EPA
United States
Environmental Protection
Agency
Office of
Reseach and
Development
Environmental Monitoring
and Support Laboratory
Las Vegas, Nevada 89114
EPA-600/7-77-144
December 1977
QUALITY CONTROL FOR
ENVIRONMENTAL MEASUREMENTS
USING GAMMA-RAY
SPECTROMETRY
Interagency
Energy-Environment
Research and Development
Program Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad categories
were established to facilitate further development and application of environmental
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 ENERGYENVIRONMENT
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 systems. The goal of the Pro-
gram is to assure the rapid development of domestic energy supplies in an environ-
mentally-compatible manner by providing the necessary environmental data and
control technology. Investigations include analyses 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 environmental issues.
This document is available to the public through the National Technical Information
Service, Springfield, Virginia 22161
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EPA-600/7-77-144
December 1977
QUALITY CONTROL FOR ENVIRONMENTAL MEASUREMENTS
USING GAMMA-RAY SPECTROMETRY
by
Lee H. Ziegler
Monitoring Systems Research and Development Division
Environmental Monitoring and Support Laboratory
Las Vegas, Nevada 89114
and
Hiram M. Hunt, Ed.D
Professor, Radiation Technology
University of Nevada, Las Vegas
Las Vegas, Nevada 89154
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL MONITORING AND SUPPORT LABORATORY
LAS VEGAS, NEVADA 89114
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DISCLAIMER
This report has been reviewed by the Environmental Monitoring and Support
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Mention of trade names or commercial products does not constitute endorsement
or recommendation for use.
11
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FOREWORD
Protection of the environment requires effective regulatory actions which
are based on sound technical and scientific information. This information
must include the quantitative description and linking of pollutant sources,
transport mechanisms, interactions, and resulting effects on man and his
environment. Because of the complexities involved, assessment of specific
pollutants in the environment requires a total systems approach which tran-
scends the media of air, water, and land. The Environmental Monitoring and
Support Laboratory-Las Vegas contributes to the formation and enhancement of a
sound integrated monitoring data base through multidisciplinary, multimedia
programs designed to:
develop and optimize systems and strategies for moni-
toring pollutants and their impact on the environment
demonstrate new monitoring systems and technologies by
applying them to fulfill special monitoring needs of
the Agency's operating programs.
This report describes the quality control procedures, the calibration,
collection, analysis, and interpretation of data in measuring the activity of
gamma ray-emitting radionuclides in environmental samples. The data from
these measurements are used for a wide variety of purposes including assess-
ment of health effects, establishment of standards and guides, and en-
forcement activities. This report is intended to introduce the techniques of
gamma ray spectroscopy to those persons who are initiating a radioactivity
monitoring program. The Quality Assurance Branch at the U.S. Environmental
Protection Agency's Environmental Monitoring and Support Laboratory in Las
Vegas encourages the development and implementation of quality control pro-
cedures at all levels of sample collection, analysis, data handling and
reporting of environmental radiation measurements and can provide further
assistance upon request.
orge B. Morgan
Director
Environmental Monitoring and Support Laboratory
Las Vegas
111
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TABLE OF CONTENTS
Paqe
FOREWORD iii
LIST OF FIGURES vi
LIST OF TABLES viii
INTRODUCTION 1
BASIC PRINCIPLES 3
GAMMA RAY INTERACTIONS WITH MATTER 11
TERMINOLOGY OF GAMMA RAY SPECTROSCOPY 15
EQUIPMENT 21
INITIAL SETUP 27
CONTROL CHARTS 32
DATA ANALYSES 34
CALIBRATION OF THE SYSTEM 40
STATISTICS AND UNCERTAINTIES IN MEASUREMENTS 45
INEFFICIENT STATISTICS 56
SUPERPOSITION OF SEVERAL INDEPENDENT RANDOM PROCESSES 61
STATISTICAL TESTING FOR NORMAL AND NON-NORMAL DATA 66
LOWER LIMIT OF DETECTION 79
REFERENCES 85
BIBLIOGRAPHY 88
APPENDIX A. BASIC DATA FOR SELECTED GAMMA RAY-EMITTING RADIONUCLIDES 89
APPENDIX B. THORIUM-232 SERIES DECAY DATA 95
APPENDIX C. URANIUM-238 SERIES DECAY DATA 97
APPENDIX D. URANIUM-235 SERIES DECAY DATA 99
APPENDIX E. PULSE HEIGHT SPECTRA OF SELECTED RADIONUCLIDES 101
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LIST OF FIGURES
Number Page
1 Cesium-137 decay scheme. 6
2 Decay scheme for iron-59 (Fe). 7
3 Decay scheme for cobalt-60 (Co). 7
4 Spectrum of Fe-59 at 10 keV per channel. 8
5 Spectrum of Co-60 at 20 keV per channel. 9
6 "Ideal" spectrum of Compton interactions. 12
7 Mass attenuation coefficient of sodium iodide. 14a
8 Spectrum of CS-137 at 10 keV per channel. 16
9 Typical block diagram of gamma ray spectrometer. 23
10 Gamma-ray spectrometer at the Environmental
Monitoring and Support Laboratory-Las Vegas, Nevada. 24
11 Schematic representation of a typical pulse from a
preamplifier coupled to a Nal(Tl) detector. 25
12 Schematic representation of typical pulses from a linear
amplifier in a Nal(Tl) spectrometer. 25
13 400-minute background spectrum measured with a 10.2-cm by
10.2-cm Nal(Tl) detector. 30
14 Idealized spectra illustrating interference factors and sum-
mation of gamma rays in a gamma-ray spectrometer. 36
15 Common sample holders. 41
16 Comparison of analytical results from several participants
when systematic results are not estimated correctly. 46
17 Comparison of analytical results from several participants
with correct estimation of systematic errors. 46
18 Normal distribution with a mean value, m, of 100 and a
standard deviation, 0, of 10. 48
vi
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LIST OF FIGURES (continued)
Number Page
19 Poisson distribution with a mean value, m, of 100. 50
20 Control chart for low energy (0.57 MeV) peak from
bismuth-207. 51
21 Control chart for high energy (1.063 MeV) peak from Bi-207. 69
22 Probability plot for low energy (0.57 MeV) peak from Bi-207. 74
23 Probability plot for high energy (1.063 MeV)
peak from Bi-207. 75
24 Probability plot for 10-minute background counts measured
with a 10.2-cm by 10.2-cm Nal(Tl) detector. 76
Vll
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LIST OF TABLES
Number Page
1 Compton Edge Energy as a Function of Incident Radiation
Energy 13
2 Limiting Values of r at Probabilities of 95% and 99% for
the Mean Square of the Successive Differences
Statistical Test 67
3 MSSD Test Applied to Counts of a Bi-207 Sample Obtained
with a Multichannel Gamma-Ray Spectrometer 68
4 MSSD Test for Background Measurements of a
10.2-cm by 10.2-cm Nal(Tl) Detector 70
5 Kolmogorov-Smirnov Test on Low Energy (0.57 Mev)
Gamma Rays from Bi-207 71
6 Kolomogorov-Smirnov Test on High Energy (1.063 Mev)
Gamma Rays from Bi-207 72
7 Kolmogorov-Smirnov Test on Background Measurements of
a 10.2-cm by 10.2-cm Nal(Tl) detector 73
8 Limiting Values for D in the Kolmogorov-Smirnov Test 78
9 Risk and Confidence Values 80
Vlll
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INTRODUCTION
This monograph is intended to introduce the field of gamma-ray spectros-
copy to analysts engaged in environmental radiation monitoring. The emphasis
of this document is on quality control procedures that assist the analyst
engaged in measuring and interpreting gamma-ray spectra in producing accurate
and valid data. Because of this emphasis, many interesting aspects of the
field have been neglected here. However, the references in the bibliography do
cover much omitted material of relevance and should be consulted by those who
have interest in further aspects of the field of spectroscopy.
Gamma-ray spectroscopy is a valuable tool for identifying radionuclides in
environmental media. Usually requiring a minimum of sample preparation,
gamma-ray analysis provides a. means for the specific identification and quan-
tification of radionuclides in any material. Typically, a sample which has
been shown to contain alpha or beta activity through routine screening is
assayed for gamma activity by the use of a suitable detector and multichannel
analyzer.
There are many types of detectors capable of detecting gamma rays, but
those suitable for environmental monitoring are limited in number. The ideal
detector for gamma-ray analysis will discriminate against other types of radi-
ation and will produce signals proportional to the energy and intensity* of the
gamma rays received. Factors leading to the choice of a particular detector
are cost, resolution, and sensitivity. One of the more commonly used detectors
for gamma-ray analysis is the thallium-activated sodium iodide [Nal(Tl)] crys-
tal optically coupled to a photomultiplier which is, in turn, electrically
connected to a multichannel analyzer. The Nal(Tl) detector is moderate in
cost, has a moderately good resolution, and has good sensitivity. The use of
solid state detectors is increasing, but they are still more expensive and have
less sensitivity than Nal(Tl) detectors. The resolution of solid state de-
tectors is superior to Nal(Tl) detectors, and in some cases, they are easier
to use for identifying individual radionuclides in complex mixtures of radio-
active substances. Although many of the principles of gamma-ray spectroscopy
are the same whether a lithium-drifted germanium [Ge(Li)] detector or a
Nal(Tl) detector is used, this monograph applies only to gamma-ray spectros-
copy using a Nal(Tl) detector.
There is a substantial quantity of literature available describing the
principles and applications of Nal(Tl) detectors for gamma-ray spectroscopy.
The accompanying list of references, though brief, is informative and to the
point. The publications by Crouch (1) Heath et al., (2) and Heath (3, 4) are
particularly helpful to persons who have not been introduced to gamma-ray
*Intensity is the number of gamma rays contained in a beam, emitted from a
source, or incident on a detector per unit time.
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spectroscopy. The catalog of gamma-ray spectra by Heath (4) is very helpful in
identifying radionuclides from the results of gamma-ray measurements and for
calibrating gamma-ray detection equipment for pulse height versus energy. A
good introduction to radioactive analysis of environmental media is the EPA
publication "Radioassay Procedures for Environmental Samples" edited by Douglas
(5). Reference works by Crouthamel (6) and Siegbahn (7) are also available.
Other EPA publications (8, 9) describe services available to laboratories
engaged in environmental monitoring.
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BASIC PRINCIPLES
Radioactivity is the outward manifestation of the spontaneous transfor-
mations of radioactive nuclei. The quantity of radioactivity can be expressed
in a number of ways. For example, one may specify the activity, at any given
time, in terms of disintegrations per second. The radioactivity has the di-
mension second"1 and is often expressed in curies. The curie is defined by
international agreement as the quantity of radioactivity equal to 3.7 x io10
disintegrations per second.
Several assumptions are made in defining the fundamental law of radio-
active decay. Among these assumptions are:
1. The probability of decay is the same for all atoms of a single
radioactive species.
2. The probability of decay is independent of the age of the particular
atom.
3. All atoms of a single radioactive species are identical in their
nuclear properties.
4. The intensity of the radiation originating in the sample is due to
the nuclear properties of the species present.
5. Each radioactive event is defined as the disintegration of one atom
of the radioactive species and the formation of one new atom of a new species.
(The new species may or may not be radioactive depending on the original
species.)
6. The intensity of the radiation emerging from a sample of radioactive
material can be measured with high precision and with known, or at least
reproducible, efficiency.
7. The amount of radiation originating in a sample is directly propor-
tional to the amount of radioactive material present (although the constant of
proportionality varies from species to species). For a single species, if N
is the number of atoms present at time t, the radioactivity in disintegrations
per unit time is given by the rate at which the active species is disappearing,
so that the rate of radioactive decay is
- || = + AN (Eg. 1)
where A is the constant of proportionality characteristic of the species.
X is referred to as the decay constant of the species. The above equation can
be integrated to give
N = N e'^'V (Eq. 2)
where N has the value N at the arbitrarily chosen time t . If we measure the
o o
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radiation from the sample with an instrument having an efficiency TI for the
characteristic radiations of the species, the observed "counting rate" is AnN.
Therefore, N, and consequently, XnN decrease exponentially with time.
The half-life, T, , i.e., the time it takes for the activity of the radio-
nuclide to decrease to one-half the value of activity at any given time, t, is
related to the decay constant, A, as follows:
-N -* = & *
o
-AT
In (M = - In 2 = In eh = -XT,
h
^
2-421 ,. 3,
I, is expressed in time units and A in units of reciprocal time. T. and A
must be expressed in the same time unit to balance the half-life formula, but
any unit of convenient size may be used.
Generally, one is interested in finding the activity, A (A = AN) , at a
time, t, based upon an original activity, A , at time t . The following
formula is convenient for the reason that half-life values are usually more
readily available than radioactive constants .
In 2 (t-t )
A = ~ - - ~ (Eq- 4)
Conversely, if the activity, A, is determined, then the activity, A , for any
arbitrarily chosen time, t , can be found using the relation
In 2 (t-t )
A =
o T
The disintegration law applies universally to all radionuclides , but the
constant A is different for each nuclide. The known radioactive nuclides have
decay constants between A = 2.3 x 105 second"1 (for 2e2Po) to
A = 1.51 x 1CT18 second"1 (for 2||Th) , a range of over 1024-
Gamma-ray emission is a common way for an excited nucleus to lose energy.
A gamma transition can be defined as any deexcitation of an excited nuclear
state to a state of lower energy without changing the charge, Z, or the mass,
A, of the nucleus with the emission of a gamma ray. Excited states appear as
the result of alpha or beta decay processes, nuclear reactions, direct exci-
tation from the ground state, and gamma transitions from higher excited states.
For each radioactive nuclide the possible ways of deexcitation are summarized
in the decay scheme. A complete decay scheme includes all the modes of decay
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of the nuclide, the energies of the radiations, their abundances, the sequence
in which the radiations are emitted, and the measured half-lives of any inter-
mediate states. There exist several useful compilations of the decay schemes
of the nuclides (10, 11, 12, 13).
The various nuclear transitions indicated in the decay schemes represent
only the primary processes. The complete degradation of the energy of the
nuclear transition will usually include a sequence of secondary events. Some
of these events are the emission of bremsstrahlung radiation, emission of
characteristic x-rays, emission of Auger electrons, pair formation, and emis-
sion of annihilation photons. These secondary events can also involve the
external atoms in the environment of the disintegrating nucleus, in the detec-
tor, or with other matter in the vicinity of the disintegrating nucleus and
the detector, e.g. source holders or a shield.
An example of a simplified decay scheme is presented in Figure 1. This
decay scheme indicates most of the pertinent information known about the decay
of cesium-137. The ground state of cesium-137 is indicated by the heavy hori-
zontal line at the top of the figure. The half-life of cesium-137, indicated
as 30.0 years, is shown just to the right of the ground state line. Two
arrows extending to the right from the ground state line to lower horizontal
lines indicate respectively a beta transition to a metastable state of barium
(barium-137m) and a beta transition to the ground state of barium-137. The
fraction that each transition is of the total beta emission is expressed as a
percent. In this example 94.7 percent of all beta transitions are to the
barium-137 metastable state and 5.3 percent to the barium-137 ground state
(14). Also indicated with the transition probabilities (in percent) are the
transition energies. Only the transitions from the metastable state of barium-
137 will produce gamma rays. Other than decaying with a gamma emission, the
transition can be made by ejecting a conversion electron and associated x-rays
and Auger electrons. The total internal conversion coefficient is defined as
the number of electrons ejected by the nucleus divided by the number of gamma
rays emitted for a given transition. The total internal conversion coeffi-
cient, a, accounts for all of the "conversion" electrons ejected so that the
fraction of gamma rays emitted, I,, from the intermediate level is
h = rhr (Eq- 6)
The compilations will either list the number of gamma rays per disintegration
of the parent nuclide, or the number of disintegrations going to an inter-
mediate state, and values for the internal conversion coefficient. The in-
ternal conversion coefficient for the 0.6616 MeV to ground state is 0.11.
Therefore, the fraction of gamma rays emitted is
A 1 + 0.11
= 0.90 (Eq. 7)
The fraction of gamma rays emitted per decay of cesium-137 is therefore
0.947 * 0.90 = 0.85.
A cesium-137 (1IsCs) spectrum produced by the interaction of gamma rays
with a sodium iodide (Nal(Tl) detector is presented in Figure 8 on page 16.
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30.0y
55
Cs
137
94.7% 9.5
5.3% 12.1
11/2- 0.6616
2.55m
Q0- 1.176
0.281
3/2+ 0
56 Ba
137
Figure 1. Cesium-137 Decay scheme.
The spectrum was obtained by feeding the signal from a sodium iodide detector
into a multichannel analyzer calibrated at 10 keV per channel. The prominent
peak in channel 66 represents the characteristic 0.6616-MeV cesium-137 gamma
ray. The spectrum is complex for the reason that there are other interactions
including partial exchanges of energy, characteristic rays emitted by the
detector, and those rays emitted by daughter nuclides.
Figures 2 and 3 illustrate the decay schemes of 2eFe (iron-59) and 27Co
S9.
SO
(cobalt-60) respectively. The spectra of 2eFe and zrCo produced by the inter-
action of gamma rays with a sodium iodide detector are presented in Figures 4
and 5. These spectra were obtained from the same system which was used to
obtain the cesium-137 spectrum mentioned previously, but was calibrated at 20
keV per channel for these figures. These spectra are very similar; the most
significant differences are the shape and structure of the 2?Co spectrum above
channel 70 (1.4 MeV) (20 keV per channel) compared to the shape and structure
of the lire spectrum above channel 140 (1.4 MeV) (10 keV per channel.)
i|Fe decays principally by 0.46 MeV maximum beta emission to the 1.095 MeV
level of 59Co (53 percent) and by 0.26 MeV maximum beta emission to the 1.292
MeV level of 59Co (45 percent). 1.1 percent of the beta emissions from
zeFe decay to an energy level of 1.435 MeV of 59Co. By inspection of the 2sFe
decay scheme one may see that the 70 percent portion of the deexcitation of
the 1.435 MeV level results in a 0.1430 MeV gamma ray and the 30 percent
portion results in a 0.34 MeV gamma ray. Subsequently, 95 percent of the
deexcitation of the 1.292 MeV energy level is to ground state producing a 1.292
MeV gamma ray and the remaining 5 percent decays to the 1.095 MeV level pro-
ducing a 0.193 MeV gamma ray. The deexcitation of the 1.095 MeV energy level
is strictly to the ground state of lyCo thus producing a 1.095 MeV gamma ray
100 percent of the time.
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3/2 - 45d
59
1.292
1.095
Figure 2. Decay scher.e for iron-59 (Pe> .
5.26
99+% 7.5
0.013% 12.6
0.12% 13.0
Figure 3. Decay scheme for cobalt-60 (Co).
The following calculations to determine the number of gamma rays emitted
per decay are based upon the preceding data and internal conversion coeffi-
cients. (10, p. 190). The number of 1.292 MeV gamma rays emitted per decay
of IlFe is:
|(0.70 x 0.011 + 0.45) x 0.95}
from the y
transition
1.435 MeV
level to the
1.292 MeV
level
from the
3 decay to
the 1.292
MeV level
1 + 0.00011
= 0.43
internal con-
version correc-
tion
(Eg. 8)
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103
59 F 356 134Z200 DPM02077304GO
10157316
102
10
NET
CPM
100
10-1
40
80 12O
CHANNEL NUMBER
160
200
Figure 4. Spectrum of Fe-59 at 10 keV per channel.
8
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105
4l775n
10*
103
NET
CPM
102
10
1.33 Mev gamma ray full energy
energy equivalent to
CHANNEL NUMBER
Figure 5. Spectrum of Co-60 at 20 keV per channel.
9
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The number of 1.095 MeV gamma rays emitted per decay of leFe is:
|(0.30 x 0.011) + (0.05) (0.70 x 0.011 + 0.45) + 0.53J Y^~^00014 = ฐ'56 (Eq* 9)
from the y tran- number of transitions from from the internal
sition 1.435 MeV from the 1.292 MeV level B tran- conversion
level to the to the 1.095 MeV level sitions correction
1.095 MeV level to the
1.095 MeV
level of
6O,-,
27Co
The beta decay I|Fe to the 1.292 MeV level of f^Co is not time related to
the beta decay of IfFe to the 1.095 MeV level of f?Co. Experimen tally the
1.292 MeV and the 1.095 MeV gamma rays are detected independently. lyCo, on
the other hand, decays primarily through one beta branch to a 2.5057 MeV level
of aaNi. fsNi decays by emitting a 1.17 MeV gamma ray followed by a 1.33 MeV
gamma ray to reach ground state. These two gamma rays are emitted in cascade
and occur within a few picoseconds of each other for a given nuclear decay and
also exhibit angular dependence. The internal conversion coefficients are
small (approximately 0.00017), consequently the intensities of the 1.17 MeV
and 1.33 MeV gamma rays are very nearly equal. There is one 1.17 MeV and one
1.33 MeV gamma ray per disintegration of 2ฐCo. The summing of the two gamma-
ray responses in the Nal(Tl) crystal account for the pulses above the singles
peak in the 60Co spectra which does not occur in the 59Fe spectra.
Lederer, et al., (10), has tabulations of the types, approximate energies
and intensitities of the major radiations of all the radionuclides . The
Nuclear Data Sheets (11) are compilations of recent data, give complete decay
schemes, but don't always present the number of gamma rays emitted per dis-
integration of the parent radionuclide . The Nuclear Data Sheets however list
the internal conversion coefficients by which the number of gamma rays emitted
per disintegration can be calculated as indicated in preceding paragraphs.
10
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GAMMA-RAY INTERACTIONS WITH MATTER
A knowledge of the basic processes by which a photon interacts with
matter is essential to an understanding of the gamma-ray response of a scintil-
lation detector. Photons interact with the scintillator (crystal or phosphor)
of a gamma-sensitive scintillation detector producing a tiny quantity of light
called a scintilla. When all of the energy of a gamma ray is absorbed by the
scintillator of a scintillation detector, the quantity of light that is pro-
duced is very nearly proportional to the energy of the absorbed gamma photon.
The quantity of light produced in the scintillator falls on a photocathode
causing the ejection of electrons. The electrons ejected from the photocath-
ode are multiplied in number by a photomultiplier tube. A good scintillation
detector will deliver to its associated recording instrument a measureable
current pulse or a measureable electric charge that is proportional to the
energy deposited in the scintillator by the gamma ray.
Matter absorbs energy from gamma rays principally by (a) the photoelec-
tric effect, (b) Compton scattering, and (c) pair production. These effects
are described briefly in the following paragraphs. It must be kept in mind,
however, that the information produced by (or response from) a scintillation
detector results from the energy deposited in the scintillator.
Photoelectric effect:
The photoelectric effect is the process by which a photon is annihilated
through the total transfer of its energy to an electron in the vicinity of an
atomic nucleus. The photoelectron leaves the neighborhood of the atomic nu-
cleus with a kinetic energy of the interacting photon minus the binding energy
(energy to remove the electron from its orbit about the atomic nucleus).
Gamma-ray absorption by means of the photoelectron effect is possible only
when the photon has more energy than the binding energy of the electron.
Electrons have much smaller ranges in matter than gamma rays. Consequently,
the probability that an electron might escape from a scintillator when emitted
near its surface is much smaller than the probability that a photon might
escape under similar circumstances. Therefore, almost all photoelectric
events result in complete absorption of the photoelectron energy.
The nucleus of an atom in the scintillator from which a photoelectron has
been ejected is left in an excited state. When the ejected electron is re-
placed, there is an emission of a characteristic x-ray photon. The x-ray
photon may escape from the scintillator, thus producing what is called an
"escape peak." More commonly, the x-ray photon will also be absorbed in the
scintillator which results in the recording of an event in a "full energy
peak." The probability that an x-ray will escape from the scintillator is
generally small so that the peak resulting from a photoelectric event without
the x-ray being detected is much smaller than the full energy peak. When a
7.6-cm by 7.6-cm Nal(Tl) detector is used, the escape peak is 6 percent of the
11
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full energy peak for 100 keV photons, but only 1.2 percent of the full energy_
peak for 200-keV photons. The spectra of cerium-141 and cerium-144 in Appendix
E are illustrative of full energy peaks accompanied with escape peaks recorded
by Nal(Tl) detectors. The iodine escape peak is 29 keV below the full energy
peak.
Compton scattering;
Incoherent or Compton scattering results when a photon collides with an
electron giving up part of its energy to the ejected electron, with the scat-
tered photon retaining the remaining energy. The ejected electron loses its
energy in the scintillator. These high energy photons have a high probability
of escape. The maximum energy that can be deposited by Compton events in
scintillators represents the maximum quantity of light that can be produced by
the incident gamma photons if the scattered photon does not interact with the
scintillator. The broad region of lower energy and less height in the Compton
spectrum is principally representative of the Compton electron energies that
are converted to quantities of light in the scintillator when their correspond-
ing Compton photons escape. Figure 6 is a pictorial representation of a scin-
tillation spectrum for Compton events.
Compton Plateau
Compton edge Full energy peak
e>
ฃ
ซ
*
ENERGY
Figure 6. "Ideal" spectrum of Compton interactions.
12
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In the Compton process the energies of the scattered photon and electron
have the following relationships:
= - - - -
- cos 9)
(Eq. 11)
(1 - Cos 6)
where E is the incident gamma ray energy in MeV, E is the scattered electron
energy in MeV, 0.511 is the rest mass energy of an llectron and G is the angle
between the direction of the incident photon and the scattered photon. The
energy of an electron at the Compton edge, E , is related to the energy of
the incident photon as follows: ce
Ece = EY ^^~ (E<5' 12)
where E is in MeV. Table 1 lists the energy of the Compton edge as a func-
tion of the incident photon energy.
TABLE 1. COMPTON EDGE ENERGY AS A FUNCTION OF INCIDENT RADIATION ENERGY
E (MeV)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
E (MeV)
ce
0.03
0.09
0.16
0.25
0.33
0.42
0.52
0.61
0.70
0.80
E (MeV)
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
E (MeV)
ce
0.90
0.99
1.09
1.19
1.29
1.38
1.48
1.58
1.68
1.78
Pair production;
Pair production is possible when the incident photon has an energy in
excess of 1.02 MeV (the rest mass energy of an electron-positron pair). Pair
production occurs in the presence of the coulomb field of an atomic nucleus.
The incident photon disappears and an electron-positron pair is created. The
total energy of the electron-positron pair will be equal to the total energy
of the incident photon and their kinetic energy will be equal to the total
energy minus 1.02 MeV. An unstable condition occurs when a positron comes to
rest in the field of an electron. The positron and electron are annihilated
and two photons of 0.511 MeV are emitted. All of the energy of an incident
photon may be absorbed by the scintillator or one or both of the 0.511 MeV
13
-------
electrons may escape detection. Consequently, the following transfers of
energy to the scintillator are possible:
1. All of the energy of the incident photon.
2. The energy of the incident photon minus 0.511 MeV (single escape
annihilation peak).
3. The energy of the incident photon minus 1.02 MeV (double escape
annihilation peak).
An incident photon will interact with a scintillator by one of the three
processes described in the preceding paragraphs. The fraction of photons that
interact by any one process is related to the mass attenuation coefficient for
that process at the energy of the incident photon. The total mass attenuation
coefficient, y/p (cm/g), is the linear sum of the individual mass attenuation
coefficients:
(y/p)total = (y/P)photoelectric
+ (y/p)Compton + (y/p)pair production (Eq' 13)
The total probability, P, of photon interaction with a scintillator is a
function of the size of the scintillator and the total mass attenuation coef-
ficients. The following formula may be used:
p.l- e" [(U/P) total] X (Eq. 14)
where x is the thickness of the scintillator in grams per square centimeter
(gm/cm ) seen by the incident photon. The total mass attenuation coefficient
for Nal (Tl) is shown in Figure 7. (.15).
14
-------
10.0
1.0
\
V
\
1
>
\
\
\
\
V
\
\
\
\
v
\
\
\
\
\
\
\
\
>
V
\
1
N
\
\
\
.
s
N
s,
\
^
^-^
i
i
!
0.1
0.01
10
20 30 40 SO 60 70 8090VO
200 300 400 500
ENERGY (kev)
WOO
2000 3000 40005000
10,000
Figure 7. Mass attenuation coefficient of sodium iodide.
14 a
-------
TERMINOLOGY OF GAMMA-RAY SPECTROSCOPY
Several terms are commonly used in describing prominent portions of the
spectrum obtained from a spectrometer. Figures 5 and 8 illustrate these
terms.
1. Efficiency the term that relates some predefined (by predetermined
convention) observed count rate to the true disintegration rate of the specific
radionuclide in the sample which is being counted. Although several defini-
tions of efficiency are used, the basic concept is:
. . counts per unit time , _.
efficiency = .r-r . . . , . (Eq. 15)
disintegrations per unit time
With experience, one can choose the conventions best suited for a particular
analysis. Whichever convention is chosen, it should be used consistently. One
should avoid choosing conventions which are based upon the edges of regions
that lie in rapidly varying parts of a spectrum.
2. Full energy peak a peak which represents complete transfer to the
detector of the energy of a monoenergetic incident photon. The peak is promi-
nent in Figure 8 with its center located at channel 66. Full energy peaks in
Figure 5 are located in channels 57 and 64.
3. Peak energy the energy of the center of a spectral peak. This
energy can be obtained from tables concerning the disintegration schemes of
radionuclides when the radionuclide is identified, or from a previously deter-
mined calibration when using calibration standards with known gamma-ray ener-
gies.
4. Peak area the area under a spectral peak. Several conventions
(16, pp. 245-251) are used in determining peak areas. Any one of the conven-
tions will be satisfactory, but only one should be used to assure consistency
in analyzing data and calibrating'the spectrometer.
5. Compton edge the termination of the Compton plateau below the full
energy peak which represents the high-energy boundary of the Compton distri-
bution. The energy of the Compton edge is related to the energy of the full
energy peak by:
E. ... . (Eq. 16)
_ full energy peak
Ece = full energy peak ' 1 + 3.9lBfull energy peaR
where E is expressed in MeV.
For the 0.661 keV gamma ray in Figure 8, the Compton edge falls at 0.48 MeV.
6. Compton area the area under the portion of the spectrum which is
15
-------
10*
103
102
NET
CPM
1377423Q)
peak energy = 0.
peak height
energy peak
backscatter peak
i iJ.-j.rtas.U4in, i.
(energy of
backscatter pea
= O.ISMev)
;*;;;;T!I
full width at half maximum = 6ft channelsL
! i out of 66 channels - 10% i
peak area = shaded region
Compton edge
(energy of Compton
edge = 0.48Mev)
Compton valley
peak to valley ratio = 6*103 : 2.2x102 = 27 : 1:_J
- : I . . : > i . .-- i.. i i i ! . 'ซ.
peak to Compton ratio = 6x10ฐ
CHANNEL NUMBER
Figxire 8. Spectrum of Cs-137 at 10 keV per channel.
16
-------
due to partial energy transfer by Compton interaction (e.g., the area under the
Compton plateau) . This should not include counts due to the other effects ,
such as the backscatter peak, but can be used for each geometry when systematic
care is used.
7. Compton valley the low portion of the spectrum immediately pre-
ceeding the full energy peak.
8. Backscatter peak Another characteristic of the Compton area is the
backscatter peak. When photons emitted from the sample interact (by Compton
effect) with surrounding materials such as the background shield, the photons
that are scattered through an angle of approximately 180ฐ have a possibility of
interacting with the crystal detector. Quite often these "backscattered"
photons result in a peak which is superimposed on the Compton continuum. The
energy of the "backscatter peak" is equal to the energy of the incident gamma
ray minus the energy of the ejected electron. This backscatter peak energy can
be calculated by the equation:
E
Energy backscatter peak = ^ + ^ Q1 (Eq. 17)
Y
where E is the incident photon energy.
The backscatter peak becomes less noticeable as the incident gamma
energy increases. This is due to the fact that with increasing energy the
total Compton cross section decreases, and the angular distribution of the
scattered photons from Compton interaction becomes more predominant in the
forward direction; therefore, the backscattering becomes less. Unlike the
Compton edge, the backscatter peak has a maximum energy of 0.256 MeV.
The backscatter peak may also be affected by the geometry relation-
ship between the sample and crystal. This effect is especially observed when
comparing a well crystal with a flat crystal. The flat crystal will have a
more prominent backscatter peak, due to the greater probability of the photons
interacting with other substances before they interact with the crystal.
Examples of backscatter peaks are shown in Figures 5 and 8.
9. Escape peaks Escape peaks are denoted as spectrum peaks at some
energy less than the photopeak energy. These result when discrete amounts of
energy escape from the crystal. Using a similar nomenclature, the so-called
Compton continuum might well be called a Compton escape continuum.
The most predominant type of escape peak is due to pair-production
interaction and its subsequent annihilation radiation. When the pair-produc-
tion positron interacts with an electron, they both disappear and two 0.51-MeV
photons are given off at 180ฐ from each other. If this annihilation takes
place near the surface of the crystal, one of the two photons may escape the
crystal while the other is absorbed. By* repetitions of this occurrence, a
second peak occurs in the spectrum which is at an energy 0.51 MeV less than the
photopeak. Of course, this type of escape peak will only be seen for incident
gamma rays of over 1.02 MeV as pair production will not occur below this en-
ergy. There is also the possibility that both annihilation photons will
17
-------
escape, causing a second escape peak to occur at 1.02 MeV less than the photo-
peak energy. The occurrence of two such escape peaks, at 0.51 and 1.02 MeV
less than the photopeak, is sometimes referred to as pair peaks.
A second type of escape peak is due to the fact that the photoelec-
tric absorption in sodium iodide scintillation crystals occurs mainly in the
iodine K-shells. This requires a minimum of 33.2 keV energy in the incident
radiation in order to eject a K-shell electron from the iodine atom. The
binding energies of the K- and L-shell electrons are 33.2 and 5.2 keV respec-
tively. A characteristic x-ray equal to the differences between these binding
energies, 33.2-5.2 = 28 keV, is emitted when the K-shell vacancy is filled. If
this X-ray is emitted near the boundaries of the detector, there is an appre-
ciable probability of its escape. This results in another peak in the spectrum
28 keV less than the photopeak and is referred to as the iodine X-ray escape
peak. Iodine escape peaks are significant features of spectra of gamma rays
with energies between 33 and 200 keV. The energy of the escape peak may be too
low to appear in the spectrum, or at higher incident gamma energies (approxi-
mately above 200 keV) it may be incompletely resolved from the photopeak.
Further, the probability of generating an iodine X-ray escape peak declines
with increasing energy of the incident radiation. For the most part, this is
a result of greater penetration of the more energetic radiation into the
crystal before the photoelectric interaction takes place, with the resulting
smaller probability for escape of characteristic X-rays originating deeper in
the crystal. Figures E-36 and E-37, Appendix E, illustrate iodine X-ray escape
peaks.
10. Sum peaks "sum peaks" is the general terminology for portions of
gamma-ray spectra that are the result of more than one photon interacting with
the crystal within a sufficiently short period of time so that the combined
light emissions of the crystal are seen as one single light pulse by the
photomultiplier tube.
One common type of sum peak is associated with positron annihilation
radiation when a positron-emitting source is counted in a well crystal. In
this case, the two back-to-back 0.51 MeV gamma photons may both interact,
resulting in a spectrum peak at 1.02 MeV.
Some of the 0.51 MeV photons may escape, resulting in both a 0.51 and
a 1.02 MeV peak from positron emitters. With a flat crystal there is little
probability that a 1.02 MeV peak will occur, and the 0.51 MeV peak will be the
only indication of a positron emitter.
Coincidence sum peaks result when two or more gamma rays are emitted
from a nucleus in cascade, and are absorbed by the detector. Coincidence sum
peaks have been discussed previously in describing the spectra of zyCo.
Figure 5 illustrates this type of sum peak.
Accidental sum peaks occur when gamma rays from two or more nuclei, or
origins, are detected simultaneously. The intensity of an accidental sum peak
varies as the product of the intensities of the peaks being summed. At low
count rates, they will be weak. As the count rate increases, the intensity of
18
-------
the accidental sum peak will increase faster than the intensity of the full
energy peaks being summed. Figure E-2, Appendix E, shows an accidental sum
peak resulting from the coincidence of a 1-274 MeV gamma ray and a gamma ray
from a positron annihilation.
The intensity of coincident full-energy peaks is linearly related to the
efficiency and geometry of the source-detector combination. The intensity of
a sum peak is proportional to the product of two efficiency terms and is
proportional to the square of the geometrical efficiency. Thus, to tell if a
peak is a full-energy peak or a sum peak one can either change the geometry of
the counting system or otherwise vary the efficiency of gamma detection of the
gamma rays. For example, suppose the intensity of one gamma ray is related to
the activity of the sample by:
"""I = ElAo (Eq* 18)
where E is the probability of detecting the peak, A is the activity of the
sample, and I is the measured intensity of the gamma ray. The intensity of
the second gamma ray is related to the activity of the sample by:
I, = E.A^ (Eq. 19)
ฃ* ฃ O
and that the gamma rays are emitted in coincidence; then the intensity of the
sum peak is:
I = E_E0A (Eq. 20)
sum 1 2 o
If the efficiencies of detection are reduced by two, and a second
measurement is made, the recorded intensities designated with asterisks will
be:
El Zl
T* = A =
1 1 2o 2
!* = _ฑ -ฑ. A = -^ (Eq. 21)
sum 2 2 o 4
Thus, by changing the efficiencies by a factor of 2, the ratio of Ii/l2
remains the same, but the ratio of either full energy peak to the sum peak
(Ii/I or I ?/I ) increases by 2.
if sum " sum
11. Resolution the resolution of a spectrometer is a measure of its
ability to resolve two peaks that are fairly close together in energy. The
resolution of a full energy peak is defined as follows:
R = M x 100 (Eq. 22)
E
19
-------
where R = the resolution in percent
AE = the full width of the full energy peak at half of the
maximum count level [full width half maximum (FWHM)],
measured in energy units (channels times the energy per
channel)
E = energy of the photopeak (energy represented by the centroid
of the photopeak)
In Figure 8 the full energy peak is in channel 66 and the FWHM is
5.5 channels. With a calibration of 10 keV/channel, the resolution is calcu-
lated to be 8.3%.
Using Figure 8 for reference, one could choose channels 52 thru 55
to determine the low energy boundary of the full energy peak. It is recom-
mended that channels 59 through 66 not be used for this selection since
instrumental drift and small changes in resolution can lead to selecting a
different efficiency. Channels 77 through 85 would provide a satisfactory
boundary on the high energy side. If computer analysis is not available, one
should take as much leeway as possible in defining regions to determine count
rates.
The convention for activity is not as simple as it first seems.
Activity per se is defined as the number of nuclear disintegrations per unit
time. Some conventions choose to relate this to the parent activity of a
nuclide which has radioactive daughters. Other definitions relate efficiency
only to the number of gamma rays of a particular energy. When suitable sam-
ples, e.g. those that only emit one gamma ray, or those that emit two gamma
rays not in coincidence, are available, it is recommended that one determine:
__. . sum of all the counts per unit time
total efficiency = :rr ,. ., (Eq. 23)
activity of the sample v H '
sum of the counts in full energy
,. ^. . peak per unit time .
gamma efficiency = rf- -f- .- (Eq. 24)
number of gamma rays emitted from
the sample per unit time
__. . counts in a defined area . ^_.
sample efficiency = :rr . (Eq. 25)
e activity of the parent radionuclide
where the number of gamma rays is determined from the activity by N , which
is the gamma branching ratio times the activity. Yg
When measuring sample efficiency, one must know that the sample is in
equilibrium, or make a curve relating efficiency to the time of purification of
the sample.
20
-------
EQUIPMENT
Gamma ray scintillation detectors are usually obtained from commercial
suppliers as an integral unit consisting of a Nal(Tl) crystal optically
coupled to a photomultiplier. The detector unit is constructed light-tight
and hermetically sealed because of the hygroscopic nature of the Nal(Tl)
crystal. Some detector units are furnished without a bias network or tube
base, which must then be ordered separately from any of the vendors.
A Nal(Tl) crystal fluoresces with a blue light when exposed to ionizing
radiation. The light emitted from the crystal is proportional except for low
values due to the energy deposited in the crystal by the ionizing radiation.
Photomultipliers are able to detect the light pulse and produce a correspond-
ing charge pulse. The amount of charge produced by the photomultiplier is
proportional to the amount of light incident on the photocathode of the photo-
multiplier which in turn is proportional to the light produced by the interac-
tion of the gamma rays with the Nal(Tl) crystal. The optical efficiency of
the gamma ray scintillation detector is enhanced by:
1. Optically coupling the Nal(Tl) crystal to the photomultiplier tube
by the use of ophthalmological petroleum jelly or a silicone oil to reduce
light losses through total internal reflection.
2. Rough grinding the surfaces not in contact with the photomultiplier
tube to improve the transmission of light to the exit surface.
3. Placing a reflective material, e.g., magnesium oxide or alpha alum-
inum oxide (Linde 'A1ฎ abrasive), in contact with the exposed surfaces of the
Nal(Tl) crystal.
Gamma rays have well-defined and unique energies. When a gamma ray is
totally absorbed in the Nal(Tl) crystal, the resulting light pulse and the
subsequent current pulse from the photomultiplier will be quantified and the
amplitude will be proportional to the energy of the gamma ray. This electri-
cal pulse (charge), as measured by a multichannel analyzer, is called the full
energy peak or, sometimes, the photopeak. If the gamma ray is not totally
absorbed in the Nal(Tl) crystal, the resulting pulse will be of a lesser
magnitude than the full energy peak and constitutes a pulse in the Compton
continuum. The Compton continuum extends from essentially zero to a maximum
energy value called the Compton edge.
The number of gamma rays that are totally absorbed versus the number of
gamma rays partially absorbed is a function of (a) the energy of the gamma
rays, (b) a combination of the source geometry and detection geometry, (c) the
ฉRegistered trade name.
21
-------
material surrounding the source and the detector. Although it is possible to
calculate the portion of gamma rays that will be totally absorbed, it is
easier and usually more accurate to measure this portion by using calibrated
radionuclide sources for each radionuclide and geometry of interest.
Nal(Tl) crystal sizes suitable for environmental analysis range from
5.1-cm diameter (2-inch) by 5.1-cm thick (2-inch) to 22.9-cm diameter (9-inch)
by 10.2-cm thick (4-inch). The more commonly used sizes are the 7.6-cm (3-inch)
by 7.6-cm (3-inch) and the 10.2-cm (4-inch) by 10.2-cm (4-inch). Detection
efficiency is a function of volume; thus the larger Nal(Tl) detectors are more
desirable, but they are also more easily damaged and more expensive. Further-
more, the larger the detector, the more poorly it measures low-energy gamma
rays. Large detectors require a thicker shield to protect the Nal(Tl) crystal,
resulting in the absorption of many photons. Also, those photons which do
enter the crystal tend to interact the farthest from the light exit, resulting
in a lower efficiency through excessive light loss. Small samples may be
analyzed efficiently and with high resolution by the use of well detectors.
The well detector Nal(Tl) crystal is metal-sheathed and has a cavity or well
into which radioactive samples are placed for counting. The geometrical
factor for samples in a well counter is as much as twice that possible for a
cylindrical detector, resulting in a proportionally higher sample count rate.
Components of gamma spectroscopy systems have been largely standardized
following the advent of the U.S. Energy Research and Development Administration
(formerly U.S. AEC) "NIM" (nuclear instrumentation module) specifications.
Amplifiers, single channel analyzers and other components supplied by one
manufacturer can be used with the components supplied by other manufacturers.
Unfortunately, the NIM standards are not complete and there are, therefore,
some units that are not interchangeable. The most notable exceptions to
compatibility between modules are found in printing units such as printing
timers and printing sealers. If any part of a data readout system is different
from the other parts of the data system, one must ascertain the compatibility
of the units. The other area of possible noncompatibility is between ampli-
fiers and preamplifiers. If a separate power supply and signal cable are used
for the preamplifier, the noncompatibility does not matter. However, if the
power and signal for the preamplifier are connected directly to the amplifier,
care must be used to make sure the units are compatible. In most cases, a
small wiring change will be necessary, but this is easily accomplished by any
electronics technician.
The NIM bin and power supply is the mainstay of modern electronics. All
other modules go into this one unit. Amplifiers, single channel analyzers,
power supplies, timers, sealers, etc., are compatible with these units. A
fully-wired NIM bin gives the user all the versatility available.
There are many configurations and electronic options available for gamma
spectroscopy. The following basic gamma spectroscopy system is adequate for
routine environmental analysis, but other combinations of components are also
used. The necessary components are:
1. A Nal(Tl) detector, 7.6-cm by 7.6-cm or 10.2-cm by 10.2-cm, optically
coupled to a photomultiplier tube.
22
-------
2. A tube base or stand to support the detector and to support the
detector and samples.
3. A preamplifier.
4. NIM bin.
5. A linear amplifier.
6. A high voltage supply.
7. A multichannel analyzer having a minimum of 200 channels.
8. Signal and power cables.
9. A readout unit.
10. A radiation shield
Figure 9 is a typical block diagram and Figure 10 is a photograph of a
gamma spectroscopy system in use at the Environmental Monitoring and Support
Laboratory in Las Vegas, Nevada.
Source
A
Multichannel Analyzer
expected shape of electronic signal
from detection of gamma ray.
Figure 9. Typical block diagram of gamma ray spectrometer.
23
-------
Figure 10. Gamma-ray spectrometer at the Environmental Monitoring and
Support Laboratory, Las Vegas, Nevada.
The tube base is connected directly to the detector-photomultiplier tube
combination. High voltage is usually connected directly to the tube base
although it can be fed through the preamplifier in some cases. The preampli-
fier should be coupled to the tube base with as short a cable as possible to
reduce electronic noise. The detector and preamplifier should be suitably
mounted in a shield of iron or lead to reduce the background from radiation as
much as possible. Mounting of the detector-photomultiplier tube for environ-
mental measurements is very important. The mounting should be stable so that
samples can be positioned reproducibly and close to the detector. The shield
must be large enough to hold the detector and any sample that will be counted.
The shield should be at least large enough to accommodate a 4-liter Marinelli
beaker. (See Figure 15.)
The signal from the photomultiplier tube is fed to the preamplifier and
the signal from the preamplifier is fed to the linear amplifier. The final
signal from the linear amplifier should be between 1 and 10 volts for most
analyzers, though some older analyzers require other signal levels.
A typical signal from a preamplifier is shown in Figure 11. The signal
has an amplitude of approximately 5 millivolts, a rise time of 100 nanoseconds
and a 50-microsecond decay. This pulse is amplified and shaped by the linear'
24
-------
amplifier resulting in a pulse similar to that sketched in Figure 12.
100nsec
5 mv
50 msec
O
Figure 11. Schematic representation of a typical pulse from
a preamplifier coupled to a Nal(Tl) detector.
Figure 12. Schematic representation of typical pulses from a linear amplifier
in a Nal(Tl) spectrometer.
25
-------
The signals from the linear amplifier are analyzed by the use of a multi-
channel analyzer. This instrument sorts the electrical pulses from the linear
amplifier according to their magnitude and records each in its appropriate
"channel." Multichannel analyzers for Nal(Tl) detectors should have a minimum
of 200 channels, a display unit, usually an oscilloscope, and a means for
recording the data, e.g., a teletypewriter, paper tape punch, parallel printer,
or magnetic tape.
26
-------
INITIAL SETUP
The counting room should be specifically set up for counting source
preparations. Laboratory work should not be performed in the same room, or at
least not in the same work area, as the detector shield. The counting room
should be well ventilated to eliminate the possibility of radon buildup. The
temperature should be regulated to within 2 degrees Celsius. Although it is
not mandatory for some applications, the counting area should be free of vi-
bration when high resolution or high precision experiments are being performed.
The electric power supply for counting instruments should be well regulated
and isolated from motors, air conditioners, electric adding machines and type-
writers/ etc. An electrical interference filter placed in the electric power
supply of the offending appliances or device is usually more helpful than
placing it in the electric power supply of the counter. A separate ground to
earth should be provided and used. Adequate space should be provided between
shields and instruments to facilitate safe use and maintenance. No sources
should be left or stored in counting rooms in order that the background may be
kept as low as possible. Sources should be stored where they are secure from
loss and do not constitute a radiation hazard.
With the shield in place, the detector mounted., and the electronics
assembled, initial calibration can begin. The high voltage is usually ad-
justed to 1000 volts. Using a check source of cesium-137 or cobalt-60, the
amplifier gain should be adjusted to produce pulses on the order of 5 volts,
or approximately at half of maximum channel number on a multichannel analyzer.
After the photomultiplier tube has had voltage applied for 1 to 3 days, a test
should be made to see if the count rate is independent of small variations in
applied voltage. First one turns on the analyzer. If the number of events
being recorded in the lower channels of the analyzer is large, the low-level
discriminator may need adjusting. If there are no counts being recorded it is
possible that the low-level discriminator has been adjusted incorrectly. In
this case the discriminator should be adjusted until low-energy events are
being detected, and then adjusted until no low-level events are being detected.
This will produce an approximate setting to be used for determining the cor-
rect bias on the detector. Using a gamma-emitting check source, adjust the
voltage to 900 volts or 100 volts lower than the manufacturer's suggested
operating voltage. Count the source for a convenient period of time and
record the total number of counts in the full energy peak. At least 10,000
counts should be acquired. Increase the voltage by 10 volts, and re-count the
source. Repeat until the high voltage has been increased to 1100 volts or 100
volts above the manufacturer's suggested operating voltage. If necessary, the
gain on the main amplifier may need adjustment to keep the full energy peak in
the range of the analyzer. A plot of.the counts versus the applied voltage
should be flat, or nearly so, for at least 100 volts. The appropriate high
voltage is at the center of this plateau or at the manufacturer's suggested
operating voltage. The bias should be adjusted to this value and left on
27
-------
continuously except for maintenance.
The next step is to correctly calibrate the system for energy. To do
this, a source with two gamma rays differing significantly in energy, or two
sources with differing gamma-ray energies are used. A practicable energy per
channel should be chosen. Ten keV per channel is extremely convenient, but
twenty keV per channel can be used. A calibration at five keV per channel may
be used advantageously for identifying spectral components below 200 keV.
Other energies per channel can be used, but should only be used by experienced
investigators. Ten keV per channel will cover 0 to 2.56 Mev for a 256-channel
analyzer, which is a good range for environmental monitoring. Bismuth-207 or
a combination of cesium-137 and cobalt-60 are convenient sources for energy
calibration.
Once the check sources are chosen, and the energy range is selected, the
gain of the amplifier is adjusted to put one peak in the correct channel for
that peak. The other peak is located. If it is too close to the other peak,
more gain and more low-level discrimination is indicated and vice versa. By
alternately adjusting the gain and a low-level discriminator or the zero to
the analog to digital converter (ADC), both peaks can be placed in their
proper channels. It is possible to estimate peak positions accurately to
within 0.1 channel using a parabolic fit to the data. The peak is located by
finding the channel with the most counts. A set of data is then obtained
consisting of the channel number and the counts in that channel. The first
set, the channel below the peak channel, is labeled (0, Ng) , the peak channel
is labeled (1, Nj), and the third channel, the channel above the peak, is
labeled (2, N2). For ease of calculation, the minimum count of NQ and N2 is
subtracted from NQ, NJ and N2. Thus three pairs of numbers are obtained. For
convenience in this derivation assume N2 be the minimum.
(0, NO')
(if N!T)
(2, 0)
where NQ' = NQ - N2
N} NX N2
N2' = N2 - N2 = 0
These are then used in the equation for a parabola
y = ax2 + bx, + c (Eq. 26)
where x is the first number, and y is the second number in the pairs of num-
bers so far determined. Using these pairs, three equations are obtained.
NO'
NX' = a + b + c
0 = 4a -f 2b + c
28
-------
These equations are then solved for a, b, and c, e.g.,
Nl" ~ No' = a + b
- NO' = 4a + 2b
a = -!5(2N1' N0') (Eq. 27)
b = NX' - N0' a (Eq. 28)
The peak is found by differentiating the parabolic equation (dy/dx) and solv-
ing the derivation for dy/dx = 0, e.g.,
^ = 2a x + b (Eq. 29)
x = ~ 2a (Eq- 30)
The peak then is located at the channel called 0 plus the value of x, or the
peak channel previously found minus 1 plus the value for x.
With persistence, both peaks should be brought to within 0.1 channel of
the proper location. After this is accomplished, a third peak should be
determined to verify the energy calibration. The energy calibration should be
verified daily and records of verification kept as part of an ongoing quality
assurance program. It is recommended that a source, or sources, be made for
this purpose.
The next phase involves establishing a background rate, checking time,
and determining reproducibility. Backgrounds should be measured daily for at
least 20 days and nights to determine expected fluctuations in the rate.
Backgrounds should be determined at various times of the day and for night
counting. Long counts, as well as counts for the expected or usual analysis
time, are needed to verify any pattern or to obtain statistical accuracy. A
100-minute background measured with a 10.2-cm by 10.2-cm Nal(Tl) detector is
shown in Figure 13. Six prominent peaks appear in this spectrum. The 0.511
MeV peak arises from annihilation radiation of cosmic positrons. The 0.61,
0.72, 1.13, and 1.76 MeV peaks are due to radon daughter products. Potassium-40
accounts for the 1.46 MeV peak. Any other prominent peaks in the background
indicate nearby sources which should be removed, or contamination of the
counting area which needs to be decontaminated. The shape of the background
shown in Figure 15 shows the typical higher count rate at lower energies that
occurs naturally. I
The time base on the analyzer should be checked with the same check
sources used in determining the energy alignment. Counts for all time periods
(usually 10 to 400 minutes) are taken, and the count rate determined. The
count rate (counts/unit time) should be the same for all time periods used. A
calibrated pulse generator can be used for this check. Pulsers that use 60-
cycle alternating current for their signal are commonly used and are quite
accurate. These not only check consistency in the analyzer timing, but can
indicate the accuracy of the absolute timing of the analyzer.
Timing tests should be conducted at moderate count rates, i.e., 200
counts per second (cps), and with the analyzer set in the "live time" mode. A
29
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10
10 0
10-1
GROSS
CPU
10-2
10-3
03.5
80 120
CHANNEL NUMBER
160
200
Figure 13. 400-minute background spectrum measured with a
10.2-cm x 10.2-cm Nal(Tl) detector.
30
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weak high energy source having a half-life sufficiently long that a decay
correction need not be used, e.g., zinc-65 should be used for this test.
After the timer accuracy has been established, a "live time" test should be
made. The most probable error in a live timer will be at high count rates
which should not be encountered in environmental monitoring, but might occa-
sionally occur when counting standards have too much activity. The live-
timer test is based on the following reasoning: if the live timer works
accurately for a particular setting, the analyzer will be "alive"that is, in
readiness to accept signal pulsesfor the same accumulated time regardless of
count rate. Therefore, if a weak source and a hot (high activity) source are
counted simultaneously, the total counts of the weak source recorded should be
the same as if the weak source were being counted by itself. A hot low-energy
source and a weak high-energy source are used for the live-timer test. Typical
sources used are mercury-203 (15,000 cps) and zinc-65 (200 cps) .
First, the hot source and weak source are counted simultaneously. Next,
the weak source is counted alone. The counts in the photopeak of the weak
source are totaled for both runs. A comparison of the totals indicates the
accuracy of the live timer. A pulser can be used in the place of the weak
source and thereby eliminate the uncertainty due to the error in integration
of the weak source photopeak. However, consideration should be given to the
possibility of errors due to momentary lock-in of the pulser with the analyzer
live timer. If there is a simple test or check for random coincidence, it
would be of interest. Live timers of analyzers evaluated by other laboratories
have shown inaccuracies ranging from 12 percent down to less than 0.5 percent
for input rates up to 30,000 pulses per second. (I).
31
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CONTROL CHARTS
Before initiating calibration procedures for quantitative work, quality
control charts should be prepared and a routine should be established for
maintaining the control charts. A daily plot of the gross background per unit
time is the first chart to prepare. Any statistically significant deviation
from the average rate should be investigated, and the reason for the change
eliminated. Short (10 to 15 minutes) repetitive counting on a given day will,
in fact, produce background rates with the expected standard deviation, as
will short repetitive counts of a check source. Long counts (400 minutes to
1000 minutes) taken over a long period of time generally will show fluctua-
tions in the background rate larger than counting statistics would indicate.
These fluctuations arise mainly because of changes in radon levels in the
counting room. However, one can still determine the observed standard devi-
ation, and this deviation should then be used to prepare the quality control
chart.
The standard deviation (a) for N counts is ฑ i/N. The control chart,
therefore, has days for the horizontal axis and counts for the vertical axis.
Horizontal lines at N, N ฑ la, N ฑ 2a, and N ฑ 3a should be drawn on the
chart. As the number of determinations is increased, the number of points
plotted between N and N ฑ la should approach 68 percent of the total number of
points; the number of points between N and N ฑ 2a should be close to 95 per-
cent of the total number of points. There should be almost no (less than 0.2
percent) data points outside of the lines indicating 3a deviation from the
average. Any point outside this range is suspect, and an immediate redetermi-
nation of the background should be made. If the redetermination is also out
of the control limits the cause for the change in the background should be
determined and corrective action taken. If the change is an increase in the
count rate, a source has been left in the counting area, the counting area has
become contaminated and should be decontaminated, or the electronics is adding
counts. A cause for a decrease in the background rate could be electronics or
the presence of material in the counting area which is acting as a further
shield for the counting system. Backgrounds for each type of sample and
sample configuration to be analyzed should be documented and plotted on the
control charts, as they can be quite different.
Similar charts should be made for each of the two peaks which are used
for determining energy calibration. The total number of counts in each peak
is determined and this becomes the center line for the graph. Again, ฑ la,
ฑ 2a, and ฑ 3a lines are indicated and the data plotted daily. Any number
outside of the ฑ 3a control limits indicates that corrective action is needed.
Background should be subtracted from the counts accumulated in the analyzer.
The section on data analysis explains how to determine the total number of
counts in each peak.
32
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Other parameters that should be plotted on the control charts are peak
position of each peak (channel number), and the full width at half-maximum for
each peak. To determine full width at half-maximum, the number of counts in
the peak channel is determined. Then the adjacent channels above and below
the peak that have counts less than and greater than one-half of the peak
intensity are found. Assuming linearity, the half-maximum points are found by
linear interpolation. The difference in the channel numbers plus 1 is then
the full width half-maximum. Data can be plotted as number of channels,
percent of energy, or in keV.
When all of the sample data remain within the control limits, it may seem
like a waste of time to continue obtaining control data on a daily basis.
However, if the data go out of control, the immediate identification of a
problem will be extremely gratifying. Also, the first unusual analysis of an
environmental sample will not require a recalibration for confirmation. The
continuing effort in maintaining these quality control charts is the cheapest
insurance available for assuring precise and accurate data from the counting
system.
33
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DATA ANALYSES
If the pulse height spectrum from an environmental measurement is rela-
tively simple, a straightforward hand analysis can be made. Areas of each
photo peak are determined as described earlier. Then the activity of each
radionuclide is given by
A = -ฃ- (Eq. 31)
o e $
where A is the calculated activity, A the count rate observed, e is the effi-
ciency of the detector at the energy of the gamma ray producing the full
energy peak, and 6 is the fraction of gamma rays emitted per disintegration.
This method is adequate for simple spectra that have only a few well-separated
full energy peaks. Care must be used to determine A consistently. e has to
be defined carefully. In the simplest case, e is determined directly by
calibration with a standard. If e is determined from an e-versus-energy plot,
care must be taken to account for all events giving the full energy peak.
Escape losses at low energy should be considered. A more common problem is
that of losses due to coincidence gamma rays. If the gamma ray is part of a
cascade, there is a good chance that the full energy peak will be smaller than
it should be and that there will be a coincidence sum peak in the spectrum.
Analyses of coincidence is somewhat more complicated and generally a computer
will be needed to correct for coincidence losses.
The so-called "matrix" method is widely used for more complex spectra.
This method requires that the background be stable and well known, and that
good reference samples have been prepared and measured. The matrix method has
been used satisfactorily for analyses of up to eight radionuclides. It is
amenable to calculation by hand for four or less radionuclides, but a computer
is recommended for analyses of five to eight radionuclides.
Deciding on the number of radionuclides and selecting them constitute the
first step. Good standards should then be obtained and single radionuclide
spectra run for each of the geometries with the appropriate sample matrix. The
background should be removed from each of the spectra.
The next step is to select a full energy peak for each radionuclide.
Care should be taken in the selection. Often the strongest gamma ray should
be used, but on occasion, two gamma rays will overlap and another line should
be used. After selecting the full energy peaks, select the channels which
will be summed to determine the area of the peak. Generally, it is best to
use the full peak area, rather than the peak as defined at 1/3 or 1/2 peak
height. Normalize each spectrum so that the area of the full energy peak is
equal to 1 (unity).
Determine the area for every full energy peak of the interfering radionu-
clides that lie in that portion of the spectrum in which the full energy peak
34
-------
of the radionuclide of interest is found. This area is then called the inter-
ference factor, F , .
ab
F is the ratio of the area of radionuclide b to the full energy peak of
radionuclide b in the area of the full energy peak of radionuclide a.
Once the set of interference factors is determined, the matrix can be set
up. Two examples are described below.
Assume radionuclide a_ gives the spectrum labeled A in Figure 14 and
radionuclide b_ gives the spectrum labeled B in Figure 14 after the background
has been removed. Areas under each region are labeled.
If the two radionuclides were put in the same sample, under reasonable
conditions the resulting spectrum would be that labeled C in Figure 14.
The count rates are given by
Nl = s
N2
Solving for C and C we have
C
and
C,
or
c
,,_
ab b
F. C + C,
ba a b
Nl
N
2
1
F
ba
1
Fba
1
Fba
Fab
1
Fab
1
Nl
N2
Fab
1
Nl - FabN2
1 - FabFba
(Eq. 32)
(Eq. 33)
(Eq. 34)
and
C, =
N., - F, N.
2 ba 1
1 - F F
1 ab ba
(Eq. 35)
then if the activity of radionuclide a_ is in picocuries per gram (pCi/g) - EaC
and that of radionuclide b_ is in picocuries per gram (pCi/g) = Ej-C^
where E and Eb are previously determined efficiencies for radionuclides a. and
b_, we are able to determine the activities of radionuclide a_ and b_ when they
are in the sample together.
For four radionuclides, the set of linear equations will look like this:
NI = G! + F12C2 + F13 C3 + FmCit (Eq. 36)
35
-------
SPECTRUM A
10
10 15
CHANNEL NUMBER
20 ,
SPECTRUM B
o
LU
o
o 30
10 15
CHANNEL NUMBER
20
10
0 I I I I I I I I I I
SPECTRUM C
I I
10 15
CHANNEL NUMBER
20
Figure 14. Idealized spectra illustrating interference factors
and summation of gamma rays in a gamma-ray spectrometer.
36
-------
N2 = F21C1 + C2 + F
N3 = F31C! + F32C2 + C3
F2itCit (Eq. 37)
(Eq. 38)
(Eq. 39)
Where F. . = the fractional area of isotope j_ i-n the region used to define
the full energy peak of isotope i_, and
C . = the count rate of isotope i_.
The solution to these sets of equations is :
GI = {N1[(l-Flt3F31+) - F32(F23-F43F2Lt) + F42 (F23F3tt-F2l+) ]
- N2[F12(l-Ftf3F3tt) - F32(F13-FH3Fltt) + F42 (F! 3F3l+-Flt+) ]
+ N3[F12(F23-F43F2U) ~ (Fi3-F43F14) + F42 (F! 3F24-F23Fltt) ]
- Ntt[F12(F23F3u-F2tt) - '(F13F3l+-Fltt) + F32 (Fl 3F24-F2 3Fll+) ] }/A (Eq. 40)
C2 =
C3 =
{-N1[F21(l-Flt3F34) - F31(F23-Fl+3F2i+)
+ N2[(l-Fi+3F3l+) - F31(F13-Flt3F14) +
- N3[(F23-FLf3F21+) - F2i(F13-Flt3F1if) + F41 (F! 3F2^-F23Fllt)
- F21(F13F31+-F11+) + F31 (Fj 3F2l+-F23Fltf )
{N1[F21(F32-Fi+2F3it) - F31(l-Ftf2F2it) + F4i (F3it-F32F2if) ]
- N2[(F32-Fit2F34) - F31(F12-F1+2F14) + F^ (F12F3lt-F32Fltf)
+ N3 [ (l-Ftt2F2i+) - F2 i (F^2-Fit2F^i1.) + F^j (F^2F2it-F^if) J
- F21(F12F34-F32F14) + F3i(F12F2if-F1if)
d-F32F23)]
!(F12-F32F13)
(Fl2F23_Fl3)
-Pi 3>
{-Ni[F21(F32F43-Fit2) - F3i(Flt3-F42F23)
+ N2[(F32F43-Fit2) - F31(F12Fit3-F42F13)
- N3[(F43-Flt2F23) - F21(F12F43-Fit2F13)
+ N,J(1-F32F23) - F21(Fi2-F32F13) + F31
Where A
- F32 (F23-F43F24) +
- F21[F12(l-F43F3tt) -
(F23F34-F24)
(Eq. 41)
(Eq. 42)
(Eq. 43)
(Eq. 44)
37
-------
- Fltl[F12(F23F3it-F2if) - (F13F3tt-F1it) + F32
Another form for the solution of these equations can be found using the Gauss
Reduction.
Rewriting equations 36 through 39, after dividing by the coefficient of
GI we get
cl + F12C2 + F13C3 + FmCtt = NX (Eq. 45)*
Ci + C2 + C3
Ci
. 47)
Subtracting equation 46 from 45, equation 47 from 46, and equation 48 from 47,
we get
X1C2 + X2C3
X5C6 + X6C3 + XyCit = X8 (Eq. 50)
X9C2 + X10C3 + X11C4 = X9
Where X: = F12- -- x? =
1 1Z F21 X F21 F31
X9 .
F21 F31 11 F31
Xl2 =
*Equation 36 divided by FU which is 1.
38
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Continuing the process
c' + if C3 + If c- - If
Subtracting equation 53 from 52 and equation 54 from 53 leaves
Where
X5 x5 X9
Xl = X2._ Xjj
X5 Xl7 X5 X9
xl X5 io X5 Xg
Again, continuing the process, we obtain
Xl5 X18
. 53,
= X15 (Eq. 55)
X16C3 + XiyC^ = X18 (Eq. 56)
Xl3
^T (Eq. 57)
X17
Xl3 X16
By putting C^ in equation 55, we can solve for 3, then putting 03 and C^ in
equation 52 we solve for 2- Cj is determined by putting the values determined
for C2, 3 and C/^ in equation 45.
39
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CALIBRATION OF THE SYSTEM
After the method of data analysis has been selected, the final steps in
calibrating the counting system are the selection of sample types having suit-
able geometries and the preparation of calibration standards containing the
isotopes that are expected to be found in the various types of samples. Geom-
etries should be chosen that are easily prepared and are readily reproducible.
Fewer geometries facilitate the ease of calibration but limit the samples that
can be analyzed. Some sample types commonly used, each having its own pecu-
liar geometry, are:
1. Marinelli beaker, 4-liter
2. Plastic container, 400-ml
3. Plastic container, 200-ml
4. Air filter, 5.1-cm
5. Air filter, 10.2-cm
6. Liquid scintillation counting vial, 20-ml
7. Ampul, 5-ml
8. Point sources
9. Charcoal cartridges
10. Filters, 2.54-cm
These sample types are shown in Figure 15. Except for the Marinelli
beaker, source holders should be fabricated for the other geometries to assure
reproducible counting on a routine basis. The source holders can also be used
for protecting the Nal(Tl) crystal from accidental contamination from a leaky
or improperly prepared source. Over a period of time many laboratories make
small variations in their laboratory technique and/or sample preparation
technique without verifying carefully the changes in calibration due to these
minor changes. These changes can result in a systematic change in the count-
ing and lead to large systematic errors in reported data. Because of the low
levels of activity usually encountered, most counting is done with the source
as close as possible to the detector. Great care must be used in positioning
samples near the detector for the reason that small variations in the geometry
enormously affect the counting efficiency of the detector. Also, the samples
should always be at room temperature, unless special precautions have been
taken to avoid sudden thermal changes in the crystal which can crack it.
The accumulation of radionuclides for the calibration library is a formi-
dable task. There are more than 115 different radionuclides reported to be
emitted by nuclear reactors. Sixty-six of these have half-lives greater than
2.5 days and 55 emit gamma rays. Also, the number of naturally-occurring
radionuclides is not small. The sample type can be used to select those
radionuclides which can be considered for analysis. Appendix A lists some,
but not all, of the gamma-emitting radionuclides most likely to occur in the
samples obtained.
40
-------
400 ml. PLASTIC CONTAINER
200 ml. PLASTIC CONTAINER
SCINTILLATION
VIALS
CHARCOAL CARTRIDGE"
5 ml. AMPULES
2.54 cm. FILTER
Figure 15. Common sample holders.
41
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Calibrated radionuclides need to be obtained. These calibrated radio-
nuclides in turn are used to prepare calibration samples for analysis. Each
radionuclide is prepared for each sample type and geometry. The preparation
entails careful work and should be done using the best analytical techniques
available. Generally, the calibrated radionuclide should be diluted gravi-
metrically and the carrier content and chemical form of the sample maintained.
The calibration sample should simulate the type of matrix to be analyzed as
nearly as possible. The calibration sample has to be homogeneous and stable.
At least one background or "unspiked" sample should be prepared for each geom-
etry and sample matrix. These calibration samples are then counted and the
data abstracted for the calibration library. Activity levels should be ad-
justed to give count rates no more than 100 times the activity of the samples
to be analyzed, but preferably about 10 times the activity levels expected.
SAMPLES AND STANDARDS PREPARATION
Sample Collection
It seems imperative that something be said about the collection of sam-
ples in this section on sample preparation. If a proper method or technique
of sample collection is not used/ the collected sample will not be representa-
tive of the environmental area or medium being monitored. A great deal of
thought and care must be exercised in the collection of samples. There are
several situations in which the analyst's treatment of the sample isor
should bedictated by the technique of the sample collection. For example,
if an environmental water sample is collected for the measurement of radio-
isotopes and nothing is done to adjust the pH of the sample at the time of
collection, then the analyst must make such an adjustment and allow time for
the sample to become homogeneous before analyzing it. The type, if any, of
preservative added when collecting milk samples, is a dictating factor in the
analytical method. There must be correlation between the analytical method to
be used and the sample collection technique. It can be said that sample
preparation begins with its collection.
Homogeneity of Sample
Homogeneity of the sample is essential for both accuracy and precision of
analysis with a Nal(Tl) detector. Therefore, every effort must be made to
insure homogeneity. Some samples, as collected, are not homogeneous and must
be made homogeneous before analysis (such as soils and vegetation samples).
Other samples (such as water and milk) are more likely to be homogeneous when
collected but may become inhomogeneous in the sample container unless special
precautions are taken.
Samples such as soil can be made homogeneous by sieving, grinding, re-
sieving, and regrinding, until all of the sample can be passed through a 170
meshor finerscreen and then thoroughly blended.
Water samples collected in any kind of container may lose significant
fractions of their radioisotope and trace elements content to the walls of the
container, thus changing the activity of the sample and making it nonrepre-
sentative of its source. Such changes in the sample can be avoided in most
42
-------
cases by lowering the pH of the sample to below a pH of 1. An acid such as
hydrochloric or nitric which gives soluble salts with most cations should be
used (167 ml of concentrated HC1 or 125 ml of concentrated HNO3 added to a 1-
gallon (3.78-liter) sample will give a sample solution an acidity of 0.3N-
0.5N). It is best to add acid at the time of sample collection. If acid is
not added until the sample reaches the laboratory, there is some uncertainty
as to the time for desorption from the container walls, in which case a wait-
ing period of at least overnight should be allowed between acid addition and
sample analysis. For the addition of acid to samples at the time of collec-
tion, fractions of concentrated acid should be measured into polyethylene
bottles with Poly-Sealฎ caps in a laboratory just before going to the field
for sample collection. Concentrated nitric acid should not be stored in
polyethylene bottles for more than just a few days. In a few cases, the
addition of carriers to the sample may be necessary.
Homogeneity of a sample is demonstrated by analyzing at least three ali-
quots of the sample and checking results for precision. Homogeneity for any
sample should never be assumed without some mixing just prior to taking ali-
quots for analysis.
Stability of Sample
The stability of a sample relates to the physical, chemical, or biologi-
cal state of the sample and often affects its homogeneity. Samples that are
both chemically and physically stable should remain quite homogeneous once
they are mixed. Acid added to water samples and formaldehyde or some other
preservative added to milk act as stabilizers and help maintain homogeneity.
The chemical and physical form of some elements or radioisotopes as they
exist in nature need to be known beforehand in order to stabilize the sample
from the time it is collected until the time it is analyzed. In fact, for
some kinds of analyses the stability of some samples upon removal from their
environmental source may be so questionable as to dictate analysis at the site
of the source.
Standards and Reference Samples
The concept of standards and reference samples may vary somewhat from
laboratory to laboratory so that for the sake of discussion here some defini-
tion is needed. A standard source is here defined as an amount of an element
or compound in some stable form, the content of which is traceable to National
Bureau of Standards (NBS) source materials. The definition is here extended
to include solutions of standard source materials, as it is possible for
solutions of many materials to be made quite stable.
Many times standard source materials received from NBS or another sup-
plier must be diluted for specific uses. The greatest of care must be taken
in making such dilutions to maintain the integrity of the diluted standard
source. The diluent must be physically and chemically the same as the stand-
ard source matrix.
ฉRegistered trade name
43
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A weight-to-weight dilution in contrast to a weight-to-volume or a
volume-to-volume dilution should result in a more accurate diluted standard
source and thus help to insure its integrity.
A particularly useful aid in making weighed deliveries of standard source
solutions is the polyethylene doll's baby bottle with the neck drawn out to
provide a small opening. Standard source solutions can be drawn into the
bottle and weighed deliveries made from the bottle (delivered amounts deter-
mined by weight differences). Solutions can also be stored in the bottles by
simply sealing the tip of the bottle with a mild flame. Water loss through
the walls of these bottles is no more than 3%-5% per year at ambient tempera-
tures .
Once a dilution of a standard source material has been made, then making
the diluted standard source a homogenous source is of utmost importance. Just
as the integrity of the original standard source material rests with its sta-
bility and homogeneity, so also rests the integrity of the diluted standard
source. Solutions of diluted standard source materials should be shaken
vigorously and inverted at least 10 times to insure thorough mixing.
In contrast to a standard source, a reference sample is here defined as a
known quantity of sample matrix to which has been added a measured amount of a
standard source (also, often called a control sample). These samples are
taken through the same analytical procedure as other samples and they give
results from which yield factors are determined.
Reference samples are made from measured aliquots of homogenous sample
materials. After the addition of standard source material, the sample should
be mixed thoroughly so that the standard source material will be subjected to
the same sample matrix influences throughout the analytical procedure as other
samples being analyzed.
44
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STATISTICS AND UNCERTAINTIES IN MEASUREMENTS
Experience and theory indicate that it is impossible to measure any
physical quantity exactly, i.e., with no error. Refinement of theoretical and
experimental methods will reduce, but not eliminate, the possible error of a
measurement. A statement or other indication of the possible error must ac-
company any reported measurement of a physical quantity for the reason that
there is always a gamble on its relative correctness.
In reporting the results of sample activity, the statement of uncertainty
in the measurement should reflect both the uncertainty resulting from the
statistical nature of radioactivity and a liberal estimate of all the system-
atic errors involved in the measurement. Definitions of the terms accuracy,
precision, systematic errors, and random errors must be understood to ade-
quately report on the uncertainties of physical measurements.
1. Accuracy is the comparison of a measurement to its true or accepted
value. An accurate measurement is one which results in a value very close to
the true value. An inaccurate measurement results in a value that is not
close to the true value. In order to obtain accurate values the measurements
have to be precise. In no way, however, does precision indicate accuracy.
2. Precision is only a measure of the degree of agreement of repeated
measurements of the same property. Precision is expressed in terms of disper-
sion about the arithmetic mean of the results of repetitive testing.
3. Random errors are those that arise from:
a. the statistical nature of radioactive decay,
b. variations in sample size, source-detector geometry, yields in
preparation, etc., about a mean value of the respective variable.
4. Systematic errors are those ubiquitous errors arising from assump-
tions that are not measured or evaluated. These are, without doubt, the most
difficult to understand and correct. Systematic errors are present as uncer-
tainties in the activities of the standards used, as limitations in gravimet-
ric and volumetric apparatus and in other standards. For example, they are
ever present as fluctuations in the concentration of radon in the detector
environment and in the assumption that temperature, humidity and barometric
pressure do not affect the measurements. Some systematic errors enter as
gross personal errors, e.g., forgetting to convert seconds to minutes, dpm to
picocuries, ad infinitum.
The inconsistencies presented in comparison data are remarkable in that
the uncertainties indicated seldom overlap. An example of inconsistent
45
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expressions of uncertainties is indicated in Figure 16. Such figures are
typical when measurements of a single quantity by different participants are
compared. The data plotted are obviously in error for the reason that the
uncertainty of a measurement must overlap the true value no matter how inac-
curate the data.
Measured Value
Known Value
( 1
T ' '
I '
1 J
i
- i 1
I
T
1 T
1
1.10
105
100
95
90
B
H
Figure 16. Comparison of analytical results from several
participants when systematic results are not estimated correctly.
Figure 17 is a more realistic plot in which the range of uncertainty
overlaps the true value. Figure 17 shows what is expected when all errors are
indeed known and treated properly. Figure 16 arose from not describing or
from leaving out systematic errors. The random numbers in a few cases are not
treated correctly. There is an overwhelming tendency to treat counting errors
as the systematic error because they can be determined easily, and they appear
to be small. Systematic errors, however, tend to displace the mean whereas
random numbers tend to establish the mean.
Measured Value
Known Value
1.10
1.00
.95
.90
B
H
Figure 17. Comparison of analytical results from several
participants with correct estimation of systematic errors.
46
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In order to analyze the uncertainties in measurements, a knowledge of
statistics and of compounding errors is essential. Two frequency distribu-
tions used in analyzing the results of measurements will be discussed. These
are the normal distribution and the Poisson distribution. The normal distri-
bution and the Poisson distribution are similar for large values of their
respective parameters. Differences, however, still remain significant. It is
very important to know what these differences are so that we can understand
what our measurements are telling us and what they are not telling us. The
conceptual differences remain significant.
The normal distribution applies to a continuously variable observed
magnitude, such as that which results from making many measurements of the
distance between two spectral lines. The Poisson distribution is applied to
discontinuous variables, such as particle counting rates, which take on suc-
cessive integer (whole number) values.
The normal distribution states that the probability (dP ) that x will
lie between x and x + dx is
dP = e 20* dx (Eq. 58)
X 0/2~
where e = 2.7183 (the base of the natural system of logarithms)
m = true value of the quantity whose measured values are x
a = standard deviation, which is a parameter which describes the breadth
of the distribution deviations (x-m) from the mean. The standard deviation is
one of the two parameters, m and a , of the normal distribution.
Figure 18 illustrates the general form of the normal distribution drawn
for a mean value, m , of 100 and a standard deviation, 0 , of 10. The ordi-
nates are normalized so that the total area under the curve is unity [1]. Thus
the area included between any two abscissas, Xj and X2 , is the probability
that a single measurement of x would lie between X! and X2 while a very
large number of measurements of x would have a mean value of m (m = 100
in Figure 18).
The maximum slope of the normal distribution curve falls at the points
x - m = ฑ a. The value of this slope is:
0 /2ire
Tangents to the normal distribution curve at these inflection points intersect
the x axis at x - m = ฑ20. The ratio of the ordinate y^ at these sym-
metrical points of maximum slope to the maximum ordinate, y^ , is
Y = _1
0/2T
at x = m is y /y = e"*5 = 0.6065. The half width is 0/2 In 2 = 1.1770 at
y = y /2 (hal? maximum) and is 0/2~ = 1.4140 at y = y /e (1/e of maximum).
47
-------
00 80.00 90.00 100.00 110.00 120.00 130.00
m o-
m cr
m
m + a- m+ 2o-
Figure 18. Normal distribution with a mean value, m, of 100 and
a standard deviation, a, of 10.
48
-------
Poisson* s distribution describes all random processes whose probability
of occurrence is small and constant. Poisson's distribution has wide and
diverse applicability and describes the fluctuations of such random processes
as the disintegration of atomic nuclei, the emission of light quanta by excited
atoms, and the appearance of cosmic ray bursts. The Poisson distribution
applies to substantially all observations made in experimental gamma-ray
spectroscopy.
The probability of observing a value, x, of a variable which has a
Poisson distribution and a mean value, m, is given by
x
_ m m . ._-.
P = - e (Eq. 59)
x x!
where m may have any positive value and x is an integer. The Poisson
distribution has only the parameter, m, in contrast to the two parameters of
the normal distribution.
Provided one numerical evaluation of P has been made, other neigh-
boring values may be computed quickly by using the following exact relation-
ships :
P . = - P (Eq. 60)
x-1 m x
P
_,,
X+l X+l X
P = e~ (Eq. 62)
o
Some modern electronic calculators have programs that will compute P .
It should be noted that for moderately large values of m (say 100) other
values for P may be found quickly by determining a value of P and then
using the above relationships to find P
The Poisson distribution is slightly asymmetric favoring low values of
x. Thus, substitution of x = m in equation 60 shows that if the mean value
is integer the probability of observing one less than the mean value is the
same as the probability of observing the mean value.
A good approximation of P where x > 10 for any value m (do not
confuse) is :
(Eq. 63)
The probability of actually observing the mean value in a series of observa-
tions of a random process of constant average value is zero. If, however, the
49
-------
integer nearest the mean value of a set of data is accepted in lieu of the
mean, substitution of x = m in equation 63 results in the following values:
m
10
100
1000
m
0.127
0.040
0.013
Note that the probability of observing x = m is surprisingly small when the
integer nearest the value of m is substituted.
The Poisson distribution must always be represented by a histogram be-
cause x can assume integer values only. Figure 19 illustrates the Poisson
distribution for m = 100. The slight asymmetry of the Poisson histogram
0.40
0.36
0.00
70.00 80.00
90.00
100.00
110.00 120.00 130.00
Figure 19. Poisson distribution with a mean value, m , of 100.
50
-------
should be noted as well as the similarity between it and the symmetry of the
normal distribution in Figure 20. For small values of m, say between m = 1
and m = 10, the Poisson distribution is very asymmetric and is not well
approximated by the normal distribution.
23020 .
x + avTT
22870 .
22720 ,
22570
22420 j
22270
o
X = 22570
22120
X -
Figure 20. Control chart for low energy (0.57 MeV) peak from bismuth-207.
Only the mean of a random process can be approached for the reason that an
infinite amount of data would have to be collected, whereas the data at hand,
however large, are finite. The mean is a mathematical entity about which the
data may be either symmetric or asymmetric depending upon the type of distri-
bution. The decided asymmetry of the Poisson distribution for low values has
been noted. The modal value (the most probable value) and the median (the
value which is as frequently exceeded as not) are measures of central tendency,
but are not weighted by each individual datum. Consequently, the best approxi-
mation to m is the arithmetic average, x, of the n separate measurements,
xlt x2, x3 ..., Xn , which may be expressed
n i=n
m ~ x = - 2 x. (Eq. 64)
The "expectation value" of x is m when the above formula is applied to the
data obtained from a large number of random trials.
The spread of random data about the mean value may be expressed by a
parameter called the standard deviation, a. The standard deviation (often
abbreviated S.D.) is defined as the square root of the average value of the
squares of the individual deviations (x - m) for a large number of observa-
tions. In a normal distribution, about 32 percent of a large series of indi-
vidual observations will deviate from the mean value by more than ฑa , thus
68 percent of the individual observations will lie within ฑa .
51
-------
The standard deviation for any frequency distribution may be obtained
from the general formula
- 65)
o * *> p
x=-oo
The general formula in terms of a large series of n measurements of x
becomes
i=n
a2 = ^ V(x.-m)2 (Eq. 66)
n Z/ i
For the normal distribution, the evaluation of equation 65 by integration
gives
J x=0ฐ x=0ฐ
a2 = f (x-m)2dP = -^- /" (x-m)2e-(x-m)/2a2c
/ ^ _, /^ /
J OvzTT */
dx = a2
x=-ฐฐ x=-ฐฐ
because the standard deviation is simply one of the two independent parameters
of the normal distribution. As a consequence of the preceding material, the
standard deviation may have any value.
The standard deviation for the Poisson distribution has a definite value
because there is only one parameter. The expansion of equation 65 in terms of
the parameter, m, for the Poisson distribution is
x=ฐฐ
2 \~* (x-m) 2m -m ._ rn.
az = 2_, ^ e = m
x=0
Therefore the standard deviation a for the Poisson distribution is m.
The value calculated for the standard deviation is actually an estimate
because the number of observations, no matter how large, is finite. The best
approximation of the standard deviation of a distribution in terms of a finite
number of observations is
T i=n i=n
2 ~ n -^ \"* / ~\ 2 _ 1 V / ~ 2
The n-1 term represents the reduction by 1 in the number of individual
equations, and therefore degrees of freedom, that results when the distribution
about x is considered. In the special case of a single observation, x = x,
the standard deviation is indeterminate.
When the distribution of n individual measurement of x about their
estimated mean value x is approximately normal, we may assume that some 68
percent of the x. values will lie within x ฑ a. If one additional
52
-------
observation is made, it would have a 68 percent chance of lying within x ฑ a.
Therefore the standard deviation, 0, of the distribution is also the standard
deviation of a single observation.
If one or more additional experiments are conducted under identical
conditions and for which there will be n observations each, the respective
means may be expected to have a much greater chance than 68 percent of lying
within the band (x ฑ 0-). The means of a number of experiments would take on
an essentially normal distribution in which some new mean value X2 will lie
within the band (x ฑ a-). The measure of the distribution of the means 0-
x x
will be smaller than o.
The theory of errors indicates that a series of K mean values, x, Xฃ,
X3, ..., x , in which each mean is determined from n observations, will
tend to exhibit a normal distribution about their grand average x .* This
will be true if n is sufficiently large even though the distribution of the
parent population x. is not normally distributed as in an asymmetric Poisson
distribution. The distribution of mean values tends to be much more nearly
normal than the distribution of the parent population. A theoretical justifi-
cation of the relationship between 0 and 0- based on a normal distribution
of x follows. When a large series of k measurements of the mean value x,
each of which has n measurements of x, the grand average, x, will approach
the true mean, m. The standard deviation of x depends upon n in the
following manner:
j=k
2
(0-)2 = f V (x.-m)2 = (Eq. 69)
x k /* j n
Upon considering a single series of n measurements of x the result is
reported as (x ฑ 0-) where
1 S1
x = - Y x. (Eq.70)
n iti 1
0- = (Eq. 71)
X i
vn
ฐx = J 11 11 if
-------
Equations 69 and 72 may be shown to be valid for the Poisson distri-
bution. If a total, v , of
n
I*-
L i
random events is observed, the standard deviation by equation 65 in this
single observation is
/i=n
x.
(Eq. 73)
the result would be given as
i=n
/i=n
v ฑ o = 2J xi ฑ - I > x
i=l t i=l
The fractional standard deviation, F.S.D., would be
L=n
1=1
Consider the total of a number of observations
i=n
i=l
(Eq. 74)
(Eq. 75)
and the same observations in n groups of contiguous and equal intervals as
i=n
x =
The average of the n groups would be
i=n
X = n {'*>
and the standard deviation of the mean would be
L=n
/
/n
n
1=1
. .
(Eq. 76)
54
-------
The result of the measurements would be reported as
,i=n /i=r
ฑ Y*i\ (Eq. 77)
which has the same fractional standard deviation as Equation 75. This is the
same as dividing equation 74 by the number of groups n into which the data
were subdivided. The point is made that observation of a total
i=n
randomly distributed events has a fractional standard deviation of
i=n
i=l
As a consequence of this exercise one may observe that the standard deviation
for 100 events is 10 percent and for 10,000 counts 1 percent. No manipulation
of the same total data can reduce the size of the fractional uncertainty due
purely to randomness.
55
-------
INEFFICIENT STATISTICS*
The preceding work treats of efficient statistics by which the probable
accuracy of a mathematical estimate is assured within the limits imposed by
the quantity and distribution of data. The calculations for efficient statis-
tics are often so time-consuming that preliminary estimates of statistical
values are desirable. Techniques for obtaining preliminary estimates of
statistical values have been given the term inefficient statistics. Appli-
cation of inefficient statistical methods requires acceptance of certain
assumptions, chiefly in regard to the type of distribution. The practical
aspects of inefficient statistical methods result from either dealing with a
limited quantity of random data or dealing with only a limited quantity of the
total data that have been collected. Inefficient statistics may be subdivided
as macrostatistics in which n is greater than 100 and microstatistics in
which n is equal to or less than 10.
1. Macrostatistics (n > 100)
a. The estimate of the mean of a large symmetrical population based
upon the median (50-percent point or the point where one-half the data lies
below and the other half lies above) has an efficiency of 64 percent. This is
to say the estimate would have the accuracy that would be obtained if only 0.64
of the data had been used. Thirty-six percent of the information, then, is
ignored.
b. Another technique for estimating the mean is to take the aver-
age of the two observations which lie 29 percent inside the upper and lower
extremes of the data collected. These observations are at the 29- and 71-
percent points of the distribution. The result has the same accuracy as the
mean calculated from 81 percent of the observations.
c. When the mean is estimated by choosing the average of the 20-,
50-, and 80-percent points, the loss of information is, effectually, 12 per-
cent.
The estimate of the standard deviation for n = 100 based upon
the 93-percent and 7-percent points utilizes approximately 65 percent of the
information contained in the data. The formula is
(93-percent point) - (7-percent point)
This estimate is based upon the approximation that 86 percent of the data in a
normal distribution falls within m = ฑ 1.50 . '
*(18, pp. 902-904)
56
-------
2. Microstatistics (n < 10)
For n <_ 10 , the median is a more accurate estimate of the mean
than the average of the extreme data for all values of n other than 3 and 5.
The median is taken as the value of the middle datum when n is odd and as
the average of the middle score when n is even.
a. The efficiency of using the median as an estimate of the mean
has an efficiency equal to or greater than 0.64 for all n .
b. The average of the third value from each end of a distribution
n = 7 to 10 (and probably higher) has an efficiency about 0.84.
Estimates of the standard deviation of a small sample, in which
n is from 2 to 20 may be made from the following:
Range = (largest observation) - (smallest observation)
/i=n
(x,-x)2
(Eq. 78)
The efficiency for n = 3 is 99 percent and declines to about 85 percent for
n = 10 . The following table gives a few values for the denominator when n
> 10 .
n
Range/a
10
3.08
15
3.47
20
3.73
30
4.09
50
4.50
100
5.02
The relative efficiency of range as an estimator of standard deviation
decreases as n increases. By dividing the data into equal groups of seven
or eight observations and using the average of the ranges of the groups it is
possible to improve the estimate of the standard deviation.
An estimate of the standard error (standard deviation of the mean value)
for a small sample is
_ g _
ฐx ~ 7T J n(n-l)
(Eq. 79)
An estimate of chi-square for small samples having a Poisson distribution
i=n
- ^
57
-------
Examples ;
1. Find the probability P of observing the value 19 in a Poisson
distribution whose mean is 15. X
SL ~m sl9 ~15
~ S ~
x ~ x! ~ 19 19!
= 5.577 x 1Q~2 or = 5.6%
2. Using P = 5.577 x io~2 from Example 1, find p , P , , and P
3 x x-l x+i c
a. p = * p = p = if. x 0.05577
x-1 m x 19-1 15
= 0.0731 or - 7.3%
-2
x 5-577 x 10
= ^| x 5.577 x 1Q~2 = 4.183 x 10~2
or = 4.2%
c. P0 = e~m = e~15 = 3.059 x lo~?
or = 0.0000306%
3. a. Find the probability P in a Poisson distribution that the next
observation x will be 31 when the mean m is 34.
1 f34)31e-(34-31)
/2ir(31) W
= 7.165 x 10~2 x 1.752 x 1Q1 x 4.978 x 10~2
-2
= 6.25 x 10 or 6.3%
b. Find the probability PX in a Poisson distribution that the next
observation will be x = m ='34.
58
-------
_i WX e-(m-x)
/2^ W
3ฑt -(34-34)
34 e
/2Tr(34)
- 6.842 x 1Q~2 x l x l = 6.842 x lo~2
or 6.8%
4. Find the approximate mean by finding the arithmetic average of the
following data: 8, 5, 7, 6, 7, 4, 9, 11, 5, 6.
i i=n
J- v~ป
m = x = ) x.
by inspection, the number of observations n is 10.
m ~ x = (8 + 5 + 7 + 6 + 7 + 4 + 9 + 11 + 5 + 6)
= 6.8
5. Using the data in Example 4, find the standard deviation in terms of
a finite number of observations
Setting up a table for the data and results of calculations:
X.
8
5
7
6
7
4
9
11
5
6
x
6.8
6.8
6.8
6.6
6.8
6.8
6.8
6.8
6.8
6.8
x.-x
1.2
-1.8
0.2
-0.8
0.2
-2.8
2.2
4.2
-1.8
-0.8
(xฑ-x) 2
1.44
3.24
0.04
0.64
0.04
7.84
4.84
17.64
3.24
0.64
59
-------
2xฑ = 68 x = = 6.8
1=10 _ 1=10
2 (x.-x) =0 2 (x.-x)2 = 39.6
1=1 1 1=1
a2 = x 39.6 = 4.4 a = /4.4 = 2.098
6. Estimate the standard deviation from the data in Example 4. By
rearranging the data on the basis of largest to smallest (or by inspection), it
is found that the range is 9-4=5.
range 5 _
a - - * = = 1.
7. Using the table value for n = 10, find the estimate of the standard
deviation of the data in Example 4. From the table when n = 10 , range/a =3.08
9-4 5
8. Using inefficient statistics, find the estimate of the standard
deviation when n = 300 and the observed values at the 93- and 7-percent points
are 61 and 44 respectively.
(93-percent point) - (7-percent point) 61-44 _ .
(j s: - * - - - * - = - - - = 5 m งฃ> /
9. Using inefficient statistics, find an estimate of the standard error
using the data in Example 4.
range 9-4 _ _
a- = - 3 = = 0.5
x n 10
10. Using inefficient statistics, find the value of chi-square for the
data in Example 4.
2 _ range 9-4 , ___
X - = , n = 3.676
mean 6.8
60
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SUPERPOSITION OF SEVERAL INDEPENDENT RANDOM PROCESSES
A generalization of the Poisson distribution is required in gamma-ray
spectroscopy because samples usually contain more than one gamma-emitting
nuclide and all the gamma rays are detected during the period of measurement.
Although the spectra of the radioactive background and the gamma emitters in
the sample result from random events detected during the period of measurement,
they may be treated as layer-upon-layer. Hence, the term superposition when
considering the total spectrum made up of two or more spectra.
Referring to the matrices described in Chapter 10, the activity or counts
due to radionuclide i can be written
C._ = a..N. + a.-N. + a.,N, + a..N. + a.cN._ + a.-N,. ,_ 01.
il il 1 ' i2 2 i3 3 i4 4 i5 5 16 6 (Eq. 81)
where the a's are the numbers found when the equation is solved.
Using values for a particular Nal(Tl) detector at the Quality Assurance
Branch of the Environmental Monitoring and Support Laboratory-Las Vegas,
Nevada, and the following conditions for a 4-liter Marinelli beaker containing
3.5 liters of water
Channels for Term for
Interference Sum of Efficiency
Isotope Factors Channels (Counts/pCi)
51Cr 28-36 N51Cr 0.01392
106Ru 47_56 N106Ru 0.02252
137Cs 62-72 N137Cs 0.07850
134Cs 74-86 N131tCs 0.07190
65Zn 104-120 N65Zn 0.03339
60Co 124-138 ' N60Co 0.05483
the following formulas are obtained:
51Cr (cpm/3.5 liter) = _
1.000(N51Cr) - 0.300254(N106Ru) - 0.252904(N137Cs)
- 0. 372847 (NmCs) - 0.078011 (N65Zn) - 0.089156 (N50Co) (Eq. 82)
106Ru (cpm/3.5 liter) =
0 000(N51Cr) + 1.093667(N106Ru) - 0.145403(N137Cs)
- 0. 656015 (NmCs) - 0.111432(N65Zn) + 0. 092489 (N60Co) (Eq. 83)
61
-------
137Cs (cpm/3.5 liter) =
0.000(N51Cr) - 0.245768(N106Ru) + 1.003305(N137Cs)
- 0.282704(N134Cs) - 0.072860(N65Zn) - 0.084018(N60Co) (Eq. 84)
134Cs (cpm/3.5 liter) =
0.000(N51Cr) + 0.052171(N106Ru) + 0.006090(N137Cs)
+ 1.077541(N134Cs) - 0.266478(N65Zn) - 0.191901(N60Co) (Eq. 85)
65Zn (cpm/3.5 liter) =
0.000(N51Cr) - 0.085519(N106Ru) + 0.011547(N137Cs)
+ 0.018941(N134Cs) + 1.017764(N65Zn) - 1.255153(N60Co) (Eq. 86)
60Co (cpm/3.5 liter) =
0.000(N51Cr) - 0.004314(N106Ru) + 0.000515(N137Cs)
- 0.071606(N134Cs) + 0.019198(N65Zn) + 1.013625(N60Co) (Eq. 87)
Thus, for 65Zn the values of the a's are:
ai = 0.00000
a2 = - 0.085519
a3 = + 0.011547
34 = + 0.018941
a5 = + 1.017764
a6 = + 1.255153
The uncertainty in the value measured for C. is expressed as
a2(C.) = a.^ + a.22N2 + a^ + a^ + a.^ + a^^ (Eq. 88)
or the variance a2 for the counts obtained for zinc-65 is
a2(cpm/3.5 liter 65Zn) =
0.00731(N106Ru) + 0.000133(N137Cs) + 0.00359(N134Cs)
+ 1.0359(N65Zn) + 1.575(N60Co)
and the uncertainty is, therefore, expressed as a . For zinc-65, it is seen
that the estimated uncertainty is very strongly influenced by the amount of
cobalt-60 in the sample.
The terms in the preceding paragraph do not consider background to be a
factor, but we should realize that backgrounds are important at the levels
being measured. First, let us assume that gross counts are being measured
such that we get a count M in a time t and a background count b in a
measured time of t, where b is the average background rate. The average
background rate then is
B = btb ฑ vt (Eq. 89)
62
-------
B/tb = b ฑ /b/tb (Eq. 90)
The count M can be estimated as being due to the sample count rate S and the
background count rate B .
= S + b ฑJf + ^ (Eq. 91)
"s
If the count rate of the background is subtracted from the above the result is
r^ v~ rr~
Sample Count Rate = S + b ฑ / + b ฑ / (Eq. 92)
/ "^ "^ "W "^i
T s s If b
Remember that uncertainties are summed with the formula
R2 = ri2 + r22 + ... + r 2 (Eq. 93)
where rj, r2, ..., r are the absolute values of the uncertainties in the mean
values of the several quantities, and R is the final uncertainty in the mean
value of a physical magnitude from the summation or_ the difference of several
independent observations on two or more physical quantities (such as the number
of counts in a region of a spectrum). The sample count rate then becomes
Sample Count Rate = S ฑ~ + ~ + ~ (Eq. 94)
Keep in mind that S + b is equal to the observed count rate when the sample
is counted.
The background uncertainty enters twice, once for any previous background
determinations of blank or mock sources and again for the particular sample of
interest. In the previous example of the count rate uncertainty for zinc-65,
it is necessary to add the terms1 due to two background fluctuations for each
of the regions of interest, one for the background if it has been subtracted
from the spectra before the regions of interest are totalized and one for the
standard background in these regions. If the standard background has been
known to have uncertainties larger than counting statistics indicate, this
uncertainty should be used.
In the preceding formulas for determining the activity and standard
deviation of a radionuclide in a composite spectrum, it has been implicitly
assumed that the background had been subtracted from all the measured spectra.
To include the uncertainties due to fluctuations in backgrounds, a more de-
tailed explanation follows.
63
-------
Let the background be firmly determined by previous measurements. Then
for each area chosen to represent a full energy peak or region of interest
used in determining the interference factors we have a set of background
numbers. Let us say that the backgrounds are represented by rates bi
through bg . Now if a sample is counted, the gross count rates will be la-
beled Y. = N. + B. where region N. is the net count, and B. = b. t and
t is the time required to accumulate the spectrum.
s
C. is still determined by
C. = a. N, + a. N^ + a. N_ + a. N. + a. Nc + a. N.
i ii 1 12 2 13 3 :u 4 is 5 16 6
but the standard deviation is now given by
a.2 = a. 2N_ + a. 2N. + a. 2N_ + a. 2N. + a. 2NC + a. 2NC + b.t + b.t.
x ii 1 i2 2 i3 3 !<, 4 15 5 i6 6 is i b
where t is a large time used during the establishment of the mean background
rate. The count rate is then
^M 4- a 2M 4. 4. a 2M y^ y^
(Eq. 95)
SCR. = C./t ฑ ii 1
When analyzing the results of an experiment that involves several steps,
two additional types of error analysis must be considered other than those
fundamental uncertainties resulting from counting statistics. Uncertainties
due to variations in sample size, counting geometry, etc., are easily observed
when several measurements have been made. These uncertainties result from
somewhat random, but measurable, events. Thus if a formula is used to calcu-
late an activity that has several variables, a, b, c , the errors can be
documented as probable error r , r, , r , etc.
a b c
Suppose the activity calculation A is written as
_ abc
A _ _
def
and we know the uncertainties r&, rfc, r , rd/ r , r , the fractional error
in A , (R/A), is determined as
or
R =
&)(%) f-s)
There will, however, be a few steps in the making of every measurement
where the uncertainty is not random and there is no way of controlling the
error. Such errors may arise from not being able to fabricate a standard that
simulates the sample to be analyzed. Example problems of non-random uncer-
tainty in analyzing the radionuclides present on a charcoal cartridge (filter)
are:
64
-------
a. Distribution of radionuclides in the sample is not known.
b. A standard cannot be obtained for a particular radionuclide.
c. An unknown or a different radionuclide than anticipated occurs in
the sample.
These errors should be added instead of combined in the manner that is
done for random errors. Thus, if these errors are known as k , 1 , m , and
n for the measurement of a sample, we should report the activity and the
uncertainty as:*
A ฑ/ /ซ^tJ>+|- + (r ,2 + ( ,2 + ... + ( }2 l(k+ i +m+n)^
iป/ t t, a b ฑ 3
s b
To determine the fractional error, let us assume that:
t t, | = 0.01
s b
r
= 0.02
a
T? = 0.01
b
and k = 0.03, 1 = 0.01, m = 0.02, and n = 0.03 ; then the
fractional error is
- = ฑ/(0.01)z + (0.02)2 + (0.01)2 + ^-(0.03 + 0.01 + 0.02 + 0.03)
A 3
= ฑ/0.0006 + 0.03
= ฑ(0.024 + 0.03)
= ฑ0.054 or ฑ5.4%
We should state that this result is at the la confidence level. In practice,
it is best to account for each fractional error as it is determined and to
combine fractional errors as the final values are tabulated.
*The factor 1/3 in estimating systematic errors is constant and independent of
the number of terms included in estimating the total systematic error.
65
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STATISTICAL TESTING FOR NORMAL AND NON-NORMAL DATA
In principle, the results of gamma-ray spectroscopy should follow statis-
tical laws of distribution. Consequently, gamma-ray spectroscopy systems
should be tested to determine if the data obtained have the desired distribu-
tion. The Poisson distribution is acknowledged as representative of random
data, but the assumption of a normal distribution makes calculation easier.
The error caused in using normal statistics over Poisson statistics is minimal
unless the number of data is small. If checks indicate that results follow a
normal distribution, it can be assumed that the instrument is capable of oper-
ating correctly. When checks indicate a non-normal distribution, the instru-
ment must be repaired or the system modified. Some of the common causes lead-
ing to non-normal results are:
1. Change in the radon concentrations in the air surrounding the de-
tector.
2. Line noise or faulty grounding.
3. Ground loops.
4. Temperature variations.
5. Detector failure.
6. Electronic malfunction.
An easy check of the normality of the distributions of results is to plot
both the background and the performance standard results on a control chart
for analysis. The tests described below should be repeated on a monthly or
quarterly basis and will require little effort. Although the Poisson distri-
bution is valid for gamma-ray detection, a Nal(Tl) detector will generally
have count rates high enough that the Gaussian or normal distribution law is
sufficiently accurate. Background counts will have larger fluctuations than
are expected from counting statistics because of the lack of adequate controls
and the relatively long counting times required. Generally, the background
for a Nal(Tl) detector will fluctuate 3 to 10 times greater than a Poisson
distribution would indicate during a time period of a year. The performance
standard counted for a short time (10 to 15 minutes) will more closely ap-
proximate a Poisson distribution.
The relative normalcy of counting results is not obvious through inspec-
tion of a control chart or a series of numbers. The use of statistical tests
is the only way that numbers representing counting results can be checked to
assure that the spectrometer is operating correctly. The mean square of the
successive differences (MSSD) is preferred over a chi-square analysis (16, pp.
385-390). The MSSD method is highly selective for a small number (5 to 25)
of measurements. If values are taken at random from a normal population and
classified in the order of appearance the variable (the Von Neuman statistic)
66
-------
.
r = ^ (Eq. 96)
2 2 (x. - x)2
i=l
has a probable value of 1. A value much below 1 points to either a drift or
to abnormal groups, or both, while a value above 1 reveals abnormally rapid
fluctuations. Table 2 presents the limiting values of r at the probability
levels of 95 percent and 99 percent for n between 4 and 25. It should be
kept in mind that a probability level of 95 percent means that 5 percent of
the data will be rejected falsely and a probability level of 99 percent means
that 1 percent of the data will be rejected falsely.
TABLE 2. LIMITING VALUES OF r AT PROBABILITIES OF 95% AND 99%
FOR THE MEAN SQUARE OF THE SUCCESSIVE DIFFERENCES
STATISTICAL TEST
n 0.01 0.05 0.95 0.99 n
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
0.313
0.269
0.281
0.307
0.331
0.354
0.376
0.396
0.414
0.431
0.477
0.461
0.475
0.487
0.499
0.510
0.520
0.530
0.539
0.548
0.556
0.564
0.390
0.410
0.445
0.468
0.491
0.512
0.531
0.548
0.564
0.578
0.591
0.603
0.614
0.624
0.633
0.642
0.650
0.657
0.665
0.671
0.678
0.684
1.610
1.590
1.555
1.532
1.509
1.488
1.469
1.452
1.436
1.422
1.409
1.397
1.386
1.376
1.367
1.358
1.350
1.343
1.335
1.329
1.322
1.316
1.687
1.731
1.719
1.693
1.668
1.646
1.624
1.604
1.586
1.569
1.553
1.539
1.525
1.513
1.501
1.490
1.480
1.470
1.461
1.452
1.444
1.436
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Table 3 shows an example selected from one of the author's instruments.
It is noted that this particular instrument failed catastrophically 1 month
after the end of the period in which these data were acquired. The column
captioned "Count Low" is the number of counts accumulated in 10 minutes from
the 570 keV gamma ray from bismuth-207 check source. For the low energy peak,
the average count accumulated was 22569.6, the expected spread was 150.23, the
observed a was 260.54 and r was 0.58. From Table 2 we find for n = 25 and
67
-------
TABLE 3. MSSD TEST APPLIED TO COUNTS OF A Bi-207 SAMPLE OBTAINED
WITH A MULTICHANNEL GAMMA-RAY SPECTROMETER
Xi 2-2
(Count Low) (xi+l~Xi) (xi " x)
22056
22119
22403
22666
22772
22487
22445
22416
22646
22800
22374
22572
22963
22491
22091
22557
22688
22499
22341
22694
22890
22544
22991
22813
22922
3969
80656
69169
11236
81225
1764
841
52900
23716
181476
39204
152881
222784
160000
217156
17161
35721
249621
124609
38416
119716
199809
31684
11881
564240 1902938
x = 564240/25
Sx = 150. 23
a = 260.54 a
1902938
= 22569.6
2 = 67882
263785
203040
27756
9293
40966
6823
15525
23593
5837
53084
38259
6
154764
6187
229058
159
14019
4984
52258
15475
102656
655
177578
59244
124186
1629190
i . . 2 . -.2
(Count High) (xi+l~Xi; lxi ~ x;
8982
9114
9386
9502
9571
9440
9322
9346
9537
9651
9383
9467
9659
9396
8854
9425
9555
9346
9374
9583
9664
9480
9675
9690
9586
235988
x = 235988/25
i/x = 97
0 = 209.35 a
1190010
17424
73984
13456
4761
17161
13924
576
36481
12996
71824
7056
36864
69169
293764
326041
16900
43681
784
43681
6561
33856
38025
225
10816
1190010
= 9439.52
2 = 43827
209324
105963
2864
3904
17287
0
13811
8746
9502
44724
3195
755
48171
1894
342834
211
13336
8746
4293
20587
50391
1639
55451
62740
21456
1051824
2 x 1629190
0.58 (non-normal)
2 x 1051824
0.57 (non-normal)
68
-------
a 95 percent probability, 0.684 <_ r <_ 1.316. The value obtained for r lies
outside of this range, thus indicating that the instrument is either drifting
or has abnormal groupings of data. In this particular case, the instrument
was drifting. Figures 20 (page 51) and 21 are sections of a control chart
using these data. The drift shown to exist by this test is not obvious through
visual inspection of the control chart. Data accumulated for the 1063 keV
peak show similar behavior.
9740 1
9640
9540 1
9440 1
9340 1
9240i
914(1.
x + 300
X + 200 D D D ฐ ฐ
x + 100 u D D
D
x o a a
LJ
x - 100ฐ D ฐ D
a
x - 200
x - 300
D
Figure 21. Control chart for high energy (1.063 MeV) peak from Bi-207.
Table 4 illustrates the test used in the preceding example for nine back-
ground measurements obtained from the same instrument system. Those nine
measurements were taken in one afternoon which prevented the observation of
long term drifts. The average of the background counts for the 10-minute
counting interval was x = 6342 . The standard deviation was calculated as
a = 75.5 which was within normal limits of /x = 79.6 . In this case r =
133017/(2 x 45603) = 1.46 . From Table 2, using values ฑor n = 9 , and a
probability of 95 percent, the limiting values of r become 0.512 <_ r <_ 1.488.
The calculated value for r lies within the limiting values, indicating that
the data are probably random.
The recommended test for normality is the Kolmogorov-Smirnov test (also
known as the "vodka test")(19). This test, used in conjunction with the
plotting of data on probability paper, is fairly easily performed and will add
to the documentation of data taken for the control charts. Using the data
from Table 5, the first step is to place the numbers in order beginning with
the smallest. Let x , x , ... , x designate these ordered sample values.
The distribution function S.(x) is then defined as:
S.(X) = -
Tables 5 and 6 show the rearrangement of the control data x. presented in
Table 3. The fifth columns of Tables 5 and 6 show the distribution function
of S
.
The .fifth column of Table 7 shows the distribution function of Sg.
-------
TABLE 4. MSSD TEST FOR BACKGROUND MEASURMENTS
OF A 10.2-CM BY 10.2-CM Nal(Tl) DETECTOR
10 Minute
Counts (x. -x.) (x. - x)
6408
6397 121
6218 32041
6426 43264
6250 30976
6331 6561
6294 1369
6412 13924
6343 4761
57079 133017 45603
Ex = 57078
x = 6342
T/X = 79.64
a = 75.50
133017
2 x 45603
70
-------
TABLE 5. KOLMOGOROV-SMIRNOV TEST ON LOW ENERGY (0.57 MeV)
GAMMA RAYS FROM Bi-207
X.
1
(Count Low)
22056
22091
22119
22341
22374
22403
22416
22445
22487
22491
22499
22544
22557
22572
22646
22666
22688
22694
22772
22800
22813
22890
22922
22963
22991
x.- m
i
o
-1.97
-1.83
-1.73
-0.88
-0.75
-0.64
-0.59
-0.48
-0.31
-0.30
-0.27
-0.10
-0.50
0.01
0.30
0.37
0.46
0.48
0.78
0.89
0.94
1.23
1.35
1.51
1.62
f(xj
0.06
0.07
0.09
0.27
0.30
0.33
0.34
0.36
0.38
0.38
0.38
0.40
0.40
0.40
0.38
0.37
0.36
0.36
0.29
0.27
0.26
0.19
0.16
0.13
0.11
F(XI)
0.02
0.03
0.04
0.19
0.23
0.26
0.28
0.32
0.38
0.38
0.39
0.46
0.48
0.50
0.62
0.64
0.68
0.68
0.78
0.81
0.83
0.89
0.91
0.93
0.95
Si(x)
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
0.36
0.40
0.44
0.48
0.52
0.56
0.60
0.64
0.68
0.72
0.76
0.80
0.84
0.88
0.92
0.96
1.00
D.
i
0.02
0.05
0.08
0.03
0.03
0.01
0.00
0.00
0.02
0.02
0.05
0.02
0.04
0.06
0.02
0.00
0.00
0.04
0.02
0.01
0.01
0.01
0.01
0.03
0.05
D:
i
0.06
0.09
0.12
0.01
0.01
0.02
0.04
0.04
0.02
0.06
0.09
0.06
0.08
0.10
0.02
0.04
0.04
0.08
0.02
0.03
0.05
0.03
0.05
0.07
71
-------
TABLE 6. KOLMOGOROV-SMIRNOV TEST ON HIGH ENERGY (1.063 MeV)
GAMMA RAYS FROM Bi-207
X.
1
(Count High)
8854
8982
9114
9322
9346
9346
9374
9383
9386
9397
9425
9440
9467
9480
9502
9537
9555
9571
9538
9586
9651
9659
9664
9675
9690
x. - m
i
a
-1.95
-1.49
-1.02
-0.28
-0.19
-0.19
-0.09
-0.06
-0.05
-0.01
0.09
0.14
0.24
0.29
0.37
0.49
0.55
0.61
0.65
0.67
0.90
0.93
0.94
0.98
1.04
f(xฑ)
0.06
0.13
0.24
0.38
0.39
0.39
0.40
0.40
0.40
0.40
0.40
0.40
0.39
0.38
0.37
0.35
0.34
0.33
0.32
0.32
0.27
0.26
0.26
0.25
0.23
F(xฑ)
0.03
0.07
0.15
0.39
0.42
0.42
0.46
0.48
0.48
0.50
0.59
0.56
0.59
0.61
0.64
0.69
0.71
0.73
0.74
0.75
0.82
0.82
0.83
0.84
0.85
Sฑ(x)
0.04
0.08
0.12
0.16
0.24
0.24
0.28
0.32
0.36
0.40
0.44
0.48
0.52
0.56
0.60
0.64
0.68
0.72
0.76
0.80
0.84
0.88
0.94
0.98
1.00
D.
1
0.01
0.02
0.03
0.23
0.18
0.18
0.18
0.16
0.12
0.10
0.10
0.08
0.07
0.05
0.04
0.05
0.03
0.01
0.02
0.05
0.02
0.06
0.09
0.12
0.15
Di
0.03
0.07
0.27
0.26
0.18
0.22
0.20
0.16
0.14
0.14
0.12
0.09
0.09
0.10
0.09
0.07
0.05
0.02
0.01
0.01
0.02
0.05
0.08
0.11
72
-------
TABLE 7. KOLMOGOROV-SMIRNOV TEST ON BACKGROUND MEASUREMENTS OF A
10.2-CM BY 10.2-CM Nal(Tl) DETECTOR
x.
1
6218
6250
6294
6331
6343
6397
6408
6412
6426
x =
& =
a =
x. - m
a
-1.64
-1.22
-0.64
-0.15
0.01
0.73
0.87
0.93
1.11
6342
79.64
73.50
f(x.)
i
0.10
0.19
0.33
0.39
0.40
0.31
0.29
0.26
0.22
F (x.)
Y -L
0.05
0.11
0.26
0.44
0.50
0.77
0.81
0.82
0.87
S.(x)
i
0.11
0.22
0.33
0.44
0.56
0.67
0.78
0.89
1.00
S (x)
l*r 1
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
D.
i
0.06
0.11
0.07
0.00
0.06
0.10
0.00
0.07
0.13
D!
i
0.00
0.04
0.11
0.06
0.21
0.11
0.04
0.02
The next step is to plot S.(x) versus counts/time on probability paper
(e.g., K & E Probability * 90 divisions, #46 8000) as in Figures 22, 23, and
24. A plot of "normal" data will produce a straight line on this paper. The
mean value is that value having a probability of 50 percent. Thus, from
Figure 22, the mean value is 22557. From Figure 23, the mean value is 9467,
and from Figure 24, the mean value is 6343. While the standard deviation can
be determined as the inverse of the slope as a function of confidence levels
(la = 84.13 and 15.86, 2a = 97.73 and 2.27) it is easier, generally, to cal-
culate its value.
Real data do not generally produce a straight line. The Kolmogorov-
Smirnov test, however, will indicate whether or not the data are acceptable as
a sample from a normal distribution. By using the mean value m and standard
deviation o , normal data are created from a data set from which probability
values may be generated using the following formula:
t=xi _(t-m)2/2o2
F(x.) = / dt (Eq. 97)
98>
73
-------
5 i
ID
20 i
30 i
40 i
50 i
60 i
70 i
80 i
90
95 i
98
99
99.8
999
99.99*
2
0
20 2
.
o
1 I
21 22
!2 22
-j
(.
13 22
0
ฉ
t
!4 22
xl
.
, Sc
!5 22
DO
{
ฉ'
v=F(x;)
=Sn(x)
3=F(x,)i
16 22
o
Sn(x)
i i
!7 22
% *
!8 2.
.
o
o
-
(9 23
95
90
80
,70
60
50
40
30
,20
10
5
. y
, i
02
i 01
i 001
0
Figxire 22. Probability plot for low-energy (0.57 MeV) peak from Bi-207.
74
-------
5
10
on !
ฃ.1}
in i
ou
Rn i
fin i
uu *
711 !
Rfl i
Qfl i
QR i
33 '
QR
90 '
QO .
99
QQ 0 ,
33 .0 '
QQ Q i
99.3
O
fc
O
c
o
1
0ฐ
o
o *
Sn(x)
o F(XJ)
2
.
.
ftP
95
90
80
70
60
50
40
30
20
10
2
1
0.2
0.1
0.01
8850
8950 9050 9150 9250 9350 9450 9550 9650 9750
Figure 23. Probability plot for high-energy (1.063 MeV) peak from Bi-207.
75
-------
5.
Wm
on
ZU
on 1
30 '
cn
all
en
Oil
7n
70
80 '
on
9U "
flC
3D
98
MB
QQ R
Q1 Q
O
o
o
0
rP
0
Sn(x)
o Fix,)
i 95
90
Rfl
i 70
fin
i 40
i 30
i 20
i 10
. 2
, 1
0 2
ni
6200
6300
6400
Figure 24. Probability plot for 10-minute background counts measured with
a 10.2-cm by 10.2-cm Nal(Tl) detector.
76
-------
The second column at each table gives the value of (x.-m)/a for each data
point, the third column gives the value f(x) = CL/-/2v\ exp(-S2/2) and the
fourth column gives the probability F(x.) for each data point. F(x) can
be obtained using some modern programmable calculators, or found in standard
tables (e.g., C.R.C. Handbook of Chemistry and Physics) . For the examples of
this section, the values of F(x) are also plotted in Figures 22, 23, and 24.
The test is completed by determining the absolute values
The largest value of D . or D . ' is then compared to the critical values D in
Table 8. If the maximum D. or D.' is less than D for the number of
determinations taken (n) , """then the data are acceptable and will not be
rejected. If the D. value is larger than D then we know how often the data
are falsely rejected.
The maximum value for D in Table 5 is 0.12 which is far below any crit-
ical value D. for n = 25 found in Table 8. We conclude that these data,
then, are normal. However, the maximum value for D in Table 6 is 0.27 and
there is a second value of D equal to 0.26. The critical value of D at the
95 percent confidence level for n = 25 from Table 8 is 0.27. Thus if we
reject these data, we expect to conclude falsely 5 times out of 100 that these
data are not normal. To conclude that these data are normal without further
measurements requires a great deal of optimism.
From Table 7, the maximum value for D is found to be 0.21, which is much
smaller than a critical value D for n = 9 found in Table 8. Thus it is
seen that the instrument is capable of producing normal data on any given day
provided the measurements are made fairly rapidly and in a short time period.
Needless to say at this point the instrument must also be calibrated daily,
even to produce data of dubious validity.
77
-------
TABLE 8.
LIMITING VALUES FOR D IN THE KOLMOGOROV-SMIRNOV TEST
00
Two-Sided Test
a =
n = 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0.80
0.900
0.684
0.565
0.493
0.447
0.410
0.381
0.358
0.339
0.323
0.308
0.296
0.285
0.275
0.266
0.258
0.250
0.244
0.237
0.232
0.90
0.950
0.776
0.636
0.565
0.509
0.468
0.436
0.410
0.387
0.369
0.352
0.338
0.325
0.314
0.304
0.295
0.286
0.279
0.271
0.265
0.95
0.975
0.842
0.708
0.624
0.563
0.519
0.483
0.454
0.430
0.409
0.391
0.375
0.361
0.349
0.338
0.327
0.318
0.309
0.301
0.294
Approximation
0.98
0.990
0.900
0.785
0.689
0.627
0.577
0.538
0.507
0.480
0.457
0.437
0.419
0.404
0.390
0.377
0.366
0.355
0.346
0.337
0.329
for N
0.99
0.995
0.929
0.829
0.734
0.669
0.617
0.576
0.542
0.513
0.489
0.468
0.449
0.432
0.418
0.404
0.392
0.381
0.371
0.361
0.352
> 40
a =
n = 21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
0.80
0.226
0.221
0.216
0.212
0.208
0.204
0.200
0.197
0.193
0.190
0.187
0.184
0.182
0.179
0.177
0.174
0.172
0.170
0.168
0.165
1.07
0.90
0.259
0.253
0.247
0.242
0.238
0.233
0.229
0.225
0.221
0.218
0.214
0.211
0.208
0.205
0.202
0.199
0.196
0.194
0.191
0.189
1.22
0.95
0.287
0.281
0.275
0.269
0.264
0.259
0.254
0.250
0.246
0.242
0.238
0.234
0.231
0.227
0.224
0.221
0.218
0.215
0.213
0.210
1.36
0.98
0.321
0.314
0.307
0.301
0.295
0.290
0.284
0.279
0.275
0.270
0.266
0.262
0.258
0.254
0.251
0.247
0.244
0.241
0.238
0.235
1.52
0.99
0.344
0.337
0.330
0.323
0.317
0.311
0.305
0.300
0.295
0.290
0.285
0.281
0.277
0.273
0.269
0.265
0.262
0.258
0.255
0.252
1.63
-------
LOWER LIMIT OF DETECTION
Gamma-ray spectrometers may be used to detect and analyze single or
multi-radionuclide samples. The randomness of the background count, the
randomness of the net sample count, and the similarities of some gamma spectra
indicate that there is a gross count below which it is not possible to satis-
factorily demonstrate a net count for a particular radionuclide. The net
count of a radioactive sample is proportional to sample activity when all
other factors pertaining to the detector system and sample are constant.
Consequently, there is a limit of sample activity below which it is not pos-
sible to satisfactorily demonstrate the presence of a particular radionuclide.
The lower limit of detection (LLD) is defined as the smallest amount of sample
activity that will yield a net count sufficiently large to imply its presence.
The numerical value for a LLD is not absolute, but depends upon several
factors of which the following are principle(20):
1. The preselected statistical risk one is willing to take of conclud-
ing falsely a particular sample activity is present (a).
2. The predetermined degree of confidence in assuming that the presence
of a particular radionuclide has been detected (1-$).
3. The similarities and dissimilarities of the background and radio-
nuclide gamma spectra to the spectrum of the particular radionuclide under
consideration.
4. The concentration of the radionuclide to be detected and the concen-
trations of any other radionuclides in the sample.
The simplest case of finding LLD is that in which the gross count in a
single channel is the sum of the count of a single radionuclide and the back-
ground count. It is assumed that the background and sample count rates occur-
ring in a fixed time are sufficiently large that their distribution can be
adequately approximated by a normal distribution having a mean and variance
equal to the expected number of counts. The following symbols will be used in
this discussion:
S = source strength in counts
y = calibration constant to convert counts into activity A
A = yS = source activity which may be expressed in terms of pCi
or other suitable units
C = measured background count
B
C = measured sample-plus-background count
B+S
79
-------
K = value (upper percentile of the standardized normal variate) corre-
sponding to the preselected risk for concluding falsely that
activity is present (a) (Table 9)
K = value (upper percentile of standardized normal variate) corespond-
ing to the predetermined degree of confidence; for detecting
the presence of activity (1 - $) (Table 9)
The LLD is approximately equal to:
LLD = y(K + Kj/2 C when K /C ซ 1 (Eq. 99)
Ot p B Ct B
TABLE 9. RISK AND CONFIDENCE VALUES
1-3 K
0.01
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.99
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
2.327
1.645
1.282
1.036
0.842
0.675
0.524
0.385
0.253
0.126
a is the probability for concluding falsely that activity is present. If
we will accept the risk that 10 percent of our measurements of samples without
activity will be reported as showing activity, then K = 1.282.
1-$ is the probability for concluding correctly that activity is present.
If we want 95 percent of the measurements of samples containing activity
reported as containing activity, then K = 1.645.
Two convenient formulas for approximating an LLD are:
LLD - Y(Ka + Kp) (CB+S + C^ (Eq. 100)
which may be used when a sample count has been taken near the LLD.
C
LLD -
which may be used when the counting time, t , for the sample plus background
differs from the counting time r , for the background alone. In both formu-
las, the expressions under the square root sign represent either the estimated
standard deviation of the net count or the estimated standard deviation of the
net count rate.
80
-------
Another formula for the LLD can be derived realizing that the standard
deviation, S^ , found when the activity of the sample is near the LLD ap-
proaches the standard deviation, S , when no activity is present. The
approximation for the LLD derived from a more vigorous analysis (20) results
in:
LLD = K S + K S
a o
gsd (Eq. 102)
Assuming Sd = SQ the lower limit of detection can be approximated by
LLD = (K + KJS
a 3 o (Eq. 103)
The standard error S for a net activity is the root mean square of the
standard error of the background. Therefore,
S = /S^ + "^^
o ^| sample + background background (Eq. 104)
S
for very low activity
S^
sample + background background
and
S = S /2
o background
and lower limit of detection becomes
LLD - (K + KJS, /2 (Eq. 105)
Ot p D
The standard error of an estimated radionuclide concentration parameter
depends upon the counting times of the sample and the background, the rela-
tionships between the spectrum and of a particular radionuclide and other
spectra in the library, the background, and the other radionuclides in the
sample.
Three typical counting situations in which the LLD must be considered
are:
1. Determining the LLD when the library contains the spectrum of the
radionuclide of interest and no other radionuclides are known to be present.
2. Determining the LLD for a particular radionuclide when other radio-
nuclides are included in the library, but do not occur in the sample.
3. Determining the LLD for a particular radionuclide when other known
radionuclides in the sample are assumed to be present at fixed levels and the
library contains the spectra for all radionuclides present.
The following procedures are used to obtain the LLD for the three pre-
ceding cases:
81
-------
Case 1. (Library contains the radionuclide of interest and no other
radionuclides are known to be present.) Obtain a series of background pulse
height distributions for the analyzer system to be employed using a blank
sample identical to the sample type that will be routinely used. Obtain the
average counts in the photopeak area selected to generate the matrix for anal-
ysis. For a single radionuclide, the activity can be found by A = EC
where A is the activity in some appropriate unit (e.g., picocurie), C is the
net count rate, and E is the efficiency (pCi/count per unit time). If no
activity is present, the gross count (G) will be
G = C.t + Bt
c c
= Bt
c
and the standard deviation will be
a2 =
\ S
a = $-2- + %-
V fcc *b
(Eg. 106)
and the lower limit of detection will be
/I2!
LLD * (k + k0) - + r- (Eq. 107)
Case 2. (Other radionuclides in the library, but not in the samples.)
The procedure is similar to that of Case 1. Let b. ... b be the count rate
in each region of interest for a blank sample, and let the activity for each
region be given as before
ci - Vi + ai2N2 + +
Ci - ปil*l + ai,N2+ ป +ainNn
Now for a given analysis time t
C. = a. n,t + a. n_t + + a. n t
i ix 1 c i2 2 c in n c
where n represents the count rate. From the discussion on the previous
chapter, the standard deviation is given by
a.2 = a. 2N. + ... + af N + Bn + ... + B
i ii 1 in n 1 n
= a. 2n, t + .. . + a2 n t + Bn + ... + B
, Xi 1 c in n 1 n
If no activity is present in the sample then
a.2 = a. 2b.t + ... + a. 2n t +B.. + ...B
i liic inncl n
82
-------
and the lower limit of detection becomes
LLD s
.-..NX
W *c '
a. 2b b,
in n 1
" ' t ' < +
c b
b
'" +tb
(Eq. 108)
Case 3. (Other known radionuclides in sample are present at fixed levels
and library contains spectra for all radionuclides present.) The procedure is
similar to the preceding cases with the following modifications. A mock
sample is prepared to contain fixed concentrations of the nuclides assumed to
be present in the sample exclusive of the radionuclide of interest whose
concentration must be zero. Again, all interference terms must be included.
In this case we must still add the interference from the added radionuclides
in the mock sample and a term for the background.
As in case 2 we see that
C. = a. N. + ... + a. N
i ii 1 in n
and
o.2 = a. 2nnt + ... + a. 2n t + B, + ... + B
i iilc inncl n
In this case, however, the n. will be larger than the background measured in
Case 2, and the standard deviation is dependent on the concentration of the
radionuclides added to the blank.
Also, the lower limit for detection of one nuclide is dependent on the
combination and amount of the rest of the nuclides included in the set. The
lower limit of detection is given by
LLD * (k + kj ^-^ 7 ฑ1^1+-^ (Eq. 109)
Note that as the number of radionuclides present increases there will be
an increase in the size of the standard deviation and in the lower limit of
detection. The amount of the increase will depend upon the multiple correla-
tion of the spectrum for the radionuclide of interest with the radionuclides
of the added library spectra.
Pasternak and Harley (20) have made a thorough review of the theoretical
aspects of detection limits for radionuclides in multicomponent samples.
Their experimental data were collected by a 20- by 10-cm sodium iodide detec-
tor and a 400-channel analyzer located in a room shielded with 11 cm of
steel. The estimated limits for detecting 65Zn, 60Co, and 137Cs in single
radionuclide samples were as low as 15 to 31 picocuries for 30-minute counts
from which 30-minute background counts were subtracted, and 10 to 22 picocuries
for 30-minute counts from which backgrounds obtained from 1000-minute counts
83
-------
were substracted. The variation resulted principally from the effects of gamma
peaks in the background spectra. When any two of the aforementioned radio-
nuclides or all three occurred in a sample, the precision of detection near the
lower limits was found to be materially less. Furthermore, there are wide
variations in the lower limits of detection for different radionuclide
mixtures because their spectra vary in the amounts of overlapping in the
regions of spectral interest.
The detection limits for radionuclides which had little spectral inter-
ference from other radionuclides were not materially affected in samples
having three nuclides in the library. When the library contained 10 radio-
nuclides, the lower limits of detection increased markedly over a sample (as
much as 5 to 10 times) which had only 3 radionuclides. Lower limits of detec-
tion for radioisotopes having a low yield per nuclear event were much higher
than those which had a higher yield. Beryllium-7 for example, has a principal
spectral peak produced by a photon yield of only 10 percent for each nuclear
event. By contrast, 65Zn has a principal spectral peak produced by a photon
yield of 49 percent and 60Co has a photon yield of 100 percent for each of its
two spectral peaks.
84
-------
REFERENCES
1. Crouch, D. P., and R. L. Heath. 1963. Routine Testing and Calibration
Procedures for Multichannel Pulse Analyzers and Gamma-Ray Spectrometers.
22nd Edition. U.S. Atomic Energy Commission Research and Development
Report, Physics, IDO-16923. TID-4500, 25 pp.
2. Heath, R. L. , R. G. Helmer, L. A. Schmittroth and G. A. Gazier. 1965.
The Calculation of Gamma-Ray Shapes for Sodium Iodide Spectrometers.
U.S. Atomic Energy Commission Research and Development Report, Physics.
Computer Program and Experimental Problems. IDO-17017. 158 pp.
3. Heath, R. L. 1964. Scintillation Spectrometry Gamma-Ray Spectrum Cata-
logue. 2nd Edition. U.S. Atomic Energy Commission Research and Devel-
opment Report. IDO-16880-1. Vol. 2 of 2. 364 pp.
4. Ibid. 1964. IDO-16880-2. Vol. 2 of 2. 264 pp.
5. Douglas, Geneva S., Editor. 1967. Radioassay Procedures for Environ-
mental Samples. Public Health Service publication No. 999-RH-27.
Washington, D.C. 520 pp.
6. Crouthamel, E. C. 1970. Applied Gamma-Ray Spectrometry. 2nd Edition.
(Revised by F. Adams and R. Dams). Pergamon Press, New York, New York.
753 pp.
7. Siegbahn, Kai, Editor. 1965. Alpha-, Beta-, and Gamma-Ray Spectroscopy.
North Holland Publishing Co., Amsterdam, The Netherlands. Vol. 1.
862 pp.
8. National Environmental Research Center. 1975. Radioactivity Standards
Distribution Program. National Environmental Research Center, Las Vegas,
Nevada. EPA-680/4-75-002a. 19+ pp.
9. Environmental Monitoring and Support Laboratory. 1975. Environmental
Radioactivity Laboratory Intercomparison Studies Program. Environmental
Monitoring and Support Laboratory, Las Vegas, Nevada. EPA-680/4-75-002b.
10. Lederer, C. M., J. M. Hollander and I. Perlman. 1967. Table of Iso-
topes. 6th Edition. John Wiley & Sons. New York, New York. 594 pp.
11. Nuclear Data Group, Editors. 1965-76. Nuclear Data Sheets (successor in
part to Nuclear Data, U.S. ISSN 0029-5477). Academic Press, New York,
New York.
85
-------
12. Martin, M. J., Editor. 1976. Nuclear Decay Data for Selected Radio-
nuclides. Oak Ridge National Laboratory. ORNL-5114, VC-34c-Nuclear
Physics. 54 pp.
13. Way, Katherine, Editor. 1966-76. Nuclear Data Tables. Sec. A. (Succes-
sor in part to Nuclear Data, U.S. ISSN 0029-5477). Academic Press, New
York, New York.
14. Nuclear Data Group, Editors. 1975. Nuclear Data Sheets. Academic
Press, New York, New York. Vol. 15, No. 3, p. 350.
15. Storm, Ellery, and Harvey I. Israel. 1967. Photon Cross Sections from
0.001 to 100 MeV for Elements 1 Through 100. Los Alamos Scientific Labo-
ratory. LA-3753, UC-34, Physics. TID-4500. 257 pp.
16. Kodt, L. 1973. "Radionuclide metrology," in Nucl. Instrum. Methods.
Siegbahn, K. Editor. North Holland Publishing Co., Amsterdam, The
Netherlands. Vol. 112, pp. 245-251.
17. Energy Research and Development Administration. "Standard Nuclear Instru-
ment Modules." TID-20893(Rev.3, 1969). Superintendent of Documents,
U.S. Government Printing Office, Washington, D.C.
18. Evans, Robley D. 1975. The Atomic Nucleus. McGraw-Hill Book Company,
Inc. New York, New York. 972 pp.
19. Siegel, Sidney. 1956. Nonparametric Statistics for the Behavioral
Sciences. McGraw-Hill Book Company, Inc. New York, New York. 312 pp.
20. Pasternak, B. S., and H. H. Harley. 1971. Nucl. Instrum. Methods.
North Holland Publishing Co., Amsterdam, The Netherlands. Vol. 91.
pp. 530-540.
21. Way, Katherine, Editor. 1970. Nuclear Data Tables. Academic Press, New
York, New York. Sec. A., Vol. 8, Nos. 1-2.
22. Nuclear Data Group, Editors. 1970. Nuclear Data Sheets. Academic
Press, New York, New York. Sec. B., Vol. 4, Nos. 3-4.
23. Ibid. 1971. Sec. B, Volume 6, No. 1.
24. Ibid. 1971. Sec. B, Volume 5, No. 5.
25. Ibid. 1974. Volume 11, No. 4.
26. Ibid. 1975. Volume 15, No. 2.
27. Ibid. 1975. Volume 14, No. 4.
28. Ibid. 1972. Sec. B, Volume 8, No. 5.
29. Ibid. 1971. Sec. B, Volume 5, No. 3.
86
-------
30. Ibid. 1971. Sec. B, Volume 6, No. 3.
31. Ibid. 1970. Sec. B, Volume 4, No. 6.
32. Way, Katherine, Editor. 1974. Atomic Data and Nuclear Data Tables.
Academic Press, New York, New York. Vol. 13, Nos. 2-3.
33. Nuclear Data Group, Editors. 1977. Nuclear Data Sheets. Academic
Press, New York, New York. Vol. 20, No. 2.
34. Ibid. 1976. Volume 17, No. 3.
35. Ibid. 1972. Sec. B, Volume 8, No. 2.
36. Ibid. 1971. Sec. B, Volume 5, No. 3.
37. Ibid. 1971. Sec. B, Volume 5, No. 6.
38. Amersham Searle Corporation. 1975. Research Products Catalogue.
Arlington Heights, Illinois.
87
-------
BIBLIOGRAPHY
Hodgman, Charles D., Editor. 1959. C.R.C. Standard Mathematical Tables.
12th Edition. Chemical Rubber Publishing Company. Cleveland, Ohio. 525
525 pp.
International Atomic Emergency Agency. 1960. Metrology of Nuclides. Inter-
national Atomic Energy Agency. Vienna, Austria. 472 pp.
International Atomic Energy Agency. 1967. Standardization of Radionuclides.
International Atomic Energy Agency. Vienna, Austria. 742 pp.
National Bureau of Standards. 1961. A Manual of Radioactivity Procedures.
NBS Handbook No. 80. U.S. Department of Commerce. Washington, D.C.
159 pp.
National Bureau of Standards. 1963. Radioactivity Recommendations of the
International Commission on Radiologic Units and Measurements. NBS Hand-
book No. 86. U.S. Department of Commerce. Washington, D.C. 53 pp.
National Center for Radiological Health. 1967. Radionuclide Analysis by
Gamma Spectroscopy. U.S. Department of Health, Education and Welfare.
Rockville, Maryland. 373+ pp.
Putnam, Marie, R. G. Helmer, D. H. Gipson, and R. L. Heath. 1965. A Non-
linear Least-squares program for the Determination of Parameters of Photo-
peaks by the Use of a Modified Gaussian function. U.S. Atomic Energy
Commission Research and Development Report, Physics. IDO-17016.
TID-4500 (43rd Edition). 85 pp.
Stevenson, P. C. 1966. Processing of Counting Data. Subcommittee on Radio-
chemistry. National Academy of Sciences-National Research Council. Na-
tional Bureau of Standards. U.S. Department of Commerce. Clearinghouse
for Federal Scientific and Technical Information. Springfield, Virginia.
167 pp.
Subcommittee on Radiochemistry and the Subcommittee on the Use of Radioactivity
Standards. 1974. User's Guide for Radioactivity Standards. Technical
Information Center, Office of Information Services, U.S. Atomic Energy
Commission. NAS-NS-3115. 85 pp.
88
-------
00
Radionuclide
Be-7
Na-22
K-40
Sc-46
Cr-51
Mn-54
Co- 56
Co-57
Co- 58
Fe-59
.Energy of Principal
Half-Life Ref Gamma Ray (MeV)
53.3 d 21 0.477
2.602 y 12 0.511
1.274
1.28 x IQ9 y 21 1.461
tl.461
83.8 d 12 0.889
1.120
27.704 d 12 0.320
312.5 d 12 0.835
0.511
77.3 d 21 0.847
1.038
1.238
1.771
2.035
2.599
3.254
270.9 d 12 0.122
0.136
70.8 d 12 0.511
0.811
44.6 d 12 1.099
1.292
Gamma- Ray Intensity*
F(%)
10.3
180.58
99.95
10.7
N3.30 y/s/g
of potassium)
100
100
9.80
99.978
99.974
12.9
70
15.6
7.4
16.8
7.6
85.6
10.6
30
99.45
56.1
43.6
Ref Remarks
21
12
21
21
21
22
12
21
21
21
12
12
12
-------
APPENDIX A. BASIC DATA FOR SELECTED GAMMA RAY-EMITTING RADIONUCLIDES (continued)
10
o
Radionuclide
Co-60
Zn-65
Se-75
Sr-85
Y-88
Zr-95
Half-Life Ref
5.271 y 12
244.1 d 12
120 d 12
64.85 d 12
107 d 12
65.5 d 21
Energy of Principal
Gamma Ray (MeV)
1.173
1.333
0.511
1.115
0.121
0.136
0.265
0.280
0.401
0.514
0.898
1.836
0.724
0.757
Gamma- Ray Intensity*
F(%) Ref Remarks
99.90 12
100
2.92 12
50.75
16.7 12
56.8
59.5
25.1
11.8
98.0 12
93.4 12
99.35
43.5 21
54.3
Nb-95 35.1 d 21 0.755 99.8 21 The ratio of Nb-95 activity
to that of its parent, Zr-95,
is given as a function of
time, t, by 2.155[1 - exp
(-0.00916t)j where t is in
days and the Nb-95 activity
is zero at t = 0.
Ru-103 39.35 d 12 0.497 86.4 12
0.610 5.3
-------
DATA FOI
GAMMA RAY-EM3
DBS (continued)
Energy of Principal
Radionuclide Half -Life Ref Gamma Ray CMeV)
Ru-106-Rn-106 369 d 21 0.512
0.622
Cd-109 453 d 12 0.088
Ag-llOm 250.8 d 12 0.658
0.678
0.707
0.764
0.885
0.937
1.384
, 1.505
Sn-113- 114.9 d 12 0.392
In-113m
Sb-124 60.2 d 12 0.603
0.646
0.723
1.691
2.091
Sb-125 2.77 y 21 0.176
0.428
0.464
0.601
0.607
0.636
1-131 8.04 d 12 0.284
0.364
0.637
Gamma-Ray Intensity*
F(%) Ref Remarks
20.6 21 Rh-106 is assumed to be in
9.94 equilibrium with Ru-106.
3.72 12
94.6 12
10.6
16.4
22.4
73.0
34.4
24.7
13.3
64.9 12 ln-113 is assumed to be in
equilibrium with Sn-113
after 17 hours.
97.9 12
7.21
11.26
48.8
5.58
6.3 21
29.6
10.0
18.4
5.2
11.2
6.06 12
81.2
7.27
-------
APPENDIX A. BASIC DATA FOR SELECTED GAMMA RAY-EMITTING RAPIONUCLIDES (continued)
10
Radionuclide
Ba-133
Cs-134
Cs-137
Ce-139
Ba-140
La-140
Ce-141
Energy of Principal
Half -Life Ref Gamma Ray (MeV)
10.5 y 12 0.276
0.302
0.356
0.382
2.062 y 12 0.563
0.569
0.605
0.796
0.802
30.0 y 12 0.662
137.65 d 12 0.165
12.8 d 21 0.163
0.305
0.424
0.438
0.538
40.27 h 21 0.329
0.433
0.487
0.752
0.816
0.868
0.920
0.925
1.597
2.522
32.50 d 12 0.145
Gamma-Ray Intensity*
F(%) Ref Remarks
7.3 12
18.66
62.4
8.86
8.38 12
15.43
97.6
85.4
8.73
85.0 12
80.0 12
6.2 21 The ratio of La-140 activity
4.5 to that of its parent, Ba-140,
3.2 is given as a function of
2.1 time, t, by 1.153 [1-exp
23.8 -(0.516t)] where t is in days
and the La-140 activity is
taken to be zero at t = 0.
21 21
3.3
45
4.4
23.1
5.5
2.5
6.9
95.6
3.3
48.0 12
-------
APPENDIX A. BASIC DATA FOR SELECTED GAMMA RAY-EMITTING RADIONUCLIDES (continued)
Radionuclide
Ce-144
Ta-182
Au-195
Hg-203
Bi-207
Ra-226
U-235
Energy of Principal
Half-Life Ref Gamma Ray (MeV)
284 d 21 0.134
115 d 25 0.100
0.152
0.222
0.229
0.264
1.121
1.189
1.221
1.230
183 d 26 0.099
46.59 d 12 0.279
38 y 12 0.570
1.064
1.770
1600 y 21 0.186
0.295
0.351
0.609
0.120
1.765
7.1 x lo8 y 28 0.143
0.163
0.186
0.205
Gamma-Ray Intensity*
F(.%) Ref Remarks
10.8 21
40.2 25
20.5
21.6
10.4
10.4
100
47
78.3
33.1
12 26
81.5 12
97.8 12
74.3
7.3
3.3 21 ^Equilibrium intensities
18$ (after 38 days with no
35$ loss of radon)
43$
14$
16.6$
1.7$ 28 $NorTOalized to give 54 pho-
4.6$. tons/100 a for 0.1861 y
54$
5.0
U-238
4.49 x 109 y 29
-------
VO
Radionuclide Half-Life Ref
Th-232 1.405 x lo10 y 21
Am-241 433 y 21
Energy of Principal
Gamma Ray (MeV)
0.239
0.337
0.510
0.583
0.727
0.909
0.967
1.596
2.615
0.0596
Gamma-Ray Intensity*
F(%) Ref RemarKs
40 $ 21 *Equilibrium intensity
11 *
^ 8.0 $
30 *
7.1 *
30 *
27 *
5.6 $
35.93*
35.3 21
* Intensity is measured as gamma rays emitted per disintegration.
d - day
h - hour
y - year
-------
APPENDIX B. THORIUM-232 SERIES DECAY DATA
Type
Nuclide and of Refer-
Half -Life Decay ence
Thorium-232 a 33
1.405 x 1010 y
Radium- 228 B~ 34
5.75 y
Actinium-228 34
6.13 h
Particle
Energy
(MeV)
3.830
3.953
4.010
0.046
0.45
0.49
0.62
0.99
1.02
1.12
1.17
1.76
2.10
Transition
Probability
(%)
0.20
23.3
77.3
100
4.9
5.6
5.7
7.3
4.0
6.5
33
20
13
Electromagnetic
Photon energy
(MeV)
0.591
0.057
0.099
0.129
0.154
0.209
0.270
0.328
0.338
0.409
0.463
0.562
0.727
0.755
0.772
0.782
0.794
0.830
0.835
0.840
0.904
0.911
0.964
0.986
1.247
1.459
1.495
1.501
1.580
1.587
1.630
1.638
Transition
Photons
emitted (%)
0.15
0.5
1.4
2.9
1.0
4.6
3.8
3.4
12.
2.2
4.6
1.
0.8
1.1
1.6
0.5
4.8
0.6
1.8
1.
0.9
29.
5.5
17.
0.6
1.
1.
0.6
0.7
3.7
1.9
0.5
95
-------
APPENDIX B. THORIUM-232 SERIES DECAY DATA (continued)
Type
Nuclide and of Refer-
Half-Life Decay ence
Thorium-228 a 34
1.913 y
Radium- 22 4 a 34
3.66 d
Radon-220 a 34
55.6 s
Polonium- 216 a 34
0.15 s
Lead- 212 B~ 35
10.64 h
Bismuth-212 a 35
60.55 min
(a to 208T1 is 35.93%)
3~t
($~ to 212Po is 64.07%)
Polonium-212 a 35
0.305 ys
Thallium- 2 08
3.07 min
Particle
Energy
(MeV)
5.340
5.423
5.449
5.685
6.288
6.778
0.155
0.332
0.571
6.090
6.051
5.768
5.607
0.085
0.445
0.630
0.738
1.524
2.251
8.785
0.64
1.032
1.285
1.518
1.795
Transition Electromagnetic Transition
Probability
27
73
4.9
95.1
100
100
5.1
83
13
26.8
70.2
1.67
1.12
5
1
3
2
7
86
100
4.5
2.7
24
21
50
Photon energy Photons
(MeV) emitted (%)
0.084
0.131
0.166
0.216
0.241
0.550
0.115
0.239
0.300
0.039
0.727
0.785
1.620
0.277
0.511
0.583
0.736
0.860
2.615
1.2
0.11
0.08
0.27
3.9
0.1
0.6
44. Q
3.4
1
6.6
1.12
1.5
6.9
23.
86.
1.8
12.3
100.
t Relative alpha intensity per 100 alpha decays
t Relative beta intensity per 100 beta decays
NOTE: Percentages relate to the disintegrations of the individual nuclides,
Complete decay schemes are available in the Nuclear Data Sheets.
96
-------
APPENDIX C. URANIUM-238 SERIES DECAY DATA
Type
Nuclide and of Refer-
Half -Life Decay ence
Uranium-238 a 31
4.49 x 109 y
Thorium- 2 34 B~ 31
24.1 d
Protactinium- 234_ 31
1.17 min 3~
Uranium-234 a 31
2.48 x io5 y
Thorium-230 a 33
7.7 x 104 y
Radium-226 a 33
1600 y
Radon-222 a 21
3.824 d
Polonium-218 a 21
3.05 min
Lead-214 B~ 21
26.8 min
Bismuth- 214 3~ 21
19.8 min
Particle
Energy
(MeV)
4.195
4.145
0.100
0.101
0.193
2.30
1.50
0.58
4.773
4.723
4.687
4.621
4.602
4.784
5.486
6.000
0.20
0.51
0.69
0.75
1.04
0.82
1.08
1.15
1.27
1.39
1.43
1.51
Transition
Probability
(%)
77
23
12
21
67
90
9
1
72.5
27.5
76.3
23.4
5.5
94.5
100
-100
2.2
1.3
46
43
7
2.9
6.6
4.9
4.5
1.6
8.7
18
Electromagnetic
Photon energy
(MeV)
0.063
0.092
0.093
0.767
1.001
0.053
0.121
0.068
0.186
0.242
0.295
0.352
0.609
0.768
0.806
0.934
1.112
1.155
1.238
1.2811
Transition
Photons
emitted (%)
5.7
3.2
3.6
0.2
0.6
0.12
0.04
0.4
3.3
7.4
18
35
43
4.6
1.2
3.1
14
1.7
6.4
1.6
97
-------
APPENDIX C. URANIUM-238 SERIES DECAY DATA (continued)
Type Particle
Nuclide and of Refer- Energy
Half -Life Decay ence (MeV)
Bismuth- 214 (continued) 1 . 55
1.62
1.74
1.86
1.90
3.28
Transition
Probability
(%)
17
1.2
3.5
1.0
8.6
19
Electromagnetic Transition
Photon energy
(MeV)
1.3778
1.3854
1.4017
1.4080
1.5095
1.723
1.7647
1.8477
2.119
2.204
2.448
Photons
emitted (%)
4.6
1.
1.7
2.8
2.2
3.2
16.6
2.2
1.3
5.4
1.77
Polonium- 214 a
162 ys
Lead-210 3~
22.3 y
Bismuth-210 a
5.012 d 3~
Polonium- 210 a
138.38 d
21
37
37
37
7.688
0.017
0.061
4.697
1.161
5.3048
100
80 0.046 4.1
20
1.3 x 10~4
-100
-100
NOTE: Percentages relate to the disintegrations of the individual nuclides.
Complete decay schemes are available in the Nuclear Data Sheets.
98
-------
APPENDIX D. URANIUM-235 SERIES DECAY DATA
Type
Nuclide and of Refer-
Half-Life Decay ence
Uranium- 23 5 a 30
7.1 x 108 y
Thorium-231 3~ 30
25.52 h
Protactinium- 231 30
3.248 x IQ4 y a
-
Actinium-227 a 38
21.8 y
3~
Particle
Energy
(MeV)
4.598
4.556
4.502
4.444
4.430
4.417
4.398
4.374
4.368
4.345
4.325
4.216
0.140
0.203
0.213
0.298
5.058
0.27
5.027
5.013
4.986
4.950
4.933
4.851
4.733
4.712
4.680
4.938
4.951
0.019
0.034
0.044
Transition
Probability
(%)
4
3
1.4
1.5
1.5
2
56
6
12
1
3
6
2
11
1.6
-85
11
20
25.4
1.4
22.8
3
1.4
8.4
1
1.5
0.5
0.7
-10
-35
-54
Electromagnetic
Photon energy
(MeV)
0.109
0.144
0.163
0.185
0.202
0.026
0.084
0.0273
0.283
0.300
0.303
0.330
0.407
Transition
Photons
emitted (%)
2.5
11
5
54
5
12
5.1
7
1.6
2.3
2.3
1.3
3.6
99
-------
APPENDIX D. URANIUM-235 SERIES DECAY DATA (continued)
Type
Nuclide and of Refer-
Half-Life Decay ence
Thorium-227 a 38
18.5 d
Francium-223 3~ 38
22 min
Radium-223 a 38
11.4 d
Radon-219 a 38
4.0 s
Particle Transition
Energy Probability
(MeV) (%)
5.707
5.712
5.755
5.976
6.037
0.78
0.914
1.069
1.099
5.534
5.603
5.712
Others
6.423
6.551
8.2
4.9
20.3
23.4
24.5
2.7
15.5
12.5
68
9.2
24.2
52.5
14.1
7.5
11.5
Electromagnetic Transition
Photon energy
(MeV)
0.050
0.236
0.256
0.050
0.080
0.205
0.235
0.122
0.144
0.154
0.270
0.324
0.338
0.271
0.402
Photons
emitted (%)
-10
12.5
6.3
43
10.8
1.4
4.3
~1
~3
~5
-14
-3
-2.5
9.9
6.5
Polonium-215 a 38
1.78 ms
Lead-211 3~ 29
36.1 min
Bismuth-211 a 29
2.13 min
Thallium-207 3~ 29
4.77 min
6.817
7.384
0.544
0.971
1.376
6.622
6.277
81
100
5
1.4
93
84
16
1.431 -100
0.405
0.427
0.832
0.351
0.898
3.8
1.8
3.6
13.3
-0.27
NOTE: Percentages relate to the disintegrations of the individual nuclides.
Complete decay schemes are available in the Nuclear Data Sheets.
100
-------
APPENDIX E. PULSE HEIGHT SPECTRA OF SELECTED RADIONUCLIDES
The net pulse height spectra plotted in the figures of Appendix E were
obtained using a 10.2-cm by 10.2-cm Nal(Tl) crystal. The energy calibration of
the spectrometer system was either 10 or 20 keV per channel, as indicated in
each figure title. Spectra marked with an asterisk were obtained using a
Nal(Tl) well crystal.
Figure Page
E-l. Beryllium-7 net pulse height spectrum calibrated at 10 keV 103
per channel.
E-2. Sodium-22 spectrum with an energy calibration of 10 keV 104
per channel.
E-3. Potassium-40 spectrum calibrated at 10 keV per channel. 105
E-4. Scandium-46 spectrum calibrated at 10 keV per channel. 106
E-5. Scandium-46 spectrum calibrated at 20 keV per channel.* 107
E-6. Chromium-51 spectrum calibrated at 10 keV per channel. 108
E-7. Manganese-54 spectrum calibrated at 10 keV per channel. 109
E-8. Cobalt-56 spectrum calibrated at 20 keV per channel. 110
E-9. Cobalt-57 spectrum calibrated at 10 keV per channel. Ill
E-10. Cobalt-58 spectrum calibrated at 10 keV per channel. 112
E-ll. Cobalt-58 spectrum calibrated at 10 keV per channel.* 113
E-12. Iron-59 spectrum calibrated at 10 keV per channel. 114
E-13. Cobalt-60 spectrum calibrated at 10 keV per channel. 115
E-14. Cobalt-60 spectrum calibrated at 20 keV per channel.* 116
E-15. Zinc-65 spectrum calibrated at 10 keV per channel. 117
E-16. Selenium-75 spectrum calibrated at 10 keV per channel. 118
E-17. Strontium-85 spectrum calibrated at 10 keV per channel. 119
E-18. Yttrium-88 spectrum calibrated at 20 keV per channel.* 120
E-19. Zirconium-95 spectrum calibrated at 10 keV per channel. 121
E-20. Niobium-95 spectrum calibrated at 10 keV per channel. 122
E-21. Ruthenium-103 spectrum calibrated at 10 keV per channel. 123
E-22. Ruthenium-106 spectrum calibrated at 10 keV per channel. 124
E-23. Cadmium-109 spectrum calibrated at 10 keV per channel. 125
101
-------
APPENDIX E. PULSE HEIGHT SPECTRA OF SELECTED RADIONUCLIDES (continued)
Figure Page
E-24. Silver-llOm spectrum calibrated at 10 keV per channel. 126
E-25. Silver-llOm spectrum calibrated at 20 keV per channel.* 127
E-26. Tin-113 spectrum calibrated at 10 keV per channel. 128
E-27. Antimony-124 spectrum calibrated at 10 keV per channel. 129
E-28. Antimony-125 spectrum calibrated at 10 keV per channel. 130
E-29. Iodine-131 spectrum calibrated at 10 keV per channel. 131
E-30. Barium-133 spectrum calibrated at 10 keV per channel. 132
E-31. Cesium-134 spectrum calibrated at 10 keV per channel. 133
E-32. Cesium-134 spectrum calibrated at 20 keV per channel.* 134
E-33. Cesium-137 spectrum calibrated at 10 keV per channel. 135
E-34. Cerium-139 spectrum calibrated at 10 keV per channel. 136
E-35. Barium-140 spectrum calibrated at 10 keV per channel. 137
E-36. Cerium-141 spectrum calibrated at 10 keV per channel. 138
E-37. Cerium-144 spectrum calibrated at 10 keV per channel. 139
E-38. Gold-195 spectrum calibrated at 10 keV per channel. 140
E-39. Mercury-203 spectrum calibrated at 10 keV per channel. 141
E-40. Bismuth-207 spectrum calibrated at 10 keV per channel. 142
E-41. Radium-226 spectrum calibrated at 10 keV per channel. 143
E-42. Natural uranium spectrum calibrated at 10 keV per channel. 144
E-43. Thorium-232 spectrum calibrated at 10 ke.V per channel. 145
E-44. Americium-241 spectrum calibrated at 10 keV per channel. 146
E-45. Background spectrum calibrated at 10 keV per channel. 147
102
-------
104
10 3
102
NET
CPM
10
10ฐ
. '
.
JZUJ//^
"~" *"~
1
I
1
1
1
H-
. ...
__
-
_ J
9
s
3
2
,35
CHANNEL NUMBER
Figure E-l. Beryllium-7 net pulse height spectrum calibrated at
10 TceV per channel.
103
-------
104
135870 DFH071Z7204DO
igi:573],71
103 m.
102
NET
CPU
10
10ฐ
40
SO 120
CHANNEL NUMBER
160
200
Figure E-2.
Sodium-2 2 spectrum with an energy calibration of
10 keV per channel.
~104
-------
103
DPn072473q.400
072573154
102 iffJX*!^
10
NET
CPU
10-1
10ฐ '"' -^-
ISO
20O
CHANNEL NUMBER
Figure E-3. Potassium-40 spectrum calibrated at 10 keV per channel.
105
-------
10*
173J150
103
10 2
NET
CPM
10
10ฐ
40
80 I2O
CHANNEL NUMBER
160
200
Figure E-4. Scandi\m-46 spectirum calibrated at 10 keV per channel.
106
-------
10
103
10 2
NET
CPU
10 :
10
CHANNEL NUMBER
Figure E-5. Scandium-46 spectrum calibrated at 20 kev per channel.*
107
-------
10
10
NET
CPM
10-1
10-2
77274 OfHO 410731
40
80 12O
CHANNEL NUMBER
160
2OO
Figure E-6. Chromivon-51 spectrum calibrated at 10 keV per channel.
108
-------
103
10 2
NET
CPU
10
10ฐ
CHANNEL NUMBER
Figure E-7. Manganese-54 spectrum calibrated at 10 keV per channel.
109
-------
10*
052874q94
103
102
NET
CPU
10
10ฐ
OPH04Z97404DO
40
SO 120
CHANNEL NUMBER
160
200
Figure E-8. Cobalt-56 spectrum calibrated at 20 keV per channel.
110
-------
10s
10*
103
NET
CPM
102
10
317607 DFM042374040Q
CHANNEL NUMBER
Figure E-9. Cobalt-57 spectrvim calibrated at 10 keV per channel.
Ill
-------
10
10 4
103
NET
CPM
102
10
40
80 120
CHANNEL NUMBER
Figure E-10. Cobalt-58 spectrvrai calibrated at 10 keV per channel.
112
-------
105
10
103
NET
CPM
102
10
ao 120
CHANNEL NUMBER
Figure E-ll. Cobalt-58 spectrum calibrated at 10 keV per channel.*
113
-------
10
3 fE
59 F 356 1342200 DPM02Q77304DO
1015731,63
lit:*
102
10
NET
CPM
10ฐ
10-1-i
MSPifJIJl
4O
80 12O
CHANNEL NUMBER
160
200
Figure E-12. Iron-59 spectxvua calibrated at 10 keV per channel.
114
-------
10s
1106751,341
10*
10 3
NET
CPM
102
10
CHANNEL NUMBER
Figure E-13. Cobalt-60 spectrum calibrated at 10 keV per channel.
115
-------
104
0404741.1-3
103
102
NET
CPU
10
10ฐ
Z54934 OFM0410700400
40
80
CHANNEL NUMBER
Figure E-14. Cobalt-60 spectrum calibrated at 20 keV per channel.*
116
-------
1C)3
10
NET
CPU
10ฐ
10-1
65 F 313 207662 DPn0524T30400
CHANNEL NUMBER
Figure E-15.x Zinc-65 spectrum calibrated at 10 keV per channel.
117
-------
104
103
102
NET
CPM
10
100
51,04
SO 120
CHANNEL NUMBER
Figure E-16. Seleniumr-75 spectrum calibrated at 10 keV per channel.
118
-------
1015731,65
104
10 3
NET
CPU
102
10
DPN0614730400
M!j 'MiiflM 1|1-! ji!
CHANNEL NUMBER
Figure E-17. Strontium-85 spectrum calibrated at 10 keV per channel.
119
-------
Y
88812203 287402 DFM0411740400
0514740,92
103
NET
CPU
10
10ฐ
40
80 120
CHANNEL NUMBER
Figure E-18. Yttrium-88 spectrum calibrated at 20 keV per channel.*
120
-------
104
0501741,00
103
102
NET
CPU
10
10ฐ
3341Z6 DPM0320740
CHANNEL NUMBER
Figure E-19. Zirconium-95 spectrum calibrated at 10 keV per channel.
121
-------
10*
10 3
102
NET
CPM
10
100
1385780 DPM070Z74C
ฑtft riiinri ,'rTnr
latm^itgpr
40
8O 120
CHAMWEL NUMBER
ZOO
Figure E-20. Niobiumr95 spectrum calibrated at 10 keV per channel.
122
-------
10*
10 3
102
NET
CPM
10
10ฐ
097920 PPM 1002730400
* "f" t-t- + I ' i , ! . i l -r -H-i li
CHANNEL NUMBER
Figure E-21. Ruthenium-103 spectrum calibrated at 10 keV per channel.
123
-------
103
300620 DFM0221730400
012874101
102
4O
80 120
CHANNEL NUMBER
16O
20O
Figure E-22. Ruthenium-106 spectrum calibrated at 10 keV per channel.
124
-------
105
10 3
NET
CPU
102
10 1
0.1... 30.3997000 DPtin31414n4nO
CHANNEL NUMBER
Figure E-23. Cadmium-109 spectrum calibrated at 10 keV per channel.
125
-------
10
36308L DPM10177304DO
032874q95
103
10*
NET
CPM
10
100
160
200
CHANNEL NUMBER
Figure E-24. Silver-llOm spectrum calibrated at 10 keV per channel.
126
-------
104
103
102
NET
CPU
10
10ฐ
9977 DPM1017730400
80 120
CHANNEL NUMBER
Figure E-25. Silver-110m spectrum calibrated at 20 keV per channel.*
127
-------
105 5N 113960101 24000000 DPHOTQ1751200
i t t I ' M M I I )"' nTi t i * ( ( t ' ! ! ! t t tT l"i'B-! ' i'Tl ' l-r-4-t-r-4-l-4'l-- ! ' M j T i-H ' !('( r i"t-'- t'-t-i-t-t-i
104
103
NET
CPU
102
10
062376100
200
CHANNEL NUMBER
Figure E-26. Tin-113 spectrum calibrated at 10 keV per channel.
128
-------
10.4 SB
103
102
NET
CPU
10
DPM06Q7730400
SO 120
CHANNEL NUMBER
Figure E-27. Antimony-124 spectrum calibrated at 10 keV per channel.
129
-------
10 3
102
10
NET
CPU
10ฐ
4O
SO 120
CHANNEL NUMBER
160
Figure E-28. Antimony-125 spectrum calibrated at 10 keV per channel.
130
-------
105 l
12730,91
104
103
NET
CPM
10 2
10
QPH0919730400
CHANNEL NUMBER
Figure E-29. Iodine-131 spectrum calibrated at 10 keV per channel.
131
-------
10 4
103
10 2
NET
CPM
10
10 0
CHANNEL MUMBER
Figure E-30. Barium-133 spectrum calibrated at 10 keV per channel.
132
-------
104
662619 DFH0325750400
092275Q95
103
102
NET
CPM
10
100
40
8O 120
CHANNEL NUMBER
Figure E-31. Cesium-134 spectrum calibrated at 10 keV per channel.
133
-------
270486 PPM 1205720400
041074115
103
10 2
NET
CPM
10
10ฐ
4O
80 120
CHANNEL NUMBER
Figure E-32. Cesium-134 spectrum calibrated at 20 keV per channel.*
134
-------
031075100
10 3
10 2
NET
CPU
10
10 0
DPH06ZZ7Z0400
80 ~ 120
CHANNEL NUMBER
Figure E-33. Cesium^l37 spectrum calibrated at 10 keV per channel.
135
-------
,10s
11777150
10
103
NET
CPM
102
10
DPMO 01770400
m 12
CHANNEL NUMBER
Figure E-34. Cerium-139 spectrum calibrated at 10 keV per channel.
136
-------
10*
10 3
102
NET
CPU
10
10ฐ
7402300 DPH1217730400
CHANNEL NUMBER
Figure E-35. Barium-140 spectrum calibrated at 10 keV per channel.
137
-------
10*
042274\00
10
10 2
NET
CPM
10
10ฐ
6466610 PPM 1122730400
CHANNEL NUMBER
Figure E-36. Cerixna-141 spectrum calibrated at 10 keV
138
per channel.
-------
105
700102 6725370 DPH0221-73040Q
74Q92
10*
103
NET
CPM
102
10
loame escape peax
H-H
ซ0 120
CHANNEL NUMBER
Figure E-37. Cerium-144 spectrum calibrated at 10 keV per channel.
139
-------
104
103
10 2
NET
CPM
10
10ฐ
0391771515 1OSIS
CHANNEL NUMBER
Figure E-38. Gold-195 spectrum calibrated at 10 JceV per channel.
140
-------
01074171
DPf10719740400
mitimiip
10
CHANNEL NUMBER
Pigure E-39. Mercury-203 spectra calibrated at 10 keV per charmel.
141
-------
10
10
10 3
GROSS
CPU
10 2
10
SO 120
CHANNEL NUMBER
Figure E-40. Bismuth-207 spectrum calibrated at 10 keV per channel.
142
-------
10 4
103
10 2
GROSS
CPU
10
10ฐ
135
40
80 120
CHANNEL NUMBER
160.
200
Figure E-41. Radium-226 spectrum calibrated at 10 keV per channel.
143
-------
103
Z130.91
10 2
10
GROSS
CPU
10
10-1
40
80 120
CHANNEL NUMBER
160
200
Figure E-42. Natural uranium spectrum calibrated at 10 keV per channel.
144
-------
10
10 3
102
GROSS
CPM
10
100
40
80 12O
CHANNEL NUMBER
Figure E-43. Thoriuifr-232 spectrum calibrated at 10 keV per channel.
145
-------
10*
067476140
103
102
GROSS
CPU
10
K>
CHANNEL NUMBER
Figure E-44. Americium-241 spectrum calibrated at 10 keV per channel.
146
-------
GROSS
CPU
10-3-
40
80 120
CHANNEL NUMBER
Figure E-45. Background spectrum calibrated at 10 keV per channel.
ซU.S. GOVERNMENT PRINTING OFFICE: 1978-785-327 147
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
BPA-600/7-77-144
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
QUALITY CONTROL FOR ENVIRONMENTAL MEASUREMENTS
USING GAMMA-RAY SPECTROMETRY
5. REPORT DATE
December 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Lee H. Ziegler and Hiram M. Hunt
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Monitoring and Support Laboratory
Office of Research _and Development
U.S. Environmental Protection Agency
Las Vegas, Nevada 89114
10. PROGRAM ELEMENT NO.
1NE625
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency-Las Vegas, NV
Office of Research and Development
Environmental Monitoring and Support Laboratory
Las Vegas, Nevada 89114
13. TYPE OF REPORT AND PERIOD COVERED
Final FY-77
14. SPONSORING AGENCY CODE
EPA/600/07
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This report describes the quality control procedures, calibration, collection,
analysis, and interpretation of data in measuring the activity of gamma ray-
emitting radionuclides in environmental samples. Included in the appendices are
basic data for selected gamma ray-emitting radionuclides, the uranium-235 series,
the uranium-238 series, and the thorium-232 series, Typical pulse height spectra
of selected gamma ray-emitting radionuclides measured with a Nal(Tl) detector
are included in an appendix.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Quality Control
Gamma-Ray Spectroscopy
14D
07B
18D
20F
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)'
UNCLASSIFIED
21. NO. OF PAGES
. 158
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
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