ITR-lH
A BASIC, MULTI-OPTION NEUTRON ACTIVATION ANALYSIS PROGRAM
FOR THE DIGITAL COMPUTER
by
B. W. Hoffman and S. B. Van Camerik
INTRODUCTORY DISCUSSION
A computer program has "been prepared by personnel of the Southwestern
Radiological Health Laboratory, U.S. Public Health Service, which performs
the station's required calculations for activation analysis studies. The
program was written in Fortran II, Version 2, for use with the IBM 1620
digital computer, and has the capability of calculating the neutron flux
density, an expected activation for specified conditions, or the reaction
cross-section for a nuclide in question, or performing a quantitative
determination for observed conditions.
During the activation of a sample there are several interdependent re-
actions occurring. To examine the simplest example, we have : •
B
I
I
IX
where nuclide A is activated to nuclide B, which then decays to nuclide C.
When the irradiation of A is started, there is no nuclide B or C present.
However, nuclide B immediately starts to appear and also decay to nu-
clide C. The rate of production of nuclide B is dependent upon the quan-
tity of A present, the activation cross-section of nuclide A, and the,
neutron activation flux. These quantities remain essentially constant
throughout the irradiation. The radioactive nuclide B decays at a rate
which is dependent upon the quantity of B present, and B is replenished
at a constant rate. The calculations can be effected manually, but are
laborious and time consuming when many samples are to be analyzed.
This program was intentionally • limited in scope to handle only a problem
such as the previous example. One can imagine a more complex activation-
decay scheme; such as,
- al a2 o3
A * B ^C ^etc.
i I
i ' i '
\2 I A3 |
i ^ I 05
D ---- E ------ etc.
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but for our particular application, employing a Cockroft-Walton type
neutron generator where one is limited to short irradiation times and a
relatively low neutron flux (109 n/cm2/sec); the former, simpler scheme
is of primary concern since the activity contributed by secondary acti-
vation is in most cases negligible or undetectable.
PROGRAM OPERATION AND THE INPUT-DATA CODING SHEET
An examination of the input-data coding sheet shows that one punched card
is used for each problem. In some instances, it may be desired to run
the problems in a.specified sequence. A space has been provided for
specifying the running order (l - 99). The purpose for imposing a se-
quential sample requirement is that a previously calculated or used flux
value can be further utilized in ensuing problems. For example, if a
sample and a flux monitor foil were irradiated simultaneously, the flux
value calculated from the foil could be used to calculate the sample in-
formation without having to send the data to the computer a second time.
If sequential sample running is not desired, sense switch one (1) on the
computer console is turned on. If the samples are not in sequence and
sense switch one (1) is off, a message is printed via the typewriter and
the computer halts. The cards can then be arranged or corrected. To
cause the computer to use the previous flux value, one merely leaves the
flux input-data blank.
The data sheet should be self-explanatory except for some units used. The
sample identification can be alphabetic, numeric, or both. The isotopic
mass is to be entered as the number of atomic mass units (A.M.U.), sample
weight is to be in grams, neutron flux in neutrons/cm /sec., and the acti-
vation cross-section in barns. The other units involved are explained on
the data sheet itself.
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MATHEMATICAL DEVELOPMENT AND USE OF ITERATIVE IMPROVEMENT
A) First Approximation of Flux Value
For the basic activation-decay scheme proposed earlier:
°1 °2
A *B *
I I
where M =0, indicating the target nuclide is stable, the basic
Bateman Equation is:
.* ,o , -Ait -Apt,
N2 = A! N! (e * -e 2 )
A2-Ai
As is conventional, the subscript (1) is assigned to the parameters
of the target nuclide (A) and the subscript (2) is assigned to those
of the primary activation product (B) .
therefore, when:
*
= o"i +
where :
<|> = flux (FLUX)
o. = cross section for nuclide i
i
A^ = decay constant for nuclide i
N° = no. of target atoms (AVOGAD)
t = irradiation time (l(2))
the Bateman Equation above becomes then:
iv <).(a2-a1)+A2 v"
multiplying both sides by A2, we find then:
-a1)+A2
-------
i M -ta2 -
°r XN = e -e 2e
v
Now applying the approximation e = (1-hc) selectively, the following is.
generated:
A2a1N° .
- 2
or
,
2+(ta2e
Now multiplying means by extremes, we obtain:
X2N2(a2-o1)<})+A2N2X2 = (X2a!Ni) (l-e~tX2)(j)+(A2a1N°) (ta2e~tX2-ta1)2
Factoring and transposing, the following quadratic equation in is
produced :
A2N2
= 0
_ _
which when considering o2 = Ot i.e., no secondary activation product
generated, becomes:
_ A2N2
(2)
This quadratic is then solved by conventional means for the first approx-
imation of the flux value. N.B. The approximation ex = (1+x) has been
invoked only to facilitate acquiring a reasonable first approximation of
the flux value.
B) Iterative Improvement of the Flux Value
Again considering the basic Bateman Equation (1) for the case of the
simple activation-decay scheme where as above:
AI = 0 ; certainly the case with a stable target nuclide.
a2 = 0 ; essentially, with so very little of the primary activation
product synthesized.
-------
we have :
, , .
-4>0lt -Apt,
~
Dividing by A2O}Ni and transposing, the following equation is obtained:
- PHI
- PHI
If we let the left side of this equation (3) equal PHI, as indicated, we
can now, starting with the first approximation of the flux value, improve
upon this initial value by iteratively adjusting the previously determined
flux value by a pre-determined, small increment. The constraint,
of course, for this improvement is that the previous flux value is adjusted
by this increment (0.0001ij>) until PHI changes sign or does in fact equal
zero. The flux error is then < + O.OOOl'f''
It is to be noted that throughout the above development the \2N2 term is
kept intact wherever possible, since this represents the activity (ACTIV)
of the primary activation product.
C) Calculation and Iterative Improvement of Activation Cross Section
The mathematical development for this determination is analogous to that
for the flux determination as is readily seen from the program listing
for this section.
D) Computation of the Expected Activation
With the flux ($) value having been preassigned or pre-determined and:
(sample wt.)(6.023xl023)[Fract.Abund.]
(4) N° - AVOGAD - No. of target atoms =
Isotopic Mass of Target Nuclide
and also t = T(2), X2 = 'TTT where T(l) represents the half-life
of the primary activation product, 0, previously known or calculated,
then:
-------
where again AI = 0; a2 = 0.
This disintegration rate is then corrected to account for further decay
during the transit time of the sample (T(3)) to give the investigator a
closer picture of the rate to be expected.
E) Analytical Determination
Solving equation (5) for Nj, we obtain:
NT = AVOGAD =
/
(e
-A2t,
- *
Manipulating equation (4) algebraically and substituting in the value for
N° = AVOGAD into the following equation (6) , we can then calculate the
sample weight:
(6) Sample Weight
(Nj) (Isotopic Mass of Target Nuclide)
(6.023xl023) (Fract. Abund. of Target Isotope)
Obviously this gives the investigator not only the opportunity to quantitate
an unknown sample, but also the option of calculating how much sample, the
purity of which has been reasonably well characterized, to irradiate in
order to produce, for example, a desired (threshold) level of activity.
F) Additional Note
In statement 280, the disintegration rate (ACTIV) is corrected from the
'time-center' T(5) of the counting interval back to the end of the
transit time T(3) (or to the beginning of the counting time, i.e.,
T(4) = 0). This so-called .'time-center' T(5), as calculated by state-
ment 260, represents the true time corresponding to the observed gamma
count rate. This is significant since the value of ACTIV is critically
involved in all the options of this program except the computation of
expected activation.
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Glossary of Terms* Used Directly in Fortran II, Version 2, Program Listing:
NUMR - assigned sample number
SAMPLE - other identification of sample
OPER - designates option or defines mode of operation
NEXT1 - defines running order of samples
SMASS - isotopic mass of target nuclide
FRAG - fractional abundance of target nuclide
WEIGHT - actual weight of the sample irradiated (in grns.)
FLUX - neutron flux in n/cm2/sec.
XSEC - neutron activation cross-section of the target nuclide (in barns)
T(l) and U(l) - primary activation product half-life and units
T(2) and U(2) - length of irradiation time and units
T(3) and U(3) - length of transit time of sample and units
T(4) and U(U) -.length of counting time and units
CPM - observed count rate of sample
EFF - efficiency of gamma spectrometer system
DECAY - decay constant (\2) of the primary activation product
T(5) - 'time-center1 correction to the end of the transit time
ACTIV - disintegration rate (or activity) of the sample
AVOGAD - no. of atoms of target nuclide in sample
PHI - as defined in equation (2) above
DPM - disintegration rate of the sample (to be expected)
From this list and the actual program listing, it is apparent that the
language employed very directly reflects the logic involved, facilitating
total comprehension of the.program and its utility even for the neutron
activation analyst unfamiliar with programming techniques. Here is made
available a program which will easily lend itself to programming language
conversion to match other computer capabilities and which may be readily
integrated into more complex, computerized analytical schemes as required
by a particular effort.
*In order of their appearance in the program listing.
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SWRHL NEUTRON ACTIVATION ANALYSIS
Disposition of Sample:
Act i vated:
enta:
Requested by:_
Date:
Operator:
Sample No.
Identification
Operation
Running Order
I.sotopic Mass
Fractional Abundance
Sample Weight
Neutron Flux
Activation Cross-Section
Product Half Life .& Units
^Fradiation Time & Units
Transit Time & Units
Counting Time & Units
Net Counts Per Minute
Counting Efficiency
Activation Analysis Program
12 3
(13) I I
(A8)
(Al)*
(12)
(F6.0)
(F5.0)
(F8.0)
(E8.0)**
(F6.0)
(F5.0) (Al)***
(F^.O) (Al)***
(Ffc.O) (Al)***
(FU.O) (Al)***
(F7.0)
(F5.0)
7 8 9 10 11
13
15 16 17 18 19 20
21 22 23
2»r 25
26 27 28 29 30 31 32 33
MM
35 36 37 38 39 WO
IT 8 V9 50 51 52
53
n
_5jT_5_5_
56
57
fin
si
6 5_
66 67
68
69 70 71 72 73 7^ 75
M M M T
76 77 78 79 80
11>
i
* - Defines mode of operation as follows:
F - Flux determination
D - Expected Activation determination
A - Analytical determination
C - Cross section determination
** - If neutron flux used or determined in
immediately preceeding problem is to be
used, leave blank.
*** - Indicate units of time
as follows:
S - seconds
M - minutes
H - hours
D - days
Y - years
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PROGRAM FLOW CHART
Samples
in
Order
9
Print
Error
Order
Required
Conversion
Print
.Error
Units
Conversion
Xsec, Flux
Decay con-
stant
Flux
entered if
Print error
&: incre-
ment sam-
ple number
necessary
9
No
Determine
operation:
'~F-flux
D-exp. act.
A-^anal. det
C-xsection
D
F,J
Correct'
for decay
during tran
sit and
counting
Calculate
expected
activation
Approx. &
Iterative
improve'
of flux
Calculate
wt. of
element
Approx. &
Iterative
improve /
of xsec
Print as
PPM
increment
sample
__L number
Print as
n/cm /sec
increment
sam,ple
number
Print as
Grams
increment
sample,
num.be r
Print .as
Barns
increment
sample
number
-A-
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« 16044
C SWRHL ACTIVATION ANALYSIS PROGRAM
C
C 8.W* HOFFMAN A^O 5*3, VAN CAMg«I*C USPHS OCTOBER 1966
C
IFJSF.NSE SWITCH 9)1 •!
I CQNTlttUET
DIMENSION T<3)»U<4)
2 'FORMAtl 54MTUftM SW I ON TO OVERRIDE SEQUENTIAL SAMPLE REQUIREMENT//
1)
4 FORMAT < 36HSAMPl.es WOT |M PROPER HUMMING QfiDJt*U /24HRF.PLACE AND PR£S
IS START. //|
5 FORMATC 7HS AMPLE tI3»4lH ESSQR IN UNITS OF TIM£ OR HALF LIFE,/
I/)
6 FOftMATf 7HSAMPUE «I3»2©H ILLgGAL OPERATION COOE.//)
7 F0^^4AT( 7HSAWPLE «I3»2XA9/27H FLUK DENSITY « *E10«3»19H
8 FORMAT ( 7MSAWPL? »I3t2XA9/34H EKPgCTggi ACTIVATION « »E1
!0.3»34M DPM FOR THE SPECIFIED COMDITICKA.//}
<5 FORMAT < 7HSAMPLE t!3t?XA9/99H WEIGHT OF TARGET ELEMFNT
10 FORMA T« 7HSAMPLE »|3t?XA9/2eH CROSS SECTION *
1 RARN*//)
U FORMAT* 7MSAMPLE »!3t34M NO FLUX VALUE ENTERED* //')
FLUXR«0.
?0 PAUSE
30 READ 3*NUMR*SAMPLEtOPER*NeXTl»SMASS«FAAC«tf£lGHT»FLUX»XS£C»T(l)»U(l
F SWITCH I \ 100*40
40 !F^4EXT1-^EXT-1)90»100»90
50 PRIWT 4
GO TO 20
C
C TIME CONVERSION TO MINUTES
C
100 00 200 I«lt4
no rei!»rct
GO TO 200
120 IF(UC!)-«
130 !F(U(I)-«4SJ150»140»150
T( H«T| ?)*60.
6'0 TO 200
1P(U 196 »200* 19-8
193 PRINT 3
GO TO 20
200 CONTINUE1
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C CALCULATE CROSS SECTIONS* D2W CONSTANT* AMD FLUX
C
DECAY«LOGF(2.J/TF < -9ECA Y*T I 2 9 U /« OEC A Y-
320
PHI eFLUXS' I EKPF I -FLUXOJtS£Ce? £ 2 » 8 -EW I -DEC A V*T « 2 J » / 1 OECAY-Ft.UX»XSE
' l
330
PRINT
NE
K SWITCH
r
C COMPUTATION OF
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r
340
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PRINT
N£XT*N£.XT1
FLUXR»FLUX/feO.
IFCSfNSE SWITCH
c
r ANALYTICAL
c ••
350 AVOGAO« ACT I V»l OECAY-FLUX*XSEC ) / 1 0£CAY»FI.UX«XSEC« I£XPF ( -FLUX#XSEC#T
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eX
SWITCH S>S20»30
c
C CALCULATE OF ACTIVATION CROSS
c.
360 A«-FLUX«7(2>
@« 1 .-FXPP < -DECAY07 « 2 ) > *ACTI V/ < PCCA Y^AVOGADI
r
C ITERATIVE IMPROVEMENT 0^ C«OSS
C
1 C I -ACT 1 V/ « DFCAY»XSFC»AV06AO)
370 X5EC*XSEC+o0001«XSEC
PH? spLUX^ < EXPF ( -FLUKC5XSPC®? ( 2 § £~£«PF ? -OECAY^T « 2 > H / « DEC AY-FLUX«XS£
1C J -ACTI V/ « DECAYOXSEOAVOGAOS
380
390
PRINT
1FISENSE SWITCH
S-MD
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