Nuclide 4, Detector
Nuclide 1, Detector
Nuclide 1, Detector
Nuclide 2, Detector
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
Spectrum for Std. Nuclide 4, Detector 3
Nuclide 2, Detector
Header for Std. Nuclide 3, Detector
Spectrum for Std. Nuclide 3, Detector
Header for Std. Nuclide 4, Detector
Spectrum for Std. Nuclide 4, Detector
Header for Std. Nuclide 1, Detector
Spectrum for Std. Nuclide 1, Detector
Header for Std. Nuclide 2, Detector
Nuclide 2,
Spectrum for Std.
Header for Std.
Detector
Nuclide 3, Detector
Spectrum for Std. Nuclide 3, Detector
Header for Std. Nuclide 4, Detector
-------
B-6
B.3 GEN4 INSTRUCTIONS
GEN4 input instructions are provided in table B-2; GEN4 update
instructions are provided in table B-3.
TABLE B-2. GEN4 INPUT INSTRUCTIONS
(Library Information Card)
Variable
LIB
NS
NDETS
FMT
Columns
1-12
15-19
20-24
30-69
Format
3A4
15
15
10A4
Description
Twelve character identifier for
library type. If the word
"UPDATE" is punched in columns
1-6, however, the remainder of
the card is ignored and all sub-
sequent instructions come from
those described in "Update
Instructions . "
Number of standard nuclides in a
detector set.
Number of detector sets in library.
The format under which the standard
spectra and backgrounds are to
be read.
(Standards Information Cards, Set of NS Cards)
Variable
TISOT
HA
TST
AC
AC
AC
Columns
1-8
9-18
19-28
29-38
39-48
49-b8
Format
A8
F10.0
F10.0
F10.0
F10.0
F10.0
Description
Name of standard nuclide
Half-life (days) of standard
nuclide
Counting time (minutes) for
nuclide
Activity (pCi/unit) for nuclide ,
detector 1
Activity (pCi/unit) for nuclide ,
detector 2
Activity (pCi/unit) for nuclide ,
detector 3
-------
B-7
TABLE B-2 (cont.)
(Standards Information Cards, Cont.)
Variable
AC
Columns
59-66
Format
F10.0
Description
Activity (pCi/unit) for nuclide ,
detector 4
(Background Information Card)
Variable
NBKS
NSUB
Columns
1-5
b-10
Format
15
15
Description
Number of background spectra to
read in and average.
0 = Do not subtract an average
background spectrum from each
standard nuclide spectrum as it
is read in.
1 = Subtract an average background
spectrum from all standards read
in.
(Background Spectrum Cards)
NBKS sets of cards with each set consisting of the following:
1. Background header card - (20A4)
2. Background spectrum punched on as many cards as
necessary according to the format specified on the
library information card.
(Standard Spectra Cards)
NS-1 sets of cards with each set consisting of the following:
1. Standard header card - (20A4)
2. Standard spectrum(i) punched on as many cards as
necessary according to the format specified on the
library information card.
-------
B-8
TABLE B-3. GEN4 UPDATE INSTRUCTIONS
(Update Control Card)
Variable
NDET
NSTD
NBKS
Columns
1-5
6-10
11-15
Format
15
15
15
Description
Number of detector set to be updated.
Number of library standard to be
replaced.
Number of background spectra to
read in and average.
(Format Card)
Variable
FMT
Columns
1-40
Format
10A4
Description
Format under which the background
spectra are to be read.
(Background Header Card)
Variable
NBHEAD
Columns
1-80
Format
20A4
Description
Header
std.
for new background
spectrum
(Background Spectra Cards)
NBKS sets of cards with each set consisting of the following:
1. Background header card - (20A4)
2. Background spectrum, punched on as many cards as
necessary, according to the format specified on
the format card.
Note: For each detector background to be updated, a set of
the above cards must be included.
-------
B-9
B.4 GEN4 PROGRAM
The GENU program is provided in the following computer printout.
-------
B-10
GEN4 PROGRAM
10
31
C
GENERATES STANDARD NUCLIDE SPECTRUM LIBRARY
REAL'S TISOT(20)
DIMENSION HA(20),TST(20),AC(20,4),SPECT(256),BKGNO(256I,FMT(10),
$NAHE(20),NBHEAD(20),L1B(3),AVBK(256!,NDN(41
COHMON/A/TISLiT,HA,TST,AC,SPECT,BKGfiD,FMT,NAHE,NBHEAD,LIB,AVBK
DATA KEY/'UPDAV
WRITEC6, 101)
NDNd ) = 193
NDN(2! 194
NDN(3) - 195
NDN(4) = 196
READI5.100) L1B,NS,NDETS,FMT
IF
-------
B-ll
GEN4 PROGRAM (Cont.)
32
33
C
34
40
C
50
C
100
101
102
103
104
105
106
108
110
112
114
116
117
118
119
DO 33 J=l,256
IF (SPECT(J) .GT.900000.) SPECT(J) SPECTU) - 1000000.
1SPEC T5PEC + SPECTU)
NRITE<6,112) NAME.NDN(K)
WRITE16.116) SPECT
WRITEI6.117) TSPEC
WRITE(9) NAME
KRITE19) SPECT
HRITE(9) NBHEAD
NRITE(9) AVBK
CONTINUE
FORMAT(3A4,T15,2I5,T30,10A4)
FORHAT('1GEN4 - - STANDARD SPECTRUM LIBRARY GENERATION - - RADIDAN
$ALY1ICAL LABORATORY',///)
FORMATCO1,' GEOMETRY LIBRARY TYPE - «,3A4,10X,
$ 'NUMBER OF LIBRARY 5TDS IS ',I2,10X,
i'NUMBER OF DETECTORS 15 «,12)
FORMATC1FGR DETE CTOR ' , A4 , • NUMBER OF BKGND SPECTRA TO BE AVERAGE
$D IS1.13,' BKGND SUBTRACTION FLAG IS',12.//,
$• HEADER TO FILE IS '.20A4)
FORMAT(A8,6F10.2J
FORMAT(/,1X,'NUCLIDE'r4X,'HALF-LIFE(DAYS)1.3Xt
$'CNT-TIME(HINSJ',4X,'ACT-DET-A•,4X,'ACT-DET-B ',4X,
*1ACT-DET-C',4X,'ACT-DET-D',/)
FORMAT(lX,A8.5X,F10.1,7XiF10.5,6X,F10.1.3X,F10.1.3X,F10.1.3X,F10.1
$)
FORHAT(2I5J
FQRMATC20A4I
FORHAT(11',1X,20A4,T100,'DETECTOR'.A4./J
FORKATUOF7.0)
FORMAT(1X,10F12 .1 )
FORMATCOSUM OF CHANNELS IS '.F9.ll
FORMAT(/,/,/,(IX,10F12.1)1
FORHATdHl,1 AVERAGE BACKGROUND FOR DETECTOR',A4,
STOP
END
SUBROUTINE
UPDATE
REAL*8 TISOT(20)
DIMENSION HA(20),TST(20) , AC (20 ,4 } , SPECT { 256 ), BKGND (256 I , FH T( 10 ) ,
$NAKE(20),NBHEADt20),LIB(3J,AVBK(256),NDN(31
COMMON/A /Tl SOT, HA, TST, AC. SPECT.BKGND.FMT .NAME, NBHEAD, LIB, AVBK
DIMENSION NHEAD(20,20,4), SPCTR A (256 ,20 ,41
10
C
URITE(6,150)
READ(9> LIB.NS.NOETS
RE AD (9) (TISOT(I) ,HA( I) ,TST ( 1) , ( AC ( 1 ,K ) ,K =
DC 10 I^l.NDETS
DO 10 J=1,NS
READ19! (NHEAD(K,J,H.K=1 ,20)
READ(9) (SPCTRA(K,J,I ),K=1,256)
REWIND 9
VRITE19) LIB.NS.NDETS
.4).I = 1.NS)
00560
00570
00580
00590
00600
00610
00620
00630
00640
00650
00660
00670
00680
00690
OC700
OC710
C0720
00730
00740
00750
00760
00770
00780
00790
00800
00810
OC820
OC830
00840
00850
00860
00870
00880
00890
00900
00910
00920
00930
00940
00950
00960
00970
00980
00990
01000
01010
01020
01030
01040
01050
01060
01070
C1080
01090
01100
OHIO
01120
01130
01140
01150
-------
B-12
GEN4 PROGRAM (Cont.
C
20
22
C
25
30
C
C
35
40
C
100
101
102
150
151
152
WRITEC9I JTiSOTU 5.HAU J.TSTUJ.CACU ,K8 ,K*1,4J,I=1,N5I
READC5,100,END=35» NDET,NSTD,NBKS,FMT,NBHEAD
MR HE(6,151) NDN(NDETI,NSTD.NBKS,FMT.NBHEAD
DO 22 1=1,256
AVBK(I) 0.0
DO 25 IM,NBK5
READJ5,152! NAME
READJ5.FMT) BKGND
URITE(6,101) BK&ND
DO 25 J = l ,256
AVBMJJ AVBKtJJ + BKGNDUi
XNBKS N8KS
DO 30 1=1,256
AVBK(I) AVBKUI/XNBKS
SPCTRACK.NSTD.NDET) AVBK(I)
WRITE£6,102) NDN(NDET),NSTDtAVBK
GO TO 20
DO 40 I=1,NDETS
DO 40 J=1,NS
WR11E(9> (NHEAD(K,J,I)iK=l,20l
WRITEt9) CSPCTRAtK.J.I),K=1,256J
FORMAT<3I5,10A4,/t20A4}
FORHAT(/,/,/,
-------
B-13
B.5 GEN4 FLOW DIAGRAM
The GENU flow diagram is provided as figure B-1
-------
B-14
C
Rf.AD
SPLCIFIED
i.' or
BKGNOS AND
A V!" ft AGE
Figure B-l.
flow diagram.
-------
APPENDIX C
SIMSPEC
-------
C-2
C.1 INTRODUCTION
The program SIMSPEC was written to simulate mathematically
sample spectra for ALPHA-M analysis. Operating on the
information contained in the standard nuclide library, the
program can generate multinuclide spectra with components at
any specified activity level. The pure composite spectrum
thus obtained may be operated on by channel randomization to
simulate the effects resulting from normal counting
statistics, and by specified degrees of gain and energy
threshold shifting. Input instructions are included.
Each component is generated with a specified nuclide at the
desired activity level by multiplying its standard spectrum
by the ratio of the input (desired) activity to the level of
that standard in the library. Composites are obtained by
combining all required components in an additive manner. If
so directed by program input, the spectrum is then
randomized.
Assuming the availability of a pseudorandom number
generator producing numbers KJ_ in the range 0 to 1.0, an
approximation to normally distributed random numbers J^ may
be generated with the expression
N
j. = £_, ri 2
-
* S + M , (CD
[N/12J
where S and M are the standard deviation and mean of the
desired population, respectively, and N specifies the number
of summations. Applying this operation to the randomization
of the counts in each spectrum channel, we have
Yold , (C2)
Y = Z_,\ i - 2 J *SIGW*
new
[H/M]*
where Yold and Ynew are the contents of a specified channel
before and after randomization. The quantity (Yold ) ^ will
be recognized as the estimate of a one standard deviation
error as produced by Poisson counting statistics. The use
of the SIGW value, which controls the randomization process,
is explained in the SIMSPEC input instructions.
-------
C-3
The pseudorandom number generator used to produce the values
x. is the subroutine RANDU, written in Fortran and supplied
in the IBM Scientific Subroutine Package, Version 3. This
subroutine uses the congruence technique for random number
generation. For more information on generation and testing,
see Abramowitz and Stegun, Handbook of Mathematical
Functions, U.S. Department of Commerce, National Bureau of
Standards, Applied Mathematics Series 55, 1968, R. W.
Hamming, Numerical Methods for Scientists and Engineers,
McGraw-Hill, New York, 1962; or Random Number Generation
and Testing, IBM manual C20-3011.
The desired gain and threshold shifts are produced in the
output spectrum by using Schonfeld's subroutine SHIFT. The
gain of the spectrum may be altered by input variable F, the
ratio of the measured gain divided by the desired gain.
Threshold shifts are normally affected by the input variable
SHC, which is the number of channels (or usually, fractions
of a channel) by which the spectrum must be shifted. The
energy threshold of the reference spectrum is expressed in
input variable SH. This variable may be used to match a
desired calibration between the reference and sample
spectra. As shown in an earlier section of this report, no
exact determination of the energy threshold shift may be
made easily; hence, this SH value should be set equal to 0.0
except for experimental purposes. A more detailed
discussion of the uses of these input variables may be found
in SHIFT-M, A Computer Program for Shifting Gamma-Ray
Spectra in Gain and Threshold by Linear Interpolation, an
addition and revision to ORNL-3975, E. Schonfeld, 1966.
If randomization is requested, SIMSPEC will produce
descriptive statistics of the body of random variates used
to randomize the composite spectrum. These statistical
tests are useful only for evaluating the randomizing
process. In addition, the unrandomized spectra, randomized
spectra, and the random variates may be, upon request,
passed to an intermediate dataset for subsequent data
processing. The program ANALYZE was used for this purpose,
but is not included in this report. It is available from
the authors as an object deck for the IBM Systems 360-370.
ANALYZE is a nonstandard program that might not run in
installations having other than IBM equipment.
C. 2 SIMSPEC FILE UTILIZATION
C.2.1 Standard Nuclide Library
An input file always required. Refer to documentation
regarding program GEN4.
-------
C-4
C.2.2 Auxiliary Output File
An output file is required if SIMSPEC input
variable IRX is greater than zero and if randomization is
requested (SIGW # 0). If this option is selected, a binary
unformatted record is written on Fortran logical unit IRX at
the end of each sample spectrum generation cycle. The
record contains the variables XIDT, R, YC, and SPEC, where
XIDT is the sample identification (8 bytes, alphanumeric),
and R, YC, and SPEC are vectors (each output as 256
locations) containing, respectively, the vector of random
variates, the shifted randomized spectrum, and the original
composite generated by SIMSPEC. The file consisting of
these records is equivalent to its counterpart in program
ALPHA-M, and the same DCB and storage considerations apply.
C.2.3 Primary Output File
A required file containing all SIMSPEC generation output and
intended for input to program ALPHA-M, the file consists of
variable-length, blocked records formatted as card images
and described with a DCB=(RECFM=FB,LRECL=80,BLKSIZE=800).
With this structure, approximately 140 records may be
written onto each 3330-type track. An ALPHA-M run
containing 10 samples with one analysis option each,
assuming 26 card images for each sample and the background
spectrum, will require 319 records.
C.3 JOB CONTROL LANGUAGE REQUIREMENTS
In the course of this study, an instream Job Control
Language procedure (called SIMALPH) was used to allocate
required datasets and execute the programs in the proper
order. A general description of these procedures should
serve to illustrate the requirements of the software used.
It is assumed that the reader is familiar with the usage and
syntax of IBM OS Job Control Language.
SIMALPH consists of four steps (figure C-1). The first,
SIM, executes the program SIMSPEC. SIMSPEC receives its
input instructions from the card reader (FTJ05F001) , uses
information contained in the standard nuclide library
(FT02F001), and writes input instructions and generated
samples onto a temporary dataset (FT03F001, DSN=XFER) for
ALPHA-M to receive. Simultaneously, SIMSPEC creates another
temporary dataset (FT04F001, DSN=RESID) containing the
residuals between the pure and randomized spectra generated,
for processing by program ANALYZE.
-------
C-5
[
CARD
INPUT
o
SIMSPEC
TEMPO
RARY
STORAGE
I)
i
PRINTED
OUTPUT
0
ALPHA-M
TO
DATA
BASE
ANALYTICAL
RESULTS
/LIBRARY//
DARD 11
^SPECTRA \\
A
PRINT
PLOTS
TEMPO- //
RARY
^ STORAGE'
ANALYZE
PRINT
PLOTS
TEMPO
RARY
STORAGE
\
f
ANALYZE
^
f
PRINT
PLOTS
^*
0
0
Figure C-1. Program-file dependency in SIMALPH.
-------
C-6
In step two, ANALYZE is executed to evaluate the residuals
passed to it, and, when finished, to delete this temporary
dataset. The program's output consists of print-plots that
are produced on a printer dataset.
ALPHA-M is executed in step three. The program receives
input instructions and samples via dataset XFER (FT05F001)
that is then deleted, uses information contained in the
standards library (FT03F0J01) , produces analytical results on
one printer dataset (FT06F001), print-plots on another
(FT09F001), creates temporary storage for residuals
(FT04F001), and outputs analytical data (FTJ02F0J01) for entry
into a data base. In this step, Fortran logical unit 2
(analytical results to data base) is defined as a temporary
dataset. For a production application, this disposition
would be defined as (MOD,KEEP) for continuous addition of
data.
In step four, the program ANALYZE is again executed to
evaluate the residuals produced by ALPHA-M. The output from
ANALYZE is again produced on a printer dataset and, at
termination, the temporary storage (FT02F001, DSN=RESID)
passed from step 3 (ALPHA) is deleted.
The DDnames used in this procedure are contingent upon the
following input instructions being supplied to the programs
involved. For SIMSPEC, IRX must be set equal to 4. For
ALPHA-M, NTS=3, NTM=5, IAUX=4, and IOPT=2. The use and
application of Fortran logical units 2 and 3 in SIMSPEC,
unit 9 in ALPHA-M, and unit 2 in ANALYZE, are internally
fixed. The standard definitions of units 5 and 6 for card
reader and line printer are employed in all programs.
-------
C-7
C.4 SIMSPEC INPUT INSTRUCTIONS
SIMSPEC input instructions are provided in table C-1
TABLE C-1. SIMSPEC INPUT INSTRUCTIONS
(General Control Cards - 3110)
Variable
IX
IRX
IRAEGE
IWRITE
Columns
1-10
1 1-20
21-30
31-40
Format
110
no
no
no
Description
Seed integer for randomization,
must be one to nine digits, odd.
If IRX greater than zero, residuals
will be output on Fortran logical
unit IRX.
Number of terms over whicii randomi-
zation will be summed, see text.
0 = For no print- plot of spectra
1 = To print-plot spectra
(ALPHA-M General Control Card)
Refer to table 1.
(ALPHA-M Sample Control Card)
Refer to table 1.
-------
TABLE C-l (cont.)
C-f
(Background Information Cards)
Only if ALPHA-rt variable NBR is greater than zero.
1. Background title card,, format (20A4)
2. Background component card, format (12,7X,I1,115,
F10.0) with the following information:
Variable
NBK
NDT
XPCI
Columns
1-2
10
15-24
Format
12
11
F10.0
Description
The library number of the library
standard spectrum to use for the
background.
The number of the detector set in
which the desired spectrum resides.
The number of pCi/unit activity
desired for the background.
(Sample Information Cards)
1. Sample title card, format (20A4)
2. Sample component cards, format (12,(T9,I2,T20,I1,T30,
F10.0)) with the following information:
Variable
NO
NSTD
NDET
PCI
Columns
1-2
9-10
20
30-39
Format
12
12
11
F10.0
Description
The number of components which are
to comprise the generated spectrum.
This variable appears only on the
first of the NO sample component
cards, the subsequent NO- 1 cards
should contain blanks in columns
1-2.
The number of the library standard
to be used for component i«
The number of the detector set in
which the desired standard resides.
The desired activity level for
component i.
-------
C-9
TABLE C-l (cont.)
(Shifting and Randomization Control Card, Format (4F10.0)
Variable
F
SH
SHC
SIGW
Columns
1-10
11-20
21-30
31-40
Format
F10.0
F10.0
F10.0
F10.0
Description
Gain factor (gain actual/gain desired)
Reference threshold channel (nor-
mally zero; used if it is desired
to adjust the spectrum to a
specific calibration) .
Energy threshold shift to apply;
number of channels or fractions
of a channel by which the spec-
trum will be shifted.
0 = For no randomization
1.0 = For randomization as illus-
trated in the text; intermediate
values will have the effect of
changing the magnitude of the
std. dev. of the distribution.
(ALPHA-M Option Card)
Same as in ALPHA-M (refer to table 1) as many cards specified
by NOPT on ALPHA-M sample control card.
-------
C-10
C.5 SIMSPEC PROGRAM
The SIMSPEC program is provided in the following computer
printout.
-------
C-ll
SIMSPEC PROGRAM
10
c
c
c
20
> £ S 0 & t
...SIKSPEC...
PROGRAM TO SIMULATE COMPOSITE, RANDOMIZED, SHIFTED GAMMA-RAY
SPECTRA AND PREPARE INPUT FOR PROGRAM ALPHA-M.
TENNESSEE VALLEY AUTHORITY, RADIOLOGICAL HYGIENE BRANCH, 1976
INTEGER FM,TNAME
PE4L*8 XIDT.T1SOT
DIMENSION L1<3),TISLT(22),HA(22),TST(22),AC(22,4),IS(22),PCI<22),
$TNAf.E(2C),S(20,256,4),FM(8)fSPECT(267),PCT(22),KSTD(22),NDET(22>,
$YC(257),6M257),XFRQf20),R(256),5PEC(257),X(20),PROE(20),
$GFREG(20 )
DATA SPECT/267*0 .O/, J/0/
READ INPUT INSTRUCTIONS
READ(5,300) I X,IRX , I RANGE,IWR ITE
WRITE (6,310) IX,IRX,IRANGE,1WRITE
XFACT IRANGE/2.0
DIV = SORTIFLOAT(I RANGE)/12 .0 )
FEAD DISK DETECTOR STANDARDS LIbRARY INFORMATION
REAl'(2) L1.L2.L3
WRITE(6,100) L1.L2.L3
RFAD(2) (TISCT(!),HA(I),TST(I),(AC(I,K)fK=lI4),I=l,L2)
KR ITE(6, 110 )
k'R ITE ( 6, 120) (TISOTII),HA(I),TST(1),(AC(I,K),K = 1,4),I=1,L2)
DO 10 K=1,L3
DO 10 1=1,L2
READ(2) TNAME
READ(2) (SI I,J.K),J=l,256 )
NS L2
NDETS L3
READ GENERAL CONTROL CARD
IOPT.FH
IOPT.FM
IGPT , FH
READ GENERAL ONTRL R
READ(5,130) M.N'IT.NBA.NZ.MF.NTS.NTM.MU.NH.IAUX.
t>RI IE (fe, 1AO 1N.NIT, NBA, NZ,MF,:aS , NTH.MU.NH, I AUX .
WRITE (3,130 )M, NIT, NBA, NZ.KF , NTS ,,NTM,MU,MH , I AUX ,
DO 50 K=l,50
READ SAMPLE CONTROL CARD
PEAD(5,150,END=900) XlDT.NOPT.NPP. ,NBS,IAtP,MS,TB,TSA,VRED,DAY,VK
V,RITE(6,160) K,XIDT,rOPT,NBR,N5S,IABP,HS,TE,TSA,V.RED,DAY,VM
WRirE(3,150) XIOT,NOPT,NPR,N3S,IABP,MS,Tt,TSA,VRED,DAY,VH
IF (NbR) 30,30,20
IF SPECIFIED, READ BACKGROUND HEADER AND COMPONENT
READI5.170) TNAME
WRITE(6,180) TNAME
WRITE (3, 170 > TNAME
F, E AD (5,190 J NBK,NDT,XPCI
XPCT XPC I /(AC (NBK ,NDT)/VRED)
WR1TE16.210) XPCI.NBK.NDT
00000020
00000030
00000040
00000050
00000060
00000070
00000090
OC000100
00000110
00000120
00000130
OOC00140
00000150
00000160
00000170
00000180
00000190
00000200
00000210
00000220
00000230
00000240
00000250
00000260
00000270
OCC00280
00000290
00000300
00000310
00000320
00000330
00000340
00000350
00000360
00000370
00000380
00000390
00000400
00000410
00000420
00000430
00000440
00000450
00000460
00000470
00000480
00000490
00000500
00000510
00000520
00000530
00000540
00000550
00000560
00000570
00000580
00000590
00000600
-------
C-12
SIMSPEC PROGRAM (Cont.)
25
C
C
C
30
34
35
C
C
C
41
42
C
C
C
43
C
44
C
C
C
45
C
C
C
DD 25 J=l,256
FKU) SJNBK, J.NDT )»XPCT
WRITE(fc,200) (BK(N),N=1t256)
WRUEO.FM) (BK(N),N = 1,256)
WRITE(6,220)
READ SAMPLE HEADER, COMPONENTS, AND SHIFTING INFORMATION
PEAKS,170) TNAME
kRITE<3,170) TfVAHE
VRITE(6,1BO) TNAHE
RE AD(5 ,230) NO,(NSTD
-------
C-13
SIMSPEC PROGRAM (Cont.)
c
144
C
C
C
145
.'+6
48
47
C
C
C
50
C
c
c*»*
c
90
100
no
120
130
140
150
160
170
160
190
XRSUM = 0.0
XSOSUM = 0.0
SUHI 0.
SUKT = 0 .
SIG1 = 0.
S1G2 = 0 .
SIG3 = 0.
DESCRIPTIVE STATISTICS OF THE BODY OF VARIATES
IF (51GW) 145,50,145
DO 46 1=1,256
XRSUM - XR5UH •» Rtl)
XSCSUH XSQ5UM + R t I )«R t I )
XCBSUM XCBSUM + R 1 I ) *R ( I ) »R ( I )
X4TH - X4TH + R 1 I ) »R (I ) *K (II *R ( I )
XNO = 256.
RAVG XRSUM/XNO
RSI& = SQKT«l./(XNO-l.))*(XSQ5UM-l{XRSUM**2)/XNOM)
DO 48 1=1,256
SUMI SUMI + t (R ( I 1-RAVG 1/RSIG I»*3
SUMT SUMT + ( ( Rt I 1-RAVG )/RSIG)»«4
RSKEW = SUMI/XNO
RKUkT SUMT/XNO
DL! 47 I = 1 ,256
IF«R< I) ,LE.(3.*RSIG)) .AND .(P (I ) .GE . ( - 3 . *R 5 1G ) ) J SIG3 SIG3 +1
1FURU ) ,LE.(2.*RSIGM .AI^D.CMl ) .GE.(-2.*RS1G))) SIG2 SIG2 +1
IFl (R1I) .LE.d ,*RSIG) ) .At.D.IRU ) .GE.(-1.*RSIG> )) SIG1 SIG1 +1
SIG3 - (5IG3/256. J*100.
SIG2 (SIG2/256.)»100.
SIG1 (SIG1/256. 1*100.
HRITE(6,901 RAVG,RSIG,RSKEVi,RKURT,SIGl,SlG2,SIG3
lF(IRX.&T.O]WRITE(IRX)XIDT,J,R,(YCtI),I=l,256),(SPECm,I = l,256)
CONTINUE
FORMAT STATEMENTS
»4(,»»*<.**«:t**<.<:»4<.*»»**»**«»*«<.*6i>4*»«*4e6****«fr«*«t*»**t«*****
FORhATf/,' STATISTICS FOR VARIATES',/,
$• AVERAGE =',F7.4,5X, 'STO. DfV. = ' , F7 .4 , 5X , 'S K E WN ES S =',F7.4,
$5X, 'K URTOSIS =',F9.4,/,1 PERCENTAGE WITHIN 1 SIGMA = • , F6 .2 ,
$5X,'2 SIGMA = • ,F6 .2 ,5X, '3 SIGMA =',F6.2)
FDRS'ATI//,' INSTRUCTED TD USfc FILE FOR GEOMETRY TYPE *,3A4,
$IOX, 'CONTAINING ',12,' STANDARDS FL'R ',11,' DETECTORS')
FORhATI/ax.'NUCLIDE'.^X.'HALF-LIFEtDAYSJ'.SX.'CNT-TlKEIMlNS)',
$3X,IACT-OET-A(,4X,'ACT-DET-B',4X,'ACT-DET-C1,4X,'ACT-DET-D',/)
FOR*J,AT(1X,A8,5X,F10.1,7X,F10.5,6X,F10.1,3X,F10.1,3X,F10.1,
$3X,F1C .1 )
FORI-AT (1114 ,8A4)
FfRhATI/,1 GENERAL CONTROL CARD • ,/ ,11 I 5 ,2X , 8A4 )
FORMAT (A8,5 13 ,5F9 .4)
FQRI-.ATUH1, 'SAMPLE NUMBER •,\2,/,t SAMPLE CONTROL CARD',
$/,lX,A8,513,5F9.4,/J
FURMAT(20A4)
FORKAT (1X.20A4,/)
FORMAT(I2,7X,I1,T15,F10.0)
00001210
00001220
00001230
00001240
00001250
00001260
00001270
00001280
00001290
00001300
00001310
00001320
00001330
00001340
00001350
00001360
00001370
00001380
00001390
00001400
00001410
00001420
00001430
00001440
00001450
00001460
00001470
00001480
00001490
00001500
00001510
00001520
00001530
00001540
00001550
00001560
00001570
00001580
00001590
00001595
00001597
00001598
00001600
00001610
00001620
00001630
00001640
00001650
00001660
00001670
OC001680
00001690
00001700
00001710
00001720
00001730
00001740
00001750
00001760
00001770
-------
C-14
SIMSPEC PROGRAM (Cont.)
,F8.1,» PCI/UNIT Of STANDARD',13,
FOR
40
50
60
100
99
PCI/UNIT OF
200 FORrfATUX,10F12 .1J
210 FORK ATI" BACKGROUND
$OR ',12,/)
220 FORPAT(lHl)
230 FQRKAT(I2,(T9,I2,T20,I1,T30,F10.0))
240 FORKATI' SAMPLE WILL CONSIST OF :',/,(IX ,F8
$D • , 13 , • FDR DETECTOR' ,12)1
250 FORHATffcI3.3F6.2,(2212))
260 FDRl-.ATf/,' UPTIDN CARD • , 6 1 4 , 3 F6 .2 , ( 22 I 3 ) J
270 FORMAT (4F10 .0 )
280 FORK AT(/," GAIN SHIFT RATIO IS',F7.4,' THRESHOLD CHANNEL IS
4F4.0,1 THRESHOLD SHIFT IS •,?!.<*,' RAND FLAG IS «,F3.1)
300 FGRKAT(8I10)
310 FCRKAT (IX,131('*'),/,
$40X, 'SIM5PEC - DATA GENERATION - RADIOANALYTICAL LABORATORY',/
$1X,131 ('*•),/,
$' SEED FDR RANDOM NUMBER GENERATOR IS",110,
$5X, 'RESIDUAL OUTPUT FLAG IS',I3,5X,
t'RAf.GE FOR SERIES IS',14,' IKRITE= ',12}
900 STOP
END
SUBROUTINE SHIFT (Y , YC , F,SH ,SHC ,MX I
c
c
c
E.
5CHCENFIELD, 1966
DIKENS
3
41
45
TE
JT
MX
DO
01
DO
Z
CJ
IF
IF
YC
ION Y1267),
SH
60
40
= J
( t
( J
(I )
1
F
I
F
1
-
I
J
-
1
» ( F-l .0)
* 1256+SHC
=1,256
=JT ,256
* (Z+SHC)
QJ) 41,45,
) 45,45,50
YU)
YCI257)
1 +
+ TE
40
TE
YT J
GO TO 60
CONTINUE
GO TO 60
YC(I) (Y(J)-Y(J-l I )/F
YC(1 ) Y(J-1 ) + YCt I ) *
YC(1) YCII)/F
JT = J
CONTINUE
Ycm i.o
WRITE (6,100) MX
FOR!.ATI • DATA MEANINGLESS
RETURN
END
SUBROUTINE PLOT (K , A,B )
PLOT OF TWO FUNCTIONS, A CALC'D, B ODS'D, K SAMPLE NO.
DIMENSION A(257),B(257!,LINE(101)
INTEGER NBLNK/' '/ ,NPLUS/ ' + ' / ,NSTAR/ • * •/
KRITE (6 ,99 J K
FORMAT!1H1,30X , 'PLOT OF PURE COMPOSITE, AND SHIFTED/RANDOMIZED
$CTRA, SAMPLE NUMBER•,13,//,' Ch BEFORE AFTER*)
II-QJ+F)
AFTER CHANNEL'
00001780
DETECT00001790
00001800
00001810
00001820
STANDAR00001830
00001840
00001850
00001860
00001870
, 00001880
00001890
00001900
00001910
00001920
00001930
00001940
00001950
00001960
00001970
00001980
00001990
00002000
00002010
00002020
00002030
00002040
00002050
00002060
00002070
00002080
00002090
00002100
00002110
00002120
00002130
00002140
00002150
00002160
00002170
00002180
00002190
00002200
00002210
00002220
00002230
00002240
00002250
00002260
00002270
00002280
00002290
00002300
00002310
OG002320
00002330
00002340
00002350
SPE00002360
00002370
-------
C-15
SIMSPEC PROGRAM (Cont.)
XMAX
XMIN =
-1.0E20
1 .OE20
XMAX
XMAX
XK IN
XMIN
= Adi
» 1
DC 10 1=10,200
IF (A ( I ) .GT .XMAX
IF (B( I ) .GT .XMAX
IF (Ad ) .LT .XMIN
10 IF (B ( I ) .LT.XM IN
RANGE XHAX-XMIN
XINC - RANGE /100.
DU 20 1=10,200
PO 15 J 1,101
15 LINE(J) NBLNK
NPCS (At I)-XMIN)/XINC
LINE(NPGS) = NPLUS
KPOS t&d J-XM1N J/X1NC
LINE (NPDS) = NSTAR
20 V.R 1TE 16, 100 ) 1 ,A ( I ) , B ( I )
100 FCRt'AT(I4,2FS.l ,103AI)
RETURN
END
SUBROUTINE RANDU(I X,IY,YFL )
C FROM SSP/360 V .3
IY IX * 65539
IF (IY) 5,6,6
5 IY IY + 2147433647 + 1
6 YFL IY
YFL = YFL * .4656613E-9
RETURN
END
NSTAR, LINE, NSTAR
00002380
00002390
00002400
00002410
00002420
00002430
00002440
00002450
00002460
00002470
00002480
C0002490
00002500
00002510
00002520
00002530
00002540
00002550
00002560
00002570
00002580
00002590
00002600
00002610
00002620
00002630
00002640
00002650
00002660
-------
C-16
C.6 SIMSPEC FLOW DIAGRAM
The SIMSPEC flow diagram is provided as figure C-2.
-------
C-17
f START J
\
F
READ
ALPHA-M
SAMPLE
CONTROL
CARD
NO
PRINT
CARD
AND WRITE
TO DISK
YES
PRINT-PLOT
PURE AND
SHIFTED
SPECTRA
YES
YES
Figure C-2. SIMSPEC flow diagram.
-------
APPENDIX D
TEST DATA
-------
D-2
This appendix contains a set of standard spectra for 13
radionuclides (table D-1). These spectra have been stripped
of background using a multichannel analyzer. To test
ALPHA-M, a standard library can be created from these
spectra with GEN4 (table D-2). A background spectrum is
included (table D-3).
In addition, two sets of known 3.5-liter water data with the
ALPHA-M analysis results also are included. These ALPHA-M
analyses were run with the following processing options:
DATA FORMAT 10F7.0
CHANNELS 256
ITERATIONS 5
INITIAL CHANNEL 10
FINAL CHANNEL 181
BKG COUNTING TIME (MINS) 66.67
SAMPLE COUNTING TIME (MINS) 66.67
DECAY TIME 0.0
VOLUME REDUCTION FACTOR 3.5
VOLUME MULTIPLICATION FACTOR 1.0
BKG COMPENSATED AS A LIBRARY STANDARD
WEIGHTS BASED ON RECIPROCAL COUNTS/CHANNEL
AUTOMATIC GAIN & THRESHOLD SHIFT
FULL LIBRARY
NO REJECTION
If these known spectra are run versus the enclosed standard
spectra, results similar to those included here should be
obtained. The results will not be identical since different
processing equipment may have different word size, etc.
-------
D-3
TABLE D-l. LIBRARY STANDARDS
(Geometry Type 3.5 Water)
Nuclide
144Ce
sicr
131J
106Ru
58CO
13*CS
137CS
9SZr
54Mn
65Zn
6°CO
4 0K
l*°Ba
Background
Half-Life
(d)
285.0
27.7
8. 1
365.0
71.3
767.0
11100.0
65.0
313.0
245.0
1920.0
999999.0
12.8
999999.0
Count Time
(toin)
66. 6666
66.6666
66.6666
66.6666
66.6666
66.6666
b6.6666
66.6666
66.6666
66, 6666
66.6666
66.6666
66.6666
66.6666
Total Activity
(pci)
47396.5
20677.0
3941.8
17923.9
5742.4
9616.5
16080.0
12636.9
14366.0
16344. 6
15250.0
1 1 1452.0
71167. 0
350.0
-------
D-4
TABLE D-2. LIBRARY SPECTRA
Average Background 3.5 Liter Std. Crystal (A) 4/2/75 Stripped
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
0
590
711
577
387
377
303
189
156
140
117
103
87
101
63
48
55
34
28
27
36
20
17
20
16
14
0
595
689
585
368
373
294
176
159
141
115
99
81
100
64
50
55
34
26
28
34
20
17
19
13
13
0
619
681
554
356
382
274
184
159
132
120
99
82
108
59
49
57
33
27
29
33
21
19
19
15
13
12
657
669
524
348
344
248
177
154
129
123
95
80
111
56
52
54
30
25
29
31
16
19
18
13
10
0
701
693
517
354
313
231
176
156
125
122
93
84
107
56
51
51
31
24
33
29
19
17
17
14
12
0
729
706
538
344
278
203
174
151
123
118
94
81
106
51
51
45
30
27
31
27
18
17
16
13
12
0
724
658
556
340
275
195
177
152
115
123
93
82
103
49
52
42
26
25
31
24
18
18
18
13
275
717
611
507
346
283
193
165
148
119
113
89
84
92
49
57
41
29
28
38
23
19
20
18
12
597
713
589
467
352
292
192
165
141
116
113
91
91
81
54
61
39
28
27
35
19
17
16
16
14
594
707
592
405
353
298
184
166
139
115
105
85
94
74
47
57
38
26
29
37
21
19
17
16
12
Ba-La-140 3.5 Liter Std. Crystal (A) 4/2/75 @ 1400 Stripped
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
0
31177
43824
31942
17229
51917
8554
6879
18897
8509
4351
4676
5083
2959
473b
16464
1460
1337
1052
1264
481
395
748
490
15
16
0
35337
41694
33432
17o8b
46600
8099
7232
17362
7878
4386
4670
4'J5o
2702
6298
1271^
1518
131:,
10b3
1272
464
456
758
397
7
1
18
37545
4G326
37065
168u9
37722
7972
8071
15296
6760
4700
47o2
4872
2500
8^35
9290
1532
1210
1001
1239
43o
416
813
338
4
1
19
39402
39olu
42o02
21Clj
32o4<3
7640
8675
12280
5780
4755
4732
4674
2402
11535
6319
1550
1141
980
1224
408
422
842
248
7
7
28
41129
39072
47284
22894
31908
7571
y335
10390
4867
4910
4799
4597
23^7
14727
4137
1518
1203
1019
1053
387
449
835
172
7
13
24
42592
37990
44556
23429
29717
7395
10162
9473
4464
4974
4849
4328
2348
18340
2334
1400
1202
1001
987
352
469
835
121
1
13
25
45478
36799
34541
24292
23911
7249
11202
8814
4127
5032
4976
4050
2371
21068
2061
1433
1260
1032
834
351
470
111
57
9
3168
53657
35188
24420
28690
16682
6981
13400
9123
4311
4897
4809
3798
2621
22339
1^77
1463
1232
1101
723
366
552
730
46
2
23713
55941
329t>3
19030
38499
11770
6572
16099
9183
4213
4953
5055
3492
2936
21725
1533
1482
1164
1206
621 545
376
635
690
42
4
27223
47798
31915
17491
48156
93Q4
6652
18346
9151
41c8
4C27
5104
3215
3653
19590
1491
1398
1093
1269
433
655
587
-T
/
11
-------
D-5
TABLE D-2 (cont.)
Ce-144 3.5 Liter Std. Crystal
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
4000
9591
1082
688
393
278
327
679
97
25
29
62
45
56
63
33
55
39
17
34
70
999997
3
7
1
2
0
8714
1046
617
388
323
314
448
68
97
73
63
34
25
28
39
43
7
8
44
46
4
6
999996
999999
0
0
8069
976
630
307
276
241
325
69
47
26
29
49
26
36
65
47
24
4
65
39
999998
1
999997
3
0
(A) 3/28/75 @ 1130 Stripped
1
12016
982
544
329
215
247
190
17
57
45
72
50
49
51
34
60
39
33
85
14
999999
999997
999989
6
999996
1
25719
898
547
304
199
276
88
76
74
78
43
12
56
36
54
50
23
16
80
21
999991
990997
7
0
2
1
71239
891
544
279
187
388
72
38
85
67
29
36
62
19
59
24
16
9
90
1
4
909903
999999
9
999999
0
5162
836
519
314
157
476
82
71
55
62
56
48
57
26
54
32
17
18
99
3
0
5
999994
999997
4039
1342
845
561
313
165
683
1 10
82
43
90
29
55
87
22
50
23
15
5
91
6
1
10
2
5
°537
1 143
674
525
784
2A\
720
67
°3
25
74
43
46
68
17
64
23
9
25
78
18
5
999992
999998
999996
"317
1093
69=3
359
293
229
807
75
93
66
66
33
53
81
21
65
24
12
20
79
7
1
999994
990997
8
Co-58 3.5 Liter Std. Crystal (A) 3/21/75 @ 1525
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
4000
1639
2363
1708
1109
2360
645
389
5131
74
63
103
27
50
13
29
999998
999992
999999
2
0
9
999999
1
6
7
1
1707
2616
1711
1 132
2922
592
417
3962
112
64
101
69
43
24
999996
999992
0
999998
999999
5
0
999994
2
999994
999995
0
7045
2575
1585
1075
3247
666
499
2608
1 19
51
110
66
13
10
&
999998
999984
9
4
10
999992
8
4
2
999994
999909
2382
2661
1528
1089
2941
537
604
1372
35
69
78
1 11
32
999984
22
7
16
18
999999
20
999991
3
999999
1 1
4
0
2281
2399
1388
1 129
2136
442
954
683
97
73
59
156
24
7
0
4
3
2
999998
999983
5
1
8
0
2
0
2062
2314
1418
1 176
1463
480
1527
322
78
71
78
164
33
11
23
999992
999996
999992
13
8
999997
5
999994
1
999996
1
1903
2117
1255
10^7
1067
513
2528
153
101
69
67
174
999980
19
999999
999997
999992
4
12
6
999994
6
999996
999998
648
2107
2075
1249
1 100
815
436
3742
1 16
100
52
33
143
6
22
2
999987
4
999999
17
8
8
8
999992
999996
1303
2129
1920
1 194
1351
330
406
4926
87
110
106
21
1C6
999991
999995
26
13
999985
1
999986
3
1
5
999994
999997
1509
2172
1742
1239
163°
716
434
5535
90
85
135
38
103
999991
3
6
999997
14
3
999995
999995
999994
999994
999997
5
-------
D-6
TABLE D-2 (cont.)
Co-60
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
3.5 Liter Std. Crystal (A) 3/17/75 @ 1034
4000
3767
5213
5244
3453
2979
2533
2520
2599
2492
1783
8512
2744
2121
283
280
163
136
141
115
129
84
83
269
5
12
1
4139
5392
4839
3213
3088
2437
2462
2574
2276
1888
9160
3577
1337
286
239
178
152
128
138
135
81
99
207
0
5
0
431 1
5775
4599
3048
3076
2467
2459
2705
2250
1809
9027
4973
820
298
205
157
153
106
106
119
74
136
198
999999
11
0
4889
6321
4288
2988
2953
2583
2619
2651
2123
1914
7735
6482
513
305
217
134
130
127
114
148
64
157
175
1
999998
1
5248
6769
4166
2963
2926
2401
2598
2647
2096
1994
5883
7236
338
293
231
192
141
136
101
133
53
193
99
999996
11
0
5270
6674
3954
2878
2614
2330
2735
2676
1895
2269
4274
7533
370
267
188
144
129
119
143
115
47
244
77
999998
1
2
5366
6432
3724
2864
2512
2423
2747
2654
1943
3262
2782
7122
343
282
207
159
145
122
156
101
44
262
26
5
1166
5261
6014
3722
2889
2461
2336
2640
2625
1978
4061
1975
6341
336
262
173
136
135
125
125
91
60
250
44
1
3171
5282
5834
3476
2799
2415
2426
2649
2469
1869
5573
1770
4709
309
278
147
160
145
114
120
106
54
295
21
999992
3463
5303
5309
3456
2730
2550
2381
2529
2495
1774
7137
1931
3373
290
285
137
159
112
123
113
88
59
280
11
1
Cr-51 3.5 Liter Std. Crystal (A) 4/1/75 @ 1200 Stripped
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
0
813
888
899
118
35
72
99999b
6
21
999992
999901
20
19
9 7
15
4
999998
999998
999999
7
999995
0
99999G
999996
2
0
849
876
1646
6
18
15
35
24
999992
13
21
9
14
999992
5
999992
20
999991
1
13
0
999995
999997
999993
6
1
915
779
3330
15
999971
60
999988
10
7
12
999995
999992
32
999996
1
999999
10
999998
3
999987
1
999999
3
999984
999994
1
927
714
4817
999987
6
34
33
999972
999975
999998
6
13
999995
8
999997
23
999985
7
999998
3
999996
999996
999964
5
999996
0
1019
638
4740
4
49
2
14
33
999995
1
999983
4
999995
11
999992
0
1327
572
2786
10
22
9
20
11
21
25
10
9
21
999995
999980
11 999993
999991
999994
999997
13
999998
6
1
999998
6
999994
4
999983
999997
999997
3
9
999989
999997
0
1574
584
959
46
19
999975
999998
999997
3
999989
19
14
999980
0
999996
1
999995
1
999991
5
6
999988
1
2
34
1550
639
230
30
999953
30
999986
26
14 10
17
999966
9
20
5
18
7
999991
2
999992
999996
999993
999998
999996
7
616
1276
613
68
29
999989
999986
26
6
999992
12
999991
999996
999992
20
7
999987
999999
999996
4
999997
999992
9D9997
999989
999990
717
1056
791
999983
27
3
999990
999985
999993
11
2
5
999988
16
999999
999996
4
999991
999994
4
2
2
0
-------
D-7
TABLE D-2 (corvt. )
Mn-54
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
3.5 Liter
4000
2682
4198
3329
2261
2141
1879
778
12222
999979
999971
999991
999985
999983
28
999997
10
999997
999996
999987
999999
999996
9
999985
999995
999995
Std. Crystal (A) 3/20/75 @ 1021
2
2867
4695
3108
2358
2168
1702
801
14226
999981
999985
999970
999998
999965
8
999984
999991
0
1
6
999992
2
999994
999992
9
1
0
3372
5096
3028
2223
2029
1652
840
14259
12
999978
999983
9
999969
19
6
999975
999997
999998
999993
999988
999992
0
999997
999982
5
3
3571
5257
2914
2279
2112
1426
762
12266
3
999969
999995
999986
999978
999992
999984
5
999995
2
2
99998
-------
D-8
TABLE D-2 (cont.)
Cs-137 3.5 Liter Std. Crystal (A) 3/19/75 @ 1409
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
4000
2938
5031
3282
2433
1418
1476
2095
999996
17
10
10
999992
29
999997
999984
12
3
5
5
999993
10
2
999999
999995
999987
0
3159
5426
3109
2441
1251
2290
600
30
10
11
3
999984
3
4
999996
6
3
999987
4
999993
999992
0
999995
999996
3
0
3612
5652
3010
2462
1 193
4050
1 17
999983
28
999973
14
5
0
999984
999999
1
999990
3
4
10
999988
999988
999998
999999
999996
1
3814
5017
2730
2456
1200
7293
4
12
999997
999985
1
999991
999978
999999
999979
999992
999997
7
999997
3
6
8
999997
999992
999997
999999
4058
4869
2762
2436
1067
11120
6
999995
7
999985
2
4
23
1
999995
2
2
0
999991
999989
999999
999995
999998
2
999988
0
4072
4263
2592
2355
1072
14640
21
999994
11
999990
15
999982
25
19
20
9
999994
19
999990
999993
999996
11
1
3
3
0
4038
4082
2592
2192
1013
16272
999995
40
36
999993
999995
0
999996
999992
999995
10
13
999990
2
18
999994
999991
999999
10
990
4068
3939
2655
1991
1043
14298
999985
999994
19
19
999991
7
3
9
0
6
1
999993
999979
1 1
7
999997
1
999998
2368
4191
3657
2495
1709
1077
9706
14
999985
41
999992
999989
4
2
999995
999993
11
999990
999991
999995
9
999999
12
999998
999992
2787
4600
3475
2502
1440
1159
5216
999972
32
7
4
10
999987
999993
1
999983
999998
999996
999992
6
0
3
4
999996
3
1-131 3.5 Liter Std. Crystal (A) 3/24/75 @ 1543
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
4000
14^9
7252
1637
3225
404
223
109
52
10
11
0
6
7
12
19
999996
18
999996
7
6
999997
1
3
999996
999999
1
16^3
2028
153<5
1185
449
37.7
221
7
49
33
0
6
15
999975
999992
9
999996
999993
6
999996
999999
999999
3
8
1
1
1660
1847
1 167
343
525
521
203
3
15
999997
12
7
16
999997
11
999093
999993
21
999997
999995
9
1
3
0
999099
1
1314
1629
1 128
157
533
521
195
25
17
8
41
999993
7
1
999998
19
17
999995
999998
999986
1
6
999989
999997
8
0
1881
1373
1270
130
333
510
241
29
7
999994
10
0
4
12
099994
15
12
0
8
1
1
999999
5
3
999997
0
1935
1300
1836
169
180
323
292
19
15
6
0
4
999990
999991
999984
7
13
999989
21
999998
999994
3
5
1
4
0
2264
1239
3752
157
133
222
222
33
999996
47
13
22
999995
999989
999992
999993
15
0
5
999994
8
999995
999996
999989
549
2612
1248
5043
172
139
145
202
31
16
33
19
17
.999990
1
3
999993
11
4
999998
4
7
999995
999905
999997
1432
2556
1332
7072
213
46
112
119
999983
12
22
23
17
999984
5
999984
1
999981
3
16
7
8
9QQ990
999999
3
1302
2376
1532
5903
216
145
105
2
49
49
42
999994
31
999991
0
13
2
999991
10
12
1
3
8
999996
999992
-------
D-9
TABLE D-2 (cont. )
K-40
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
3.5 Liter
4000
2677
7439
2063
1172
1203
867
747
826
81 1
972
982
350
1594
1688
8
3
17
999993
999998
999999
999996
8
2
8
999990
Std. Crystal (A) 3/27/75 @ 1331
0
7651
2446
2149
1223
1280
929
792
777
808
896
923
352
2351
975
999990
0
0
999996
5
3
7
4
1
999998
4
0
2754
2440
1897
1210
1397
919
783
766
839
868
888
346
3193
519
6
999995
16
14
999999
3
4
6
999996
3
999997
0
2791
2469
1803
1 144
1276
818
829
746
867
903
812
342
4032
226
999979
12
6
1
999988
1
4
999997
999994
3
4
0
2733
2717
1804
1158
1 168
862
931
722
889
975
770
358
4877
98
18
999995
999997
13
999980
999985
999997
999990
1
999995
6
0
2793
2796
1609
1128
980
818
962
759
828
929
674
386
5240
51
0
22
999985
999993
4
6
999996
7
999997
0
7
1
2754
2750
1508
1065
891
778
911
730
845
901
585
406
5130
26
9
999995
10
1
13
3
3
999998
1
999996
1161
2693
2629
1402
1 158
838
775
829
741
866
981
527
537
4495
7
999999
999996
14
999990
7
5
999989
6
15
1
2433
2589
2419
1422
1009
846
750
823
731
341
980
472
811
3744
6
999996
999993
6
3
999999
1
2
8
999998
999990
24^3
25 I 5
2225
1329
1072
821
823
730
789
857
977
397
1097
2614
20
999997
qgooog
0
8
099994
999999
4
999996
1
999993
Ru-106 3.5 Liter Std. Crystal (A) 3/20/75 @ 1513
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
no
180
190
200
210
220
230
240
250
4000
7538
3635
1990
1251
4098
1672
221
187
135
277
293
19
7
24
20
15
7
999995
2
999989
999996
12
999994
999999
999989
0
27/17
3644
1895
1253
6165
2319
239
211
114
265
258
999994
14
18
22
7
4
999999
9
999994
999992
999999
999990
18
6
0
2994
3457
1965
1221
7350
2835
245
249
162
21 1
205
25
31
48
28
999989
999997
3
7
999985
999999
6
999993
999991
1
0
308°
3243
1797
1 174
6029
2819
203
274
135
236
183
20
999982
13
999989
22
999988
5
999994
999995
5
999999
999993
6
3
1
7950
2983
1669
1117
4702
2212
239
233
104
234
123
21
19
13
3
999993
1 1
999998
11
6
4
23
4
999997
999998
0
2983
2677
1544
1 153
2466
1373
238
201
82
181
77
10
9
58
999997
7
4
999982
909989
1
15
0
8
999992
999997
0
3000
2460
1425
1019
1 164
826
187
234
93
133
68
47
1 1
26
999998
999988
1
13
0
3
7
999992
999988
999984
975
2980
2335
1309
1 174
606
459
216
197
163
188
20
7
36
35
29
9
1 1
ggggqg
24
999996
14
999999
1
3
2182
3170
2156
1317
1541
704
283
251
170
206
209
4
7
5
27
3
1
13
3
999997
10
999993
2
6
2
7^55
3"2Q
721°
]~£&
2460
107-i
7C2
1C6
151
232
7^2
40
12
15
45
1 1
5
1
QOQOQQ
qcjoOQR
9C""°95
999998
5
4
5
-------
D-10
TABLE D-2 (cont.)
Zn-65
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
3.5 Liter
4000
1633
2204
2174
1277
1603
1029
1001
1122
486
1204
2537
7
999985
10
19
999993
7
999989
5
1
999990
9
999995
1
4
Std. Crystal (A) 3/24/75 @ 1022
0
1633
2443
1977
1288
1904
954
1093
1204
502
1872
1387
999995
7
999982
999984
1
5
999994
999997
2
999998
0
999994
2
8
0
1853
2657
1812
1233
2019
973
1055
1 138
393
2904
707
18
5
2
3
999978
999993
11
999999
999991
13
999999
7
3
999998
0
2082
2920
1788
1170
1850
102^
1051
972
382
4091
285
22
999991
999983
1
24
9
1
999996
999992
4
1 1
999993
4
999997
1
2175
2901
1597
1224
1527
943
1042
994
359
5596
102
o
999990
3
999995
4
20
0
7
999997
5
999998
7
1
999996
2
2232
2791
1588
1206
1190
1023
1065
859
387
6582
49
14
999998
5
999970
3
999998
999982
999998
999995
999996
6
12
999993
0
2
2097
2710
1587
1164
1062
Q62
1094
790
406
7378
15
999996
999996
10
909975
999989
1
1
999995
999999
16
999995
999999
999983
421
2305
2614
1461
1264
988
990
1102
719
466
6763
8
14
999984
1
17
999995
7
999996
3
0
999989
3
999998
6
1289
2209
2303
1448
1240
926
1005
1145
588
547
5560
0
999995
0
8
999990
999996
999995
999986
999999
4
999999
999990
999995
3
1376
2328
2 ISO
1390
1417
951
1062
1090
542
803
4100
999989
23
7
1
999996
0
999985
999993
999999
2
5
3
999999
999996
Zr-95 3.5 Liter Std. Crystal (A) 3/31/75 @ 1309
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
4000
2402
3910
2909
2095
1930
892
3434
856
21
999997
27
999995
999997
24
17
999993
14
8
999995
7
2
7
999993
2
3
1
26Q8
4498
2767
2038
2046
940
5254
265
20
7
3
999984
999999
99999 1
10
19
1
999996
999996
8
7
4
3
999997
999992
1
2891
4603
2700
1953
1864
816
7320
25
999990
9
999991
999986
7
999992
1
10
2
999995
13
6
999997
999999
10
999995
999985
1
3234
4621
2591
1981
1882
811
9363
19
21
999990
9
4
999977
999995
6
999993
3
999981
0
999997
1
5
7
0
6
0
3345
4312
2419
1968
1850
797
11380
999981
999992
999992
1
999980
28
14
999995
999993
5
3
6
4
3
6
1
5
11
0
3383
4018
2324
1955
1616
821
11677
11
999991
9
999988
1 1
999985
1
16
999983
999995
999997
999996
999993
0
7
0
0
999994
0
3453
3815
2273
1868
1366
847
10364
8
16
999993
999991
5
1 1
1
999999
999993
2
999998
999989
6
5
4
5
12
868
3381
3547
2160
2076
1241
1 153
7660
999938
3
14
9
12
13
18
3
4
16
999989
999995
999995
4
999989
3
999994
2010
3501
3272
2087
2063
1057
1414
4627
29
999998
999958
999987
15
999981
999994
10
999987
2
999990
9
999992
5
2
4
2
2262
3583
3080
2053
1933
946
2229
210°
12
1 1
999979
10
999981
0
12
11
12
6
999991
990997
14
9
10
9
3
-------
TABLE D-3
TEST SPECTRA
^••.^ — ••^
100 PCI/LITER
1 .0
659 .1
814 .6
582.8
459 .6
368.0
356 .4
248 .3
144.8
144 .3
119.5
104-3
76. 1
100 .7
55 .3
5t .2
57.9
2t .6
22 .8
25.8
34.6
23.4
25.6
16.4
16.4
21 .2
BACKGD SW-
CS-137 •> BACKGROUND
784149.1 0.0
692.5
834.2
671 .1
460 .9
394 .0
348 .0
226.4
172.3
133.3
106.3
97.8
74.9
85.4
66 .6
41.7
59.3
32.7
39.7
29.9
41 .9
2fa .6
20.1
13.8
12.7
10.6
38585.
694.2
776.1
610 .1
445 .5
421 .9
354.7
197.2
153 .0
144.7
124.5
11C. 3
90 .3
105.1
64 .0
51 .3
42 .9
30.9
31 .0
28 .8
30 .8
13 .4
19.4
17.2
15.4
16.4
SAMPLE SUH=
18 .3
712.9
745.1
596.1
394.4
353.8
407.1
175.5
153.5
117.2
121 .3
95.0
87.4
117.9
50.2
56.6
52.3
29.9
15.7
34.9
27.9
14.1
21.5
18.0
10. A
6.9
43577.
0.1
801 .4
749.4
613.4
394 .2
358 .7
458 .4
162.1
150.3
134.0
117.5
85.7
86.0
113.1
40.5
56.0
39.5
30.6
28.5
28.1
27.0
23.6
20.4
17.3
10.1
7.4
0 .0
811 .5
783.0
624.0
378 .0
297.2
520-2
196.9
168 .7
122 .0
105.2
103.7
76.7
107.9
55.5
49 .7
48 .9
22 .4
22.6
38.1
31 .7
19.3
14.1
17.0
14.8
10.5
0.0
794.8
768 .7
621 .0
404.6
3C0.3
539.1
181.0
159.5
110.1
146.5
90 .6
78.7
92.3
46.5
36.4
34.6
27.0
36.1
30.1
17.5
11 .6
12.8
19.9
14.6
304 .1
794 .9
658 .5
563.2
356.7
312.0
495 .6
183 .8
133 .1
96 .3
96.7
95 .9
98 .4
108 .9
50.7
44 .4
32.1
27.6
27.4
28 .6
27.4
25.9
15.4
12.6
12 .2
625 .1
793.2
658.6
481.1
4CO .6
299.5
395.2
174.6
136.4
127.7
107.3
112 .6
103.5
82 .6
57.1
52.0
28.4
33.0
34.2
20.1
18.6
16.7
14.2
15.6
15.7
639.0
825.5
677.6
448 .1
394.3
292 .8
276.2
170.0
126.7
126.9
110.1
72.1
99 .2
69 .7
44.9
55.0
36.7
24.5
31. Z
39.3
17.5
14.4
19.6
19.0
14.4
o
I
-------
TABLE D-3 (cont.)
SAMPLE NUhBER 1
ID NO. CS - 137
PROCESSING OPTION NUMBER 1
BACKGROUND WILL NOT 6'E SUtTRACTED THli DPT1CN
HEIGHTS TL; BE PiSED ON CALCULATED SAMPLE SPECTRUM
HEIGHTS PROPORTIONAL TO RECIPROCAL COUNTS/CHANNEL
Nu REJECTION C ['EFFICIENT APPLIED
AUTOMATIC COMPENSATION RttUIPE: FOR GAIN AND THRESHOLD SHIFT
NliluER CF 1S01CPES USED FROM LIBRARY IS 14
T.HRESHflC CHANNEL SHIFT BETWEEN STDS AND SAMPLE IS C.O
LIBRARY SID. NUMBERS, IN GRDER CF DESIRED OUTPUT ARE 1 2 :
NORMALIZED RESIDUALS WILL NUT fE PLOTTED
OBSERVED AND CALCULATED SPECTRA WILL NOT BE PLOTTED
MATRIX I.N FORMATION WILL NOT BE PRINTED
9 10 11 12 13
CHOF * 0 .
CHDF = o.
CHQF = 0.
CH3F >= 0.
CHDF i 0.
L IBRARY
NUMBER
1
2
3
4
5
6
1
8
9
10
11
12
13
14
NORMALIZED
0 .0
0.1
0 .9
0.7
-0 .fa
0 .3
-0 .8
-C.6
U .5
-0 .5
AVERAGE
PERCENT
0 .
C .
1 .
0 .
0.
-0 .
-0 .
C.
0.
= -0
OF
51 THR
1,1 THR
46 Trip.
45 THR
45 THR
NUCLIDE
NAME
Ct-144
CR-5I
1-131
RU-106
C9-56
CS-134
CS-137
ZR-NL.-95
ir;-54
ZN-65
CO- 60
K-40
BA-140
BACK&R ND
RES IDUALS
0 0.0
7 -0.6
6 1 .4
0 -0.2
b -0.4
4 0.5
4 0.5
3 0 .6
7 -1.1
.0068
RESIDUALS
SHI FT = -o .0527 GAIN SHIFT
SHIFT = -0.1061 GAIN SHIFT
SHIFT = -0.1119 GA IN SHIFT
SHIFT = -O.lli^ GAIN SHIFT
SHIFT = -0.1127 GAIN SHIFT
DECAY UNCORRECTED
ACT I V IT Y STD . EPR.
8 .0393 1C .6042
37.6064 16.1012
C .1294 2 .3406
5.2724 6.5739
-2.2279 3.b864
3.0924 2.5749
97.2948 3.2677
2.3t22 2.9046
1.5637 2.6453
-0.5341 3.2912
4.0074 I.b393
43.4119 28 .7280
2.6267 2.3958
9<,.M244 2.0989
= 1 .0006
= 1.0007
= 1.0008
= 1.0007
= 1.0007
DECAY CORRECTED
ACTIVITY STD. FRR.
6.0393 10.8042
37.BOb4 18.1012
0 .6294 2 .3406
5.2724 8.5739
-2.2279 3.8B64
3.0924 2.5749
97.2948 3.2677
2.3622 2 .9C46
1.5687 2.3453
-0.5341 3.2912
4 .0074 1 .8393
43.4119 28.7280
2.6267 2.8958
94 .4244 2 .0989
COEFFICIENT ALPHA
OF VARIANCE FACTOR
134.39 0.5994
47.88 0.6750
371.90 0.9629
162.62 1.4086
174.44 1.77CO
83.27 2.1799
3.36 0.9410
121-93 0.9627
181.38 1.0022
616.24 0.6935
45.90 1.0862
66.18 0.9498
110.24 1.9728
2.22 4.5156
LLD
35.5457
59.5528
7.7006
26.2080
12.7662
8.4715
10.7506
9.5563
9.3611
10,8279
6.0512
94.5150
9.5270
6.9053
PER CHAf.NEL
0.0
-0 .7
0 .0
0 .3
-0 .1
0 .1
0 .4
-0.5
0.1
UNDER
0 .0
-1 .0
-0 .2
-0 .1
-0.2
-0.1
-0 .1
-1 .4
-0 .9
STO.
0 .0
-0 .2
-0.3
0 .4
1 .1
-0.6
-0 .6
0 .4
0 .6
OEV.
1 SI&MA *
0.0
0.5
0 .8
-0.0
0.5
1 .6
-0.5
-0.3
-0.6
= 0.6414
66.9
0.0
-0.9
-0.8
-0.1
-0.1
-1 .0
0.9
0.0
-0.8
2 S
0.0
-0.0
0.6
-0.2
-0.1
-0.4
O.B
0.3
-1.0
I&HA
-0.2
0.2
0.4
-0.8
-0.6
0.1
0.4
-0.3
0.0
SKEKNESS
- 95.3
0 .3
-1 .5
-1 .2
0 .7
0 .4
-0.3
-0 .0
0.9
-0.5
.
3
0.9
0 .4
-0 .1
1 .8
-0.2
-0.4
-1 .0
-0.7
0.1
0.1628
S1GHA
0.0
-0.6
0.4
0.3
0.9
0.4
-0.2
0.3
-0.1
-0.5
-0.2
-0 .5
-0.5
-0.5
-0.3
0.4
0.7
0.2
0 .2
0.5
0 .7
-1.2
0 .1
-0.7
0.2
0.7
0.1
KURTOS1S
'100.0
-0 .3
0.7
-0 .1
0 .5
0 .0
0 .6
-0.1
0.1
-0.8
2
-0 .4
0.3
0.2
-0 .3
-0 .2
-0.1
-0.9
-1 .3
0.2
.8257
-0.2
0.6
0.3
0.5
-1.1
0.7
1 .0
-0.9
0.0
-0 .1
-1 .1
-0 .6
0.2
0 .9
1 .7
-0.0
-0 .5
0.9
0.6
-0.1
-1 .1
0.0
1 .0
-0.9
-0.4
0.1
-0.1
a
i
SAMPLE/OPTION WRITTEN TO IOPT AT 05/27/76 17:02:49
-------
TABLE D-3 (cont.)
CONTROL INFORMATION SAMPLE NUMBER i
SAMPLE ID IS: CO - 60
NUMBER CF PROCESSING OPTIONS IS 1
COUNTING TIME (MINS.) FOR BJ
-------
TABLE D-3 (cont.)
SAMPLE NUYPER 2
ID N!l. CC - 60
PROCESSING OPTION NUMBER 1
BACK&RfUM WILL NOT BE SUBTRACTED THIS OPTION
WEIGHTS U BE BASED ON CALCULATED SAMPLE SPECTRUM
WEIGHTS PKnPCHTIC'NAL TT RECIPR1CAL CUU?;T S/CHAI.K EL
NO REJECTION COEFFICIENT APPLIED
AUTOMATIC COMPENSATION R E C LI I P E 1 FOP GAIN AND THRESHOLD SHIFT
NUMBER OF 1SOTPPES USED FKUM LIBRARY IS 1 4
THRESHTLD CHAr.VEL SHIFT BETWEEt: STDS AND SAMPLE IS 0.0
L1PRARY STD. NUMBERS, IN ORDER OF DESIRED OUTPUT ARE 123
NORMALIZED RESIDUALS WILL NOT EE PLOTTED
OBSERVED AND CALCULATED SPECTRA '.-(ILL NOT BE PLOTTED
MATRIX INFORMATION WILL MOT 6E PXINTED
8 9 10 11 12 13
CHDF - 0.56 THR
ChDF = 0.45 THR
C.-'OF = 0.42 THR
CHDF = C.4I THR
CHDF = G.40 THR
LIBRARY NUCLIDE
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NORMAL1
C .0
-0 .7
-0 .5
-0 .0
0 .0
1 .0
1 .2
-0 .2
1 .2
0.8
INJ A A
CE-
C n -
i-i
RU-
co-
cs-
cs-
ZR-
M,\-
ZN-
ca-
E
144
51
31
106
58
134
137
\3-95
54
65
60
SHIFT = -0.27E4 GAIN SHIFT
SHIFT = -0.4248 GAIN SHIFT
SHIFT -- -0 .4749 GAIN SHIFT
SHIFT = -C .-,S9I GAIf» SHIFT
SHIFT = -0.4935 GAIN SHIFT
DECAY UNCORRECTED
ACTIVITY
K-40
ZED
0
-0
-0
0
0
0
0
-0
-0
BA-
bAC
140
KG^ND
RESIDUALS
.0
.2
.6
.2
.1
.8
.3
.2
.2
0.0
0.1
-0.8
0.8
-0.8
-0 .5
-0.5
-0.3
-0.4
P ER
0 .0
-0 .2
-0.2
-0 .2
0.6
-0.5
-1 .7
-0.5
0.5
11 .«3. ?2
7.3103
-4.9429
12 .3069
-9 .1.04 1
3.2343
-2.3154
1 .7026
1 .8644
0.38C5
96 .9404
23.1337
4.0530
98 .2321
CHANNE L
0.0
0 .1
-0.3
-0.6
0.9
-0.4
0.7
0.1
-0.4
0.0
-0.1
0.3
0.9
-0 .4
0.3
1 .1
-0.6
-0.2
STD. ERR.
10 .6953
16.1592
2 .3205
7 .9590
3 .6858
2.2265
2 .1345
2 .74 18
2.873J
3.9634
2.4410
26.7016
2 .7504
2.0010
0.0 0.0
-1.2 -0.6
0.4 -0.3
0.0 -0.0
0.9 -0.1
-1.0 0.4
-0.0 -0.3
-0.6 0.9
-0.3 0.1
= 1.0025
= 1.0036
= 1.0043
= 1.0045
= 1.0046
DECAY CORRECTED
ACT IV ITY
11.9322
7.3103
-4 .9429
12 .3069
-9.4041
3.2343
-2.3154
1 .7026
1 .8644
0.8855
96.9404
23 .1337
4.0530
98.2321
0.0 0.7
-0.2 -0.5
0.1 -0.2
0.2 -0.3
0.2 -0.4
1.4 -0.2
-1.9 0.5
0.1 1.0
0.6 1.0
STO
10
16
2
7
3
2
2
2
2
3
2
26
2
2
0 .5
-C .0
-0 .4
-0.0
-0.7
-0.1
0.2
-0 .4
1.0
. ERR .
.6853
.1'592
.3205
.9590
.6858
.2285
.1345
.7418
.8731
.9634
.4410
.7016
.7504
.0010
-0 .0
-0 .1
-0.5
0.5
0.5
1.3
-0.2
-0.1
0 .5
COEFFICIENT
OF VARIANCE
89.55
221 .05
46 .95
64 .67
39.19
68 .90
92.19
161 .04
154.10
447.61
2.52
115.42
67.86
2.04
-0.3 -0.2
-0.2 0.0
-0.0 0.5
-0.9 1.1
0.0 -1.0
0.6 -0.6
-0.4 1.0
-0.1 0.0
0.6 0.1
-0 .2
-0.0
0.4
-0 .2
0.0
-1 .8
-0.3
-0.3
0.3
ALPHA
FACTOR
0 .6775
0 .68P6
1.0910
1 .4943
1 .9164
2.1560
0.7025
1 .0601
1 .1565
0.9544
1.6474
1.0088
2 .1414
4.9198
-0 .2
0 .5
0 .7
-0 .3
-0.3
-0.1
-0.4
1.0
-0.3
0.3
-0.4
0.8
0.2
0 .1
1 .6
-1 .2
-0 .5
0 .4
LLD
35. 1546
53.1637
7.6345
26.1352
12.1263
7.3319
7.0226
9.0205
9.4527
13.0396
8.0310
87.8484
9.0487
6.5833
0.4
O.B
-0.3
0.3
0.2
0.2
1 .3
0.5
0.0
0.2
-0.5
-0.7
0.4
0.0
-1 .0
0.2
-0.5
-0.1
0.0
0.7
-0.0
-0.0
0.1
0.1
0.7
0.7
0.3
AVERAGE = 0.0352 STD. DEV. = 0.6036 SKEWNtSS = 0.0630
PERCENT OF RESIDUALS USDER 1 S1GHA = 71.5 2 SIGMA * 94.8 3 SIGMA >
SUSPICIOUS CHANNELS
-115 -129
SAMPLE/OPTION WRITTEN TO IDPT AT 05/27/76 17:02:50
»*•»*»» ALPHA-M NORMAL TERMINATION «»*••••
KURTOS1S
3.5627
98.8
I
I—'
J>
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-77-089
2.
3. RECIPIENT'S ACCESSI ON- NO.
4. TITLE AND SUBTITLE
LEAST-SQUARES RESOLUTION OF GAMMA-RAY SPECTRA IN
ENVIRONMENTAL SAMPLES
6. PERFORMING ORGANIZATION CODE
5. REPORT DATE
August 1977
7. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
L. G. Kanipe, S. K. Seale, and W. S. Liggett
TVA-EP/78-02
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Division of Environmental Planning
Tennessee Valley Authority
Chattanooga, TN 37401
10. PROGRAM ELEMENT NO.
1NE - 625C
11. CONTRACT/GRANT NO.
78 BDI
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Research & Development
Office of Energy, Minerals & Industry
Washington, B.C. 20460
13. TYPE OF REPORT AND PERIOD COVERED
Milestone FY-76
14. SPONSORING AGENCY CODE
EPA/600/17
15. SUPPLEMENTARY NOTES
This project is part of the EPA-planned and coordinated Federal Interagency
Energy/Environment R&D Program.
16. ABSTRACT
The use of ALPHA-M, a least-squares computer program for analyzing Nal (T£) gamma
spectra of environmental samples, is evaluated. Included is a comprehensive set
of program instructions, listings, and flowcharts. Two other programs, GEN4 and
SIMSPEC, are also described. GEN4 is used to create standard libraries for
ALPHA-M, and SIMSPEC is used to simulate spectra for ALPHA-M analysis. Tests to
evaluate the standard libraries selected for use in analyzing environmental samples
are provided. An evaluation of the results of sample analyses is discussed.
(Circle One or More)
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b. IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
_Ecology
^Env
^Earth Atmosphere
^Environmental Engineering
Geography
Hydrology, I imnoloi
Biochemistry
Earth Hydrosphere
Combustion
Refining
6F 8A 8F
8H 10A 10B
7B 7C 13B
3. DISTRIBUTION STATEMEN1
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCLASSIFIED
!1. NO. OF PAGES
180
20. SECURITY CLASS (Tills page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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