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B.A.R.C-686
000
3
GOVERNMENT OF INDIAATOMIC ENERGY COMMISSION
ANALYSIS OF COMPLEX Nal (Tl) GAMMA-SPECTRA FROM MIXTURES OF NUCLIDES
byC. Rangarajan, LI. C. Mishra, Smt. S. Gopalakrishnan and S. Sadasivan
Health Physics Division
DHABHA ATOMIC RESEARCH CENTRE
BOMBAY, INDIA
1973
T3.A.H.C.-686
GOVERNMENT OP INDIAATCMIC ENERGY COMMISSION
u•
ANALYSIS OP COMPLEX !JaI (Tl) . r,A?/MA-SFECTnA WXjUi MIXTURES OP
by
C. Rangarnjan, U.C. Mishre . Smt. S. Gopalakriehnan and S. SedaoivanHealth Thysics Divis ion
BHABHA ATCMIC RESEARCH CENTREBO1BAY, INDIA
1973
ABSTRACT
The report describee methods o f gassa apestrua analys i s being
used In t h i s laboratory. The gamma spectra are taken with Hal (Tl)
d e t e c t o r s of d i f f e r e n t dimensions on various ault ichannel analysers .
The samples being analysed are airborne f a l l o u t r a d i o a c t i v i t y , surfaoe
d e p o s i t i o n s t milk ani other food s t u f f s and countrywide surface s o i l s .
These samples contain both natural gamma a c t i v i t i e s from t e r r e s t r i a l
sources and f a l l o u t r a d i o a c t i v i t y , mostly f i s s i o n products, due t o
nuclear explos ions . The methods of analyses described are spectrum
s t r i p p i n g , simultaneous equations and the l e a s t squares method. The
r e l a t i v e merits and demerits of the d i f f e r e n t methods and the parameters
of the instrument systems being used are a l s o g iven.
ANALYSIS OP COMPLEX Nal (Tl) GAMMA-SPECTRA FROM MIXTURES 0? ITOCLIDES
by
G. Rangarajan, U.C. Mishra, Smt. S. Gopalakrishnan and S. Sadaaivan
1. INTRODUCTION
Scintillation spectrometers consisting of Nal (Tl) detectors of
various dimensions and multichannel analysers are being extensively used
far the measurement of samples containing mixtures of gamma-emitting
(1 2)nuclldes * . Though the method is simpler than the conventional
chemical methods,, the accuracy of the estimations is dependent on the
complexity of the gamma spectrum. The samples being analysed at this
laboratory include airborne radioactivity collected on filter papers,
rain-water, soil, food stuffs etc. This report describes the various
methods of apectrum analysis being used at this laboratory. Computer
programmes written in Fortran language used in these enalysas have also
been included.
2. COMPOSITION OP A GAMMA SPECTRUM
The gamma spectrum of a s ingle mono-energetic nuc l ide cons i s t s of
a f u l l energy peak, approximately Gaussian in shape, corresponding t o the
gamma energy of t h e n u c l i d e , and a cont inuous d i s t r i b u t i o n moBtly a t
ene rg i e s lower than t h e f u l l energy peak. The f u l l energy peak i s due t o
the complete absorp t ion of gammas w i t h i n the d e t e c t o r , e i t h e r by
photoelectric effect, or by multiple interactions of various types
-2-
reeulting in complete absorption within the detector. The continuous
distribution arises due to events in which only a part of the photon
energy Is absorbed inside the detector volume while the photon carrying
the regaining energy escapes from the detector. The processes that can
give rlae to such interactions are the following:
a) Compton scattering in which the scattered photon
escapes the detector,
b) Pair-production events in which one or both the
photons escape from the detector (valid only for
thoae sources which emit gammas of energies greater
than 1.02 MeV),
c) Pair-production events occuring outside the
detector in which one or both the photons from
positron annihilation enter the detector,
d) Photons scattered by the materials outaide the
detector, such as lead shields, etc., into the
detector volume,
e) Photono degraded in energy due to self-scattering
in the sample material or by small anglt- scattering
events in the detector can,
f) "Bremsstrahlung" radiation in the case of high
energy beta emitters due to the stopping of betas
in the abnorbera placed between sample and detector
to prevent their entering the detector,
g) "Iodine Escape Peak" at lower energise due to the
escape of X-rays from the excitation of Iodine atoms
in the Nal crystal,
-3-
h) "Summing" of two photon energies either due to
random summing of energies of two or more
scattered photons particularly in the case of
very active sources, or due to cascade emission
as in Co-60, in which case their contribution
extends from lower energies to the energy
corresponding to the sun of the two photon energies*
The last mode of interactions can give r i se to contributions in
the gamma spectrum at energies higher than the photopeak energy .
It i s evident from the above description that the gamma-apectrua
of samples containing a mixture of nuclidea i s complex. The most eooaon
nethod of analysing gamma spectrum i s to use the fu l l energy peak counts
of various isotopes for estimating their ac t iv i t i e s because the f u l l
energy peak i s generally characteristic of the isotope and i t i s in this
energy region that a better sample to background counts ratio i s
obtained. The background referred here i s not only the conventional one
due to cosmic-rays and terrestrial radiations but also the continuous
portion of the spectra due to other ful l energy peaks in the sample.
If the constituent nuclidea of a sample emit gamma rays of closely
spaced energies, i t ie often advantageous to select only a small portion
of the f u l l energy peak of each of them. This reduces tae region of
mutual overlap of adjacent peaks as shown in Figure 1, thereby improving
isotope counts to background ratio for each of the radionuclides. This
method of selecting fu l l energy peak regions for the anaJgrais has sons
disadvantages also . If the region selected i s too narrow, the counts
-4 -
summed are reduced giving r i s e t o poorer s t a t i s t i c s . Also, the
errors due to gain and threshold d r i f t s in the analyser can be
s ign i f i cant . Hence the s e l e c t i o n should be made i n such a way that
the effect of d r i f t s In the sr^alyser as wel l as overlap of the
adjacent peaks i s kept to a minimum. While s e l e c t i n g these energy
regions , i f an Isotopes emits more than one gamma rays , the moat
abundant gamma energy should be taken for a n a l y s i s . If there are
several gamma energies with comparable abundances, the highest energy
which i s l i k e l y to have least compton contributions from other nuc l ldes ,
should be se l ec ted .
3 . ANALYSIS OF GAMMA SPECTRUM
The choice of the method of analysis depends on the complexity
of the gamma spectrum, i . e . the number of nucl ides present i n the
sample and the computing f a c i l i t i e s avai lable . A number of a n a l y s i s
methods are in use at th i s laboratory. The simplest method i s the
spectrum stripping technique. This method i s used when the samples
contain 2 to 3 isotopes oaly with widely separated gamma energ ie s , a s in
the case of milk samples which contain mainly Cs-137 and K-40. In cases
where samples contain 5 to 6 or more nuclides (a i r f i l t e r s , s o i l samplen
e t c . ) and the gamma spectra have several c l o s e l y spaced overlapping
peaks, simultaneous equations or least squares method i s being used.
The following sections describe the above methods in deta i l and d iscuss
the ir re la t ive advantage mi disadvantages.
-5 -
3.1 Method of Spectrum Stripping:
The principle of the method for the analysis of milk samples i s
shown analytically in Figure 2. Curve (a) shows the gamma spectrum of
the milk sample as recorded by the analyser. Curve (b) shows the
background spectrum for the sample counting period. The background
subtracted sample spectrum i s shown by Curve (c) . A standard source
spectrum for K-40 i s taken separately. After background subtraction the
at 1.46 MeV i s normalized to the sample spectrum by multiplying the
standard spectra with a suitable factor (ratio of peek counts of source
to sample) so that the K-40 peak at 1.46 MeV in'the standard source
spectrum exactly coincides with that for the sample. This factor
multiplied by the K-40 content of the standard gives the K-40 activity
in the sample. The counts in a l l the loner energy channels are also
then multiplied by the above factor and th i s normalised K-40 spectrum i s
shown in the above figure by Curve (d) . Curve (d) i s then subtracted
channel by channel from Curve (c) giving Curve (e) which represents the
gamma spectrum due to Cs-137 activity of the sample. The photo-peak
counts of 0.661 MeV gamma ray in the above curve are compared with the
photo-peak counts of Cs-137 standard spectrum to get the Cs-137 content
of the sample*
In practice, the spectrum i s divided into as many regions as
the number of isotopes present. These regions are selected around the
total energy peak as described In the earlier section. The spectra
of the standard sources are taken and for each source, the counts in
-6-
other regions as a fraction of counts in the total energy peak region
of that isotope are determined. These fractions are referred to as
the compton fractions of those regions. Thus if P.. are the counts due
to isotope J in region 1 and if P, are the counts in the total energy
peak region of the spectrum of isotope j , the compton fraction nt^,n
for region i due to isotope J is given by
f i3 " PiJAJ
If C are the counts due to sample in region i , they can be
expressed as
f i1 * P1 + f i2 ' P2 + f i i P i + •"• fiJPJ ° i
Where t.. i s unity.
Therefore for j isotopes, j equations of the above type can bs
solved.
To illustrate this method for the case of milk spectra described
above, it can be seen that since the energies of Cs-137 (0.662 MeV) and
K-40 (1.46 HeV) are far apart, there will be no contribution due to
Ce-137 in K-40 region and the above equations simplify to
Pcs + f c s , k ' P k " °1
and
Pce
Pk " C2
where C1 and 0g are the sample counts in the photo-perk regions selected
for Cs-137 and K-40 peaks respectively. The activities due to Cs-137
- 7 -
and K-40 can be estimated by multiplying P and P. by their total
energy peak efficiencies determined from their standard sources.
Factors f. and photo-peak efficiencies can be accurately determined
from fairly active standard sources of the concerned isotopes. The
geometries of standard sources and the samples should be identical
as otherwise the f factors calculated from source readings wi l l not
be valid for the samples.
The above method i s simple and does not need computers but it
i s applicable only for aamples containing 2-4 isotopes with well
separated gamma peaks. It also requires that the successive highest
energies contain no counts from lower energies either due to overlap
or due to secondary energies* If some of the peaks contain
contribution from more than one isotope, the above method i s not very
useful. For example, i f the sample contains a mixture of aged fission
products, the peak around 660 Kev contains in addition to the 662 Kev
Cs-137 gammas, secondary peaks due to Ru-106 from lh-106 (624 Kev),
Sb-125 (595 Kev) and a small contribution due to Ce-144 from Fr-144
(696 Kev). Therefore, stripping based on the assumption of the peak
being due to only Cs-137 w i l l not give correct results . The methods
described in the following sections take into account the above
complexity.
3.2 Simultaneous Equations Method
Let there be '3' iBotopes in the sample and C(i)tCU\ Cfj)
be the counts in the 'J' photo-peak regions of the various isotopes
determined according to the criterion given earl ier. If F ( 0 , F (2),
- 8 -
P (k), P (j) ore the photo-peak counts of these isotopes to be
determined, and f (1 , k ) , f (2, k).,,f (k, k\..t ( j , k) are the
compton fractions for isotope F (k) in different regions, the solution
can be found by solving ' j 1 simultaneous equations given by
f (1,1) . P (1) + . . . f . P ( k ) 4 . . . f ( 1 , j ) . P ( j ) - 0 ( i )i i i
i i «
P (1) + . . . f (k,k) . P (k) + . . . f (k, j ) . P Q) = C (k)
f (J,1) . P (1) + ... f (d,k) . P (k) 4 ... f (j, J) . P (j) - C (j)
The above equations can be represented in matrix notation as
f (1,1), f (1,2) f (i, j)
f (2,1) f (2,2) ..... f (2, j)
If (3.0 f (j,2) f (j, j) P (j)
P (2)
C (1)
C (2)
C (i)
or
The solution is represented by-1
-1The i n v e r t e d matrix / " ? _ / i s obtained by means of computer
- 9 -
when the order i s more than 2. The values of P (j) thus obtained
are multiplied by suitable efficiency factors and decay corrected,
i f required. Table 1 gives a typical set of f ( l , j ) values for
air f i l t er samples containing aged fission products, on 3nx3w Hal (Tl)
crystal for energy regions given in Figure 1a, for three gain settings•
The statist ical errors in the above values can be estimated
as follows:
If the sample has been counted for time TS and the counts
atored in 'J' regions are represented as K1, K2, KJ and if
background i s taken for time TB and the background counts of different
regions are K1', K21, . . . . . . . . K j f respectively, the errors In counts
C (1) , C (2 ) , C ( j ) used in the above formulation are given by,
K1 - K1 ' +c ( 1 ) ± A c X l / _ I s TB
C ( 2 ) ± AC (2)
V
K2 - K2' +TS TB "*
TS2 TB
TS2 TB2
and therefore the variance of the estimated values / P_/ i s obtained
by solving the matrix equation
2 2 2AP (j) « E g ( i , j ) .AC ( i ) f where g ( i , j ) are the elements of the
1 matrix /~?J ~1
estimated and converted to the same units aa F (j) values.
A computer programme for CDC-36OO using the matrix inversion
-10-
method for solving the above equations i s given In Appendix A.
Alternatively, the simultaneous equations obtained above can also
be Bolved by the method of interation. This method i s applicable
here as the criterion for the interation to succeed, namely, that
the large coefficients are along the leading diagonal of the matrix* '
i s satisfied. A Fortran programme using the method of interatlon Is
given in Appendix B.
The final equations obtained after solving the simultaneous
equations for i t s coefficients are given in Table 2 for different
gain settings. Although these equations are not used in their present
form by the computer programme of Appendix A, they are useful In
getting an idea of the stat is t ical and other errors involved as w i l l
be discussed later.
The above method, though suitable for analysis of complex gamna
spectra having a large number of isotopes, uses only the counts stored
in the photo-peak regions. The least squares method described below
i s superior to the above method as i t ut i l izes the counts stored In
a l l the channels and gives better stat ist ical accuracy.
5.3 least Squares Method
If C ( i ) are the counts recorded in the channel fi* of the
sample spectrum, one can write i t as
c (i) - X I x (i,3) . P (j) +Z(i)
where ( i ) i s the random error in the ith channel counts and f ( i , j )
i s a fraction of the photo-peak counts of the Jth isotope in i th channel.
- 1 1 -
As before f ( i , ;)) can be calculated fro« the equation f ( i , j ) =
P ( i » j ) A ( j ) where P ( i , j ) i s counts due to isotope J in channel i
and P ( j ) ia the photo-peak counts. The computer programme for
CDC-36OO for calculating these channel fractions i s gLven in Appendix C,
The programme calculates the f ( i ( j ) values for each reading of the
standard source, takes the average of a l l the fractions for a particular
standard and so calculates the standard deviation for each channel
fraction of the standard.
The principle of least squares requires that the sum of the
squares of the random errors Z ( i ) for the individual channels be a
minimum, i . e .
£ z ( i ) - E (c ( i ) - H f ( i , j ) . P ( j ) )i i i
should be a minimum.
Differentiating the above expression partially with respect to
P (j) and equating to zero gives the condition for minimum random
error. We then get f$ ' equations which after simplification can be
expressed in matrix notation as
/V7 . f?J . £vj - Z~P_7 • fcj- - - T
where /"*_/ i s the channel fraction matrix, £fj i s the transpose
of / " F J 7 , /~P_7 snA /~C_7 are column matrices in P (j) and C ( i ) values
respectively.^ the principle of least squares assumee the variance of
-12-
each observation to be the same, which is not true for the gamma
spectra, a diagonal weighting matrix £ W_J of order (n, a) where n
Is the number of channels is introduced in which each diagonal element
is the inverse of the square of the standard deviation of the channel
counts (including background counts) so that
i
TS Ib
Here W (l) i s the ith diagonal element of the weighting matrix, 3 ( l )
i s the sample count rate and B ( i ) is the background count rate In
time TS and TB respectively*
By incorporating the weighting matrix £*_J% the matrix equation
becomes,
- f*J . ZX7 - A 7 - LJ LJand the solution is given by
The P ( i ) values are converted to various activity units aa
described for simultaneous equations. The s ta t i s t ica l errors of the
estimations of various isotopes are obtained by calculating A? ( i )
which are given by the diagonal elements of the inverted matrix aa
follows.
AP (i)2 * i th diagonal elenent of [ 2 X 7 • Z"*7 • L
where R is the goodness of f i t discussed below.
-13-
Thaae AP ( i ) counts can also be converted to the Bame units
as P ( i ) by multiplying them by the activity conversion factors used
for P ( i ) .
The accuracy of the above analysis i s checked, (a) by
reconstructing the sample spectrum using channel fractions f ( i , j ) and
the estimated valueB of P ( i ) , and comparing the reconstructed spectrum
with the recorded spectrum, and, (b) by calculating the value of
"Goodness of Pit" parameter 'R1 defined as
1 ^ (0± - C' )
(n - i) n Var. Ci
where n i s the number of channels, J i s the number of Isotopes, C.i
are the recorded channel counts, C. are the estimated channel counts
and Var . C are given by 1/ff (0 ) . If 'R' i s close to unity, the
analysis i s considered good. Otherwise, i t indicates the presence of
some isotopes not included in the analysis, instrumental drifts etc.
All the above computations are done by the programme given in
Appendix D. The least squares method i s based on 'error minimizing'
principle and i s therefore particularly suitable for weak samples.
The only disadvantage i s that i t needs a computer for data processing.
4. RESULTS AND DISCUSSION
The methods of gamma spectrum analysis described above have been
used with the following three types of analyser systems in use at the
laboratory.
a) A 10-channel analyser having a 3" x 3" Nal (Tl) detector
coupled to Dumont 6363 photomultiplier
- 1 4 -
(b) A 100-channel analyser having a 3" x 3" Nal (Tl)
detector (Harahaw integral line assembly)
(c) A 256-channel analyser coupled to a 5" x 4" Sal (Tl)
detector (Harshaw integral line assmbly)
System (a) is being used for the estimation of Cs- (37 and K-40
in milk samples and the gamma spectra are analysed by spectrum stripping
method. System (b) is being used for the analysis of airborne particulate
and rainwater samples for their fission product activities Ce-144, Sb-125»
Ru-106, Cs-137 and Zr-95 and cosmic ray produced isotope Be-7» Tne method
of analysis used are simultaneous equations and least squares. System (c)
is used for analysing soil samples containing natural radioactivity due
to Uranium, Thorium and their daughter products and K-40, and fallout
radioactivity due to Ce-144, Sb-125, Ru-106 and Cs-137. The methods of
analysis used are simultaneous equations and least squares.
Appendix B gives the total efficiency . peak to total ratios
and other factors for the various systems employed.
Figure 3 gives the least square computed and the recorded spectra
of a composite source containing Oe-144, Sb-125, Ru-106, Be-7 and Csr137
as measured in system (c). The f ( i , j ) values were calculated from the
individual measurements of the isotopes of the composite source and the
spectrum analysed has been taken with a l l the isotopes put together,
A goodness of fit value nearly equal to unity can be expect id in
view of the ideal conditions in which f ( i , j ) values were derived for
the measured spectrum. In figure 3(a) analysis was carried out
deliberately omitting Be-7, and accordingly a high value of goodness of
fit of 7.5 was obtained. Here the significant difference between
-15-
caloulated and observed spectra In the region of Be-7 Is clearly seen.
A similar analysis carried out for two air f i l ter samp lea counted
In system (b) are shown In figure 4* Again the large difference in the
region of Be-7 which was emitted in the analysis i s evident. It i s also
clear from Fijure 4 that the routine analysis i s quite precise as lae
computed and measured spectra of the air f i l t e r samples show cloee agreement
when a l l the isotopes present are included in the analysis.
Table 3 gives the photo-peak counts of a fairly active composite
source as unscrambled by the two methods in comparison to the counts from
individual source countings (where no unscrambling procedures are involved).
The data show that there i s not much difference between the two methods aid
the results are correct to within +?0$. Table 4 shows a similar comparison
for air f i l l e r samples. Similar studies have been done with the large
volume sources for soi l studies. The least squares processed results for
a simulated composite source, used in these studies, along with the
individual act ivi t ies are given in Table 5. Comparative results of the
two methods of processing for two typical s o i l samples i s presented in Table 6
and the observed and least squares method computed spectra, averaged for
three channels, i s plotted in Figure 5.
4.1 The effect of analyser gain drift
Since a "drift" in tte gain of system (b) equivalent to a change
in the peak position of about a channel i s not unusual, the magnitude of
this error was investigated. The various f ( i , j ) values were obtained for
three gain settings, v i z . , the normal and two others with Cs-137 photo-peak
maximum one channel above and one channel below the normal. With these
-16-
three sets of f ( i , j ) values, a large number of samples were analysed.
The results (Table 7) show that far several samples a single channel drift
does not produce more than 15$ error and there i s l i t t l e difference in the
137magnitude of this error from the two methods. However Ce values differ95by as much as 100$ from samples in which Zr i s present in large quantities.
137 95
This i s obviously due to the overlap of the peaks of Ca and Zr
(Figure 1). In the analysis of complex spectra with significant overlap,
'gain1 and 'threshold' shift corrections are important. In studies on the
s o i l sample spectra taken in the 256 channel analyser system i t was found
(Fig.6) that a few isotopes were sensitive to 1 or 2 channel sh i f t s .
The corrections for the instrumental shifts can easily by incorporated(8 9)in the least squares analysis * abd are included in the programme given
in Appendix D.
A CKNOWLDEGHd WIT S
The a u t h o r s a r e t h a n k f u l t o D r . K.G. Vohra , H e a d , A i r M o n i t o r i n g
Section for his interest and encouragement in this work. Thanks are also
due to S/s« K-K. Varraa, D.K. Kapoor and K. Ramanathan for their help.
0 ) G.D. O'Kelley (Ed.), Applications of Computers to Nuclear and
Badiochemistry, Proe. Symp. Gatlinburg, October 1962.
(2) J.R. HeVoe and P.D. IaFleur (Eds.), Modern Trends in Activation
Analys<s, Proc. Conf., Gaitheraburg, Oct. 1968, HBS Special
publication 312 (1969).
(3 ) R^L. Heath, Scintillation Speetrometry - gamma ray apectrua catalogue,Report IDO-16880-1 (1964).
-17-
4) C. Rangar&;Jan, Computer analysis of complex gamma spectra, in,
Proc. of National Symposium on Radiation Physics, Bombay,
November 1970.
5) J.B. Scarborough, Numerical Mathematical Analysis, Oxford Book
Company, 1964.
6) C.C. Groajean and W. Ljseaert, Table of Absolute Detection
Efficiencies of Cylindrical Scintil lation Gamma-ray detectors,
University of Ghent, Belgium, 1965.
?) tf.c. Mishra and S. Sadaaivan, Nuol. Inst . Meth. 69., 330-334 (1969).
d) E. Sehonfeld, A.H. Kibbey and W. Daviea Jr . , Determinetioa of
Fuclide Concentrations in solutions containing low levels of
radioactivity by Least-Squares resolution of gamma-ray spectra,
Report CSNL-3744 (1965).
9) ?. Quittner and R.E. Wainerdi, Computer valuation of Nal (Tl)
RV& Ge (id.) ganma-ray spectra, Atomic Baergy Review, 8 , No.2,
•561-415 (1970).
-18-
Table 1
FRACTION OF PUOTOPEAK COUNTS OF VARIOUS ISOTOPES INTHE DIFFERENT PHOTOPEAK REGIONS FOR THE 100 CHANNELSYSTEM FOR THREE GAIN SETTINGS; AIR FILTER AND
PRECIPITATION SAMPLE STUDIES
Photopeak
channelregion
4 - 8
26 - 33
34 - 40
46 - 52
63 - 61
61 - 66
Ce
l.
1.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
0.
0,
Fraotlon of144
000
000
000
076
081
079
057
058
057
,075
,067
,057
,064
,070
.077
,034
.034
.004
Sb
0.
0.
0.
1.1.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
o,
125
417
388
357-
000
000
000
178
161
216
250
315
430
063
,068
,081
,025
,029
,035
photopeak countsa 10bRu
0.491
0.458
0,337
0.371
0.310
0.263
1.000
1.000
1.000
0,284
0.351
0.400
0.217
0.262
0.193
0.142
0.137
0.123
Ca137
0.169
0.123
0.164
0.209
0.197
0.L21
0.060
0.065
0.075
1.000
1.000
1.000
0.0152
0.092
0.177
0.024
0.025
0.026
InZrNb
0.
0.
0.
0.
0.
o»0.
0.
0.
0.
0.
0.
1.
1.
1.
0,
0,
0,
Isotopes*9595 +
181
151
150
271
213
215
183
182
191
,195
,089
723
,000
,000
,000
,059
,096
,162
Mn
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
1.
1.
1,
64
227
179
169
277253
245
336
235
222
120
,115
127
,797
,320
,221
,000
.000
.000
* Calibration137
1st Line C B photopeak maximum in 48th channel
Bnd Line C B photopeak naxlMim in 49th channel137
3rd Line Cs photopeak maximum in 50th ohannel
- 1 9 -
T a b l e 2
SOLUTION OF SIMULTANEOUS EQUATIONS W S IX COMPONENTSIN TU1£ 1 0 0 - CllANNliL SYSTEM Full ( i , j ) VALUES GIVfcN JH
TA11LE 1
Photopeakcounts ofisotope*
P ( C R 1 4 4 > -
P(Sb125) --:
P(Hu106) =
P(C8137) =
p ( / r95 +
95»Nh* j
P(Mn54) =
Muitip4-ri
1 .054
l.osa
1.041
-0.041
-o .osn
-0.062
-0.034
-0.036
-0.030
-0.050
-0.035
-0.034
-0.033
-0.050
-0.071
-0.027
-0.024
-0.019
+ Calibration
lyinp factors2(1-33
-0.
- ' ) .
-0.
±1-+1,
+1,
-0,
-0,
-0,
-0
-0
-0
-0
•0
+0
40
+0
-0
354
337
280
,133
.125
.164
.172
.146
.211
.207
.281
.433
.012
.009
.045
.014
.005
.ooa
of counts34-40
-0.
- 0 .
-0.
-0,
-0,
-0,
•1,
+1,
+1,
-0
-0
-0
-0
-0
.0
-0
-0
-0
.''.(iO
358
238
.290
.197
,167
.146
, 133
.113
.190
.282
.264
.091
.197
.115
.13 i
.111
.098
in46-52
-0.
-0.
-0.
-0,
-0,
-0,
-0
-0
-0
+1
+ 1
+ 1
-0
-0
-0
-0
-0
•0
OB2
038
095
.201
.184
.227
.015
.022
.004
.067
.076
.245
.033
.074
.196
.014
.011
.011
channel rucolons•>-5 3-til
- 0 .
-0.
+0.
-0,
-0,
-0,
-0,
-0
-0
-0
+0
-0
1
1
1
-0
-0
-0
013
O1H
025
.206
.165
.012
.141
.151
.134
.114
.020
.790
.O7R
,075
.200
.035
.O78
.016
61-66
+0.O003
-0.01O
-0.04S
-0.017
-0.155
-0.207
-0.216
-0.172
-0.160
•0.094
+0.014
+0.176
-0.B14
-0. 2B3
-0.214
+1.076
+1.055
+4.059
1371st Line - C B photopeak maximum In 48th channel
n7n 72nd Line - Cn photopoak maximum In 49th channel4 Of
3rd Line; - Cs photopenk maximum In 50th channel
* The photnpeak counts are equal to the algebraic mira of thegiven fractions multiplied by the counts in the respectiveohannel regions.
Table 3
PUOTOPJiAK ACTIVITIES OF TWO COMPOSITE SOURCES ANALYSED IN THE 256CHANNEL ANALYSER SYSTEM BY DIFFERENT METHODS
SourceNo.
I
II
Analysis method
Individual sourcecounting
Simultaneous equations
Least squares
Weighted leastsquares
Individual sourcecounting
Simultaneous equations
Least squares
Weighted leastsquares
Ce 1 4 4
992
997(1.00)
904(.9l)
903(.91)
1148
1506(1.31)
1392(1.21)
1408(1.23)
Sb 1 2 5
3240
2725(.
2853(.
2780(.
3392
4081(1
4279(1
4365(1
84)
88)
96)
.20)
.26)
.29)
Photopeak
Be7
2640
2783(1
2680(1
2782(1
-
-
-
counts of
.05)
.02)
.05)
Ru 1 0 6
894
1133(1.27)
1230(1.38)
1171(1.31)
997
1242(1.24)
1337(1.34)
1317(1.32)
Cs 1 3 7
4603
4481(.
4524(.
4550(.
4603
5298(1
5304(1
5179(1
97)
98)
99)
.15)
.15)
.13)
w 54Mn
-
-
-
1750
2067(1
2190(1
2033(1
I
o1
.18)
.25)
.16}
Figures in brackets give the ratio of photopeak counts derived by the method to thatfrom Individual counting
Table 4
RADIOACTIVITY OF FILTEB SAMPLES ANALYSED IN THE 100-CHANNELSYSTEM BY DIFFEBENT METHODS (ACTIVITIES IN uue/iOOO M )
Saapledate Ce Sb125 Ru106 Cs137 Mn54
S.E. L.S. W.L.S. S.E. L.S. W.L.S. S,E, L.S. VF.L.S. S.E. L.S. W.L.S. S.E. L.S. W.L.S,
1964
FEB.MAR.APfi.
UAY-IUAY-II
AVERAGE
6921110
855
539
480
735
60T1025
77T
530
400
668
520
1012
730
475
333
614
69,2 64.1 67.2
85,,5 85.4 76.1
94,0 111 78.3
58.2 56.5 47.0
44.5 51.2 36.0
70.3 73.6 60.9
318 385 324 75.2 76.0 72.6
445 453 388 119 120 110
334 333 275 111 111 100
222 222 186
197 197 147
303 318 264
66.0 67.5 56.8
60.TB 61.5 50.8
86.5 87.2 78.0
48.0 50.5 47.3
65.8 66.7 60,6
50.5 49.6 44.8
31.6 32.4 27.4 <
27.4 29.1 23.6 ^
44.7 46.7 40.7
S.E. Simultaneous EquationsLS . Least SquaresW.L.S. Weighted Least Squares
- 2 2 -
T a b l e 5
RESULTS OF LEAST SQUARES METHOD PROCESSING OF SIMULATED SOILSAMPLE SPECTRA OF DIFFERENT COMBINATIONS OF THE ISOTOPES AND
THE CONUliNTRATIONS OF THE ISOTOPES ADDED; 256-UIIANNEL ANALYSERSYSTEM
Isotopes Added
Added Concentrations
K * CB
K + U
U 4- CB
K 4- U 4- CB
K 4- U 4- CB + Ru
K 4- U 4- Cs 4 Ce
K + 11 + Cs + Sb
K 4- U 4- Th 4- Cs
K 4- U + CB 4- Ru + C«
K+U+Cs+Hu+Sb
K+U+Th+Cs+Ru
K+U+Cs+Ru+Sb+Ce
K+U+Th+Ca4-Ru+Sb
K+U+Th+CB +Ru+Co
K+U+Th+C s+Ru+Sb+C e
K+U+Th+Cs+Ru+Sb+Ce
4-2.63 muc Mn
K(R)982
981
982
982
962
982
982
982
982
982
983
982
983
983
983
995
.5
.95
.27
.28
.86
.61
.28
.47
.90
.65
.02
.91
.01
.30
.30
.44
IsotopeTJ(rag)
83.
83.
63.
83.
83.
83.
83,
83
83
83
83
83
83
83
84
86
5
40
40
53
64
64
,65
,65
.77
.78
.77
.89
.89
.89
.01
.23
valuesTh(m)
4.60
4.58
4.58
4.58
4.58
4.58
4.64
obtainedCs{muc)
50
50
50
60
50
50
50
60
60
50
50
50
50
50
50
52
.6
.62
.62
.62
.62
.62
,62
.62
.62
.62
.61
.62
.62
.61
.61
.65
Ru(rauo)
12.
11.
11.
11.
11.
11.
11.
11.
12.
15.
[)
87
90
92
89
96
96
95
01
14
Sb(muo)
26
26
25
25
25
26
26
.0
.95
.99
.99
.99
.00
.01
Ce(onto)
51.0
50.
50.
61.
51.
61.
57.
68
84
17
42 |
08j
Table 6
BESULTS OF LEAST SQUARES AND SIMULTANEOUS EQUATIONS METHODS OF DATA PROCESSING FORTWO SOIL SAMPLES FOB DIFFERENT THRESHOLD SHIFTS (SAMPLE SPECTRA SHIFTED BY THE
NUMBER OF CHANNELS INDICATED)
SampleNo.
121 A
20 A
Channelset t ing
Noraal
Normal
+ 2
- 2
+ 2+ 1+ 1 forK,U, Thothersnoraal
Noraal- 1- 2
Processingmethod
L. Square
S. Equn.
-do-
- d o -
LEAsTSQ
uAR
§
K
7.08+0.076.86
+0.106.84
6.74
3 ,,193.052.88
2.932. 852.78
U-238
3.29+0.023.G3
+0.052.88
3.12
0.6180.6430.676
0.0730.7100.760
Th-232
12.49+0.03
12.15+0.0511.19
12.91
2.853.043.15
3.173.223.18
Cs-137
588.94+0.99579.72+1.06507.7
605.3
43.549.354.9
54.759.764.0
Ru-106
52.78+1.5353.42+1.73100.6
31.6
49.028.212.7
12.52.78-1.19
Sb-125
43.22±0.6341.56+0.6744.5
50.8
18.215.714.0
13.612.011.0
Ce-144
48.05+0.9844.80+1.8696.4
9 . 0
36.927.519.6
19.211.75.31
Iuu1
Table 7
RELATIVE VARIATION OF ACTIVITY MEAbURLD IN TIIE iOO-CHANNEL S.YSTEM Foil DIFFERENTUlUNNEL-fciiLllGY CALIBRATIONS
Method C e 1 "Calibration*48 49 50
Calibration*48 49 50
Cr.l48
R,.106
ibration*49 50
Cs 1 3 T
Calibration*48 49 50
Zr*5 • Kb95
Calibration*48 49 50 4S
„ 54Mn
Calibration*49 SO
A.Simulta-neous
equations 0.96 1.00 1.04 0.85 i.00 1.06 0.99 1.00 0.96 1.13 1.00 1.00 - 0.95 1.00 1.12
B.Simulta-neous
equations 0.97 1.00 1.06 0.84 1.00 1.18 0.99 1.00 0.95 1.14 1.00 0.57 0.87 1.00 1.19 1.05 1.00 0.98
C.Leastsquaresanalysis 1.06 1.00 1.07 0.78 1.00 1.37 0.91 1.00 1.16 0.98 1.00 0.79 - 0.68 1.00 1.09 \
re' • t . _ _ _ _ _ _ _ _ _ _ _ — — — — £.
Values relative to the normal calibration (Cs peak in 49th channel) i45 95
A Based on analysis of 25 spectra of air filter samples with Zr* + NbB Based on analysis of 12 spectra of air filter samples with Zr + Nb
C Based on analysis of 6 spectra of air filter samples without Zr + Nb137* Calibration is indicated by the Cs photopeak maximum channel number
10
- 2 5 -
CHANNEl NUM6ER40
0.1
Ul
S
so
.01
I"
.01
.001 I 130 40 SO 9060 70 BO
CHANNEL NUMBER
FIGURE ". 1 . GAMMA SPECTRA OF SOURCES MEASURED IN C a ) 7.5 cm»
x 7.5cms Na l (T l ) -100 CHANNEL AND,(b) I2.5cmi * 10 emi
N a l ( T D - 2 5 6 CHANNEL SPECTROMETERS.
- 2 6 -
UJI -3
» -z
8
zo
in
Ou
1200
1100
1000
900
800
700
600
500
400
300
200
100
1000
900
eoo
700
600
400
300
200
100
Cs-137661 KcV K-40
1.46 McV
CURVEW BACKGROUND
Cs-137661 KcV K-40
1.46 McV
NORMALIZED K-40 SPECTRUM
Cs-137 IN THE SAMPLE
0 2 4 6 8 10 12 14 16 18 20 22 24 26 26 30 32 34 36 38 40
PULSE HEIGHT (ARBITRARY UNIT)
FIGURE: 2 . ANALYSIS OF MILK SAMPLE.
I I I(a) GOODNESS OF FIT s 7.S
LEGEND
CALCULATED
o MEASURED
Ct>) GOODNESS OF F I T . 1.1
10 30 40 SO 60
CHANNEL NUMBER
TO 80 90 100 no
FIGURE .3. GAMMA SPECTRA OF A COMPOSITE SOURCE MEASURED IN THE 256 CHANNEL
ANALY5ER AND CALCULATED BY LEAST SCLUARES METHOD, ( a ) SOURCE
CONTAINING Ce - 1 4 4 , Sb-125 , Ru - 1 0 6 , Cs -137 AND B « - 7 ANALYSED FOR
THE FIRST FOUR ISOTOPES ONLY . (t>) SAME SOURCE ANALYSED FOR
ALL THE ISOTOPES PRESENT IN THE SOURCE.
120
- 2 8 -
a
e 1000
300
10,000
Xo
LEGEND
CALCULATED
o MEASURED
) AIR FILTER SAMPLE OF MARCH 67
GOODNESS OF FIT c 23
f\ Cb) AIR FILTER SAMPLE OF MARCH 64
GOODNESS OF FIT .1.1
30 40CHANNEL NUMBER
FIGURED. GAMMA SPECTRA OF AIR FILTER SAMPLES MEASURED IN
THE 100-CHANNEL ANALYSER AND CALCULATED BY LEAST
SQUARES METHOD, (a j SAMPLE CONTAINING C«-144, Sb-125,
Ru-10S,Cs-137, Zr-95*Nb-95 AND Bt-7 ANALYSED FOR
FIRST FIVE ISOTOPES ONLY.(b) SAMPLE CONTAINING C«-
144, Sb-125, Ru-106,Cs-137 A Mn-54 ANALYSED FOR ALL
THE ISOTOPES PRESENT IN THE SAMPLE .
105
=>ooUJ
3a.in
w*
UJu
10
•
-
•
9X 1
, • : " • . « ,
• CCHPUTEO COUNTS
t OBSERVE
• a i *
) COUNTS
' . « Mtr
" l
<X
10 30 60CHANNEL GSOUP
SO SO 70 SO
FIGURE'. 5. OBSERVED AND LEAST SQUARES METHOD COMPUTED C0UNT5 (AVERAGE
OF 3 CHANNELS FOR CHANNEL NOS. 1 0 - 2 5 0 ) FOR A TYPICAL
OOTACAMUND 0 - s " LAYER SAMPLE.
I
OBSERVED SPECTRUM
+ 2 CHANNEL SHIFT
COMPUTED SPECTRUM
- 2 CHANNEL SHIFT
COMPUTED SPECTRUM
NORMAL COMPUTEDSPECTRUM
40CHANNEL GROUP
FIGURE: 6. OBSERVED AND COMPUTED SAMPLE SPECTRA FOR NORMAL AND
+ 2 CHANNEL THRESHOLD SHIFTS,256 CHANNEL ANALYSER, SOIL
STUDIES .
-31-
APPluMX A
c PROGRAM FOR ANALYSING GAMMA SPECTHA BY SIMULTANEOUS EQUATIONS
C M^THOn USING MATRIX INVERSIONccC THIS Li5TtNu 15 FROM CECK U3'n ?Q« 5OIL ANALYSISC A(I,j) ARF MATRIX COEFFICIENTS
c cm ARE EFFICIENCY FACTORSC C 1 ( 7 ) = C H E C K REGION FACTORSC F(I)=nECAY FACTORSC (M(I),N(I))=LOWFR AND UPPER CHANNELC MlJSflACKGROUNn CHANNEL COUNTS IN TlC M(l)=SAMpLF COUNTS IN J3 MINUTESc COMPT(UJ»=COHPTON FACTORS FOR SPECTRUM SIMULATIONC SW.Tw ApE SAMPLE ANI) TOTAL WEIGHT IN KGC AA=ARrA FACTOR G*NO OF nAYj FOR DECAY CORRECTIONC Yl»nrLYl sSAMPLF ACTfVlTltS ANU E«HORSC C H E C K , E ( 8 ) ,CHTT SCHECK REGION HESlDuAL-RECoRDED^COMPuTEnc un(i),onz(ijsRECoRDEn AND C OMPUTEU SptcTRA THREE CHANNELcC PLOT SUBROUTINE NOT LISTED HERE
N S O N A (7 ,7 } ,P i7 ,7 ! ,KNT«7 I« K J I P S J I , H ( 8 1 , N ( B J , E l « ) , C i 7 )3 C i i 7 j « F ( 4 > * M 4 ) » | . « f l ) ' L ^ ' » » « ° E L L » t | « X ( 7 ) % t ( 7 ) O E X « 7 D Y T 1 ( 7
, i E L 2 4 « 5 eCOMPT<T»250)«IGR/l.PHU01»50j» DU(801 «nDU*O) ,CT '250 )
UI'^FNSION SAM(B) ,BKG(8JUIMFN5ION K ( ) C T TUTMF.NSlflN
703 X M I j s IUTAH 1 0 , « ( A ( I » J ) i I s l , 7 j » J B l ' 7 M « C « I ) » l s l » 7 )
10 FORMAT (7F10.5>11 F0RMAT(7(10X,7F l< t ,5 i / )« / / )
PRINT 9fl5 2 4 OT 1 F , ,98 FOHMAT |10X»25HlNPUT MATRIX COEFFICIENTS,//)
PRINT ll,((Ad,Jl,Isi,7),J=l,7)PPINT l ? . < C d ) i l = l»T)
12 F0RMAT(2Xi3lHpACT0RS FOR C O N V E R ' I N G CJ»M TO UUC»E 1»(Cni)«I
IS FnKHAT(7FlO,5)PRINT 11, ( C K I I I 1 = 1,7)
d i\t* FORMAT
PRINT 15,(F(I),TS1,4)15 F0RMAT(?X,29HnECAY FACTORS FOR C E » R U , C S . M N » " « 1 ° X » « F 1 5 ,
51 FORMAT U6I5)PRINT 5 l i ( ( H ( l ) i N I ] ) ) ,1=1,8)REAP 70 '» t ( (COMPT(T,J ) ,J= l ,2So>* I a l ,T}
7O<» FORMAT (10F«,6)Un l e 1=1,7DO lf l J s l , 7
P ( I , I ) S l t O
- 3 2 -
A (CONTINUED)
CALL MATlMVRT(A,P,KHT,T)Pi»IMT 91rP I«"ATHOX.. ' ' f lHl"VFPTEn HATRjx COtRfAn ( ) !U . K i
50 FnKP'AT f 1*»I•»IREAP 5 0 l , S l ' . , T l
501 FOt<MATlAfliF<i,0DO 1? 1=1,0L(H=n
UO ">3 JsK53 LUlsL(!l*KJ|5255 HFAP
56HFAP «?01iS»T3RFAP <15, (SW,TW,AA,G)DD <?/• 1 = 1,4
94 u m s F X f F ( F ( 1 ) » R )U" 5n 1=1,A
)KKK?sNM)L l ( ! ) = 0UO 59 J=KK2,KKK?
59 LI <n=LlU)*KHj)5fi lNUr
UO ISO 1 = 1,ASA;-Hn=t 1 ( I>BKG( I ) =i. ( ! )E ( I > = S A M U > / T 3 - W K G
60 U F . L L ( n s S A M ( l j / TUO 16 I a l , 7X ( ! ) s O , nDO 17 J - 1 , 7
17 X ( n = A ( T , J ) « E ( J ) * X < I )16 Y ( I ) = X ( I ) » C t ! > / S W
i)0 19 1 = 1,7
20 J = l , 7X ( T ) = D F L ( ( I f J
Ut 'LX( l )=SQRTF(UFLX( l jU E L Y ) D E C19UO ?\ 1=1,7Y l ( I | = Y ( I j « A A « T W
21 UELYiUO 22
22 ()C H T T B O . ODO 3061=1 ,7CHTT=CMTT+Cl ( I ) «X (nCHEK=F(A)-CHTTDO 70S 1=1,?50
705 C T ( I j s ( K l ( I ) - K J t ) « T 3 / T l lDO 706 1=1,7DO 706 J=1C;25O
A (CuNTlMIJEU)
70 ' ) C T l I I t J l =X < f I U O ' I P T 1 1 » J ) « T 3ll ' l 7 , )7 1 = 1 U • O
UO
•/07 C T J ( j ) = ( C T ( J ) - C T Z ( J ) )
UOI ) n ( I ) = 0 . 0
UO 710 J=
710
711 u r u » i ) =1 o n . o712 cnriTinur709 J 1 = J j * l
P P I H T 3
PRINT 3«S»«YiMT>«Isl««i) i < Y H l jP 3 f t « ( T W , A A , G , ( n E L Y ? ( I ) , i « » « < » ) • I p t L V l ( j > » J=5 ,7 ) J
r M F F f l Cp n j M T <O r >» ( [ I P ( I I i l s l t f l f l ) * ( l i j l Z l D • l s l « 6 0 )
36 fGO Tp
100 STOPENU
SI!UR()1)TTNFMATINVRT(A,B,KOUNT,N>
?7 X=0 .
UO3J=1.Mt
I F C X 1 | 2 , 3 , 32 X = A l K 1 , . | )
A » I » j ) a A ( ! i J ) - A ( K l i J J « YS B I I , J ) s n ( l , J K
ft
A\?
910
| i i
Y-.t i'iu 1
A(II (t.n
MlK li. ?
i r
j rCOJC
' iT
ft (I. I
I ,i i "
r.y• - *
-y( fi'JT(1i4T= 1
= V ' ' .
!,Jf." 1 t %lJ)=A.J)= n
I (K l
\ + l•>*\] - N !
M)
( I , I)-A(K1,J(T ,J)-l»(Kj »J)-.jr
-M)ljHTm>9tlO»9iNUr
L=L + ).
- 3 4 -
A (CONTINULU)
LM.J
- 3 5 -
cC AMAlYSlr, OF GAMMA 5PECTRA By ST HULTANEOUS EUU*TIONS HETHOD SOLUTIC ON PY ITERATIONC COM is rOMPTON TRACTIONS fROM SOURCE SPECTRAC N=TOTAL NO OF COMPONENTSc COUNTS TS «KG SUBTRACTED SAMPLE COUNT RAU IN PEAK BFRIC NITsfjn OF ITERATIONSC t F F ( l ) ARF ACTIVITY CONVERSION FACTORS
UMF C N T ESi ) ,COMMON SOTOPE<8),COM(8tB)
1 FORMAT 115)Z F0RMAT<flF8tM3 FORMAT(AF5)«• FORMATU8,2X,2F10>5 FORMAT UOAB)6 F0RMAT(10? FORMAT<1OXI<MA8,<»X) )8
l,NITRFAD «i,(lSOTOPE«I),IsltNIDO ?U J=1,N
20 RFAH ?,(C0M(JiI>*Ial,N»L
READ ?,(EFF(I),Isi,NJVOL»TDL
21 CONTjNUrREAD 3«(COUMT5(J>iJsltN)Dn ?z Ial,N
Z? SOTOPFIT)=0,UO 23 Ksl.NTTDO 23 Msl,NCALL
23 SOTOPFIM)sCOUNTS«H)-Rl00 Z*t 1 = 1,N
24 SOTOPE (I) sSnTOPt (I) »EXPF JO, 693»THL/HLIFE (I» / [ V O L » ^ (IIIPP1NT 6,SAMPLEiV0L,TDLPRINT 7,«lS0T0PEtI}iI=l»N>PRINT «,(SOT0PE«n,Ial,N)
100 STOPEMU
SUBROUTINE SURRC(M,Ri,N)COMMON SOT0PE(B),C0M<8,»>
00 1010 R l S
RETURNEND
- 36-
A P P E N D I X C
f>rOr,HAH COMMONcc COMPTON F4CTORS FOP LEAST SUUAHES PROGRAMccC APsBACKGROU*1!1 CHANNEL COUNTS, T»B»KG CouNT TIMEC A=SnuRCp CHANNEL COUNTS. TSSSOURCE CUUNT TiMtC NN Is No OF SOURCE READING,NNI«NNZ, CHANNEI LJMTS,NM TOTAL NO OfC CHAMNFLS A N P ACT IS THE ISOTOPE
C CnHPTTtn=COMPTnN FRACTIONScc
A(2?6>. COM(552O),COMPT(256>»COMpTT<256»»COT<236)S O AP(25?)
23<t RFAP 7*(AB(I)t Isl(252)1 READ ?0,SB.TB
20 FORMAT (AB«F4)PPI^T 770,SB»TB
11 READ ?,MNi,MN2,NM,ACT2 FORr'AT <3X,1I3tAej
1F(F.OF»AO)9<>9«33 CONTIMUF
29 FORMAT <5X«12«X,FBt4)»/J93 PRIMj 4, ACT4 FOHHAT (//^OX.ftCoMPToN FRACTION* FoR*»"»26X»AB,//)
REAn 99,NN99 FORMAT II?)
DO 5,K=1,NMCOMPT(H)=0 S COT(K|«0
3 CPNTiNUF.Kl=l SK^sNM SKJsO
6 REAH 7»(A(I)»l=Kl»K2)READ 2O.S,TS
7 FORMAT(1<»F5)PRIMT 44iN
44 FORMAT (2XPRINT 770.S.TS
770 FORMAT (l0XfA8tFl0»/)PP=ODO P.l=NNl»NN2PP=PP*(A(1)-AB(D»TS/TB)
8 CONTINUE
DO 9,j=l,NM
COM«jj)sO.OCOM(jj)=<A(J)-AB«J)«TS/TB)/PpIF(COH(jj))l«tl9»19
16 COM<jj)a0.019 CONTINUF9 CONTINUE
KKl=KJK+l S KK2BKJK+NMPRINT 10
10 FORMAT!/// )12 F0RMAT(5X«12(X»F8,6))
DO l3*Ksl«NM
COMPT(K)aCOMPT <K)*COM(KT)
- 3 7 -
APPENDIX C '(CONTINUED)
13 CONTfNUF* !29,|COHpT|lt»tKal,NM»N N ) H l 5 1 5l i j N
1 * GO To 61 * DO lfttJsltNM
COMPTT(J)aCOHPT(J)/NN*l!016 CONTINUE
PRINT 10„ PRINT 1?17 FORMATC///»50X»»AVERAGE»«///
PRINT lj>t(CONPTT(J),Jsl«NH|PUNCH 4?0.(C0HPTT(J},Jsl,NMIFORMATf10F6t6)FORMAT (5Xil2re«*l60 To U
999 STOPEND
-38-
APPENDIX D
INPUT PA11AMLTERS TO BE UliAD-IN Full PHOG11AMME
= Blank for reading sources, SAMPLE for analysis
using sources already read-in.
N = Total number of channels used for readlng-in data,
Kl & K2* = First and last channel numbers used in actual
analysis,
MTL a Total number of source spectra to be read-in
for the library of standards.
MB = 0 No print-out of source and background input data,
MR s 1 Print-out of background subtracted source counts,
MB = 2 Print-out of source and associated background
counts.
TH « Channel number for zero energy aa calculated
from source spectra*
EFF (I) = Efficiency factors converting unscrambled counts
to activity for isotope I; can be photo-peak
efficiency or simply activities of sources
depending tin source input data.
NPL(I) & NPU(I) = Lower and upper channel numbers limiting the
photo-peak region of isotope (I) used in
calculating the goodness of fit for each
photo-peak area.
FOR! FnR3 ft FOR3= Respective formats to be given for reading-ln
the source, sample and background oountsv
ISOTBPE (I) • Name of isotope T.
- 3 9 -
TIME
MHK
MBK (si)
MBX (s-
NSMT
COM (i.
Bl. B2. B3. B4
TTIME*
BKS (I)*
MT
NTL
NLF
APPENDIX 1) (continued)
* Half life of isotope I.
s Time of counting of source or sample.
s Source counts taken as such: For sample,
previous background will be subtracted.
s Background to be read-in and subtracted for
both.
= Only for source, previous background will be
subtracted.
s Number of iterations for smoothening source
or sample counts. NSMT s o No data smoothening.
= Calculated channel fractions from source
spectra, source counts or compton fractions
of isotope Jt in channel I.
s Background spectrum title.
= Time of counting of background.
= Background counts in channel I.
s Number of isotopes used in the analysis of the
set of samples following this card,
s The difference (expressed as percentage)
between successive FIT values for termination
of further spectrum shifting iterations.
» Threshold value of error for rejection of the
isotopes. If the quotient of activity of an
isotope divided by its calculated standard
deviation exceeds NLF, the level of activity
is considered to be insignificant. These
Isotopes are omitted and the spectrum reanalysed,
-40-
AHl'ENDIX 1) (continued)
= Maximum number of Iterations allowed
irrespective of NTL value,
= Sequence number of fcsotope I to be called-in
from the library of standards.
S1.S2.S3.S4 = Sample title card,, If SlsTERMNT control
passes to first read statement (C0DE)o
SI s REPEAT, for recalculation of previous
sample spectrum„ Data other than the title
in this card should be repeated with
necessary modifications.
VOL = Constant dividing the activity (volume,
weight etc,,)
TDL = Time period for which decay correction has
to be applied; to be given in the same units
as Z (I).
MBl (=0) = No print out of above unprocessed input sample
and background data.
MBl (si) a Print out of background subtracted measured
and calculated counts.
MH1 (s2) = Print out of the above unprocessed input data*
NBK (si) s Background is taken as a component.
NBK (so) s Background is subtracted.
IZR s Source number for which subroutine ZIRC is
to be called; used with TT only for analysis
of Zr9 from Zr95+ Nb95 composite peak.
IZR gives the sequence number of Zr in the
library of standards.
-41-
APPENPIX P (continued)
TT * Time since formation of Zr95f In same units
as Z (I); used In the subroutine ZIRC for
seperating Zr" from the composite peak of
Zr95 % Nb95e TT = Ot subroutine ZIRC la not
called In,
WT B Weight associated with each sample. To be
used in calculating the weighted average of
a sequence of samples (along »ith TN)0
TN (=-l) s Start of calculation of weighted average in
a sequence of samples.
TN (si) s Continue calculation of weighted average.
TN (=2) s Last sample in the sequence.
KG e 1 to 4 for plot-out (linear and semilog)
of calculated and input sample spectra using
subroutine GRAPH.
KN =1,2,3,.. for plot-out of every first, second,
third etc., data points.
MN (I) m i for print-out of matrix, Inverse matrix,
unit matrix, channel-wise weight, goodness
of FIT values etc, for the specific iteration I.
* Specified separately for source and sample.
- 4 2 -
APPFNtllX n (C0NT1NUEU)
L5QMTFIT
cC ppORuAM FOR LEA 5 T 5Q|JARF S ANALYSIS or NA1(TU) G A M M A S P E C T R A
ccC OPTIONS AMDcC IF C.iHE ( S | A T F M F M T i o ) =S f lMPLE CONjRoL GOEs TO I l 5C IF r n n E I ? "LANK CONTPOL GOES TO NtXT CARnC N = T O T ' L NliM^EP PF CHAMNFL5C HTL = TnTAL NUMRER o r SOUPCt SPF.CTRA I N U I R R A R YC Hn = l OR 2 FOR SOtlPCf DATA Pr, lNT OUTC ' - ! = THKF.SHOLD CHANNEL.C r n H l . F ° " ^ « F n R 3 ARp F()RMATS F ? P " E A U J N G SOURCF. »SAMPLp A N | I n<S COljNTC EFF=FACjORS TO rOMvFRT COUNTS TO ACTIVITYC Ni>U,;jpL ARE LOWFR ANO UPPtR pF.AK C H A H N E L L I M I T SC ISOTOPF. =HAME " F SHIIDCEC I =HALF L I F F
SPECTRAOF SOtlRCF OR SAMPLE COUNTING
C B l » P ? , t n i P < ( ApE HACKGROUNI' T j T L tC TTIMF = TIMF. OF BKS COUNTINGc KI,K? ARE LHWFR Ann JPPER CHANNELS FQH CALCULATIONSC Mi= NuMnER nF SOUPCFSUSED F^R ANALYSJS FROM L J B H A R Y OF M T U SOURCESc N5=SFOUFNCE NO OF ISOTOPES USF.U IN THt PARTICULAR ANALYSISCC 51152,53.54 ARE SAMPLE TITLESc I F SI=TFRMNT CONTROL GOES TO IOcC VOL=wF.lGHT OR VOLUME OF SAMPLFC TDL= pAnioACTlVE DECAY COHRECTlON TlMtC IZR FOR ZR9^ ANALY SIS ONLY AND IS SEQUENCF NO OF ZR95 IN LlB*APYc TT FOR 7R95 ANALYSIS ONLy ANii Is TIME SINCE JR95 FORMAylON ORC SEPARATION
Cc MPK=I FOR BKS READING AND SURTRACTIONC NSMT FOR SMOOTHEM1NG NsMT TIMESC N T L = n T DlFFERNcE(PERCENT) FOR TERMINATING SPECTRAL SHIFTINGC TIONsc NLF=LOWER LIMIT OF ACTIVITY IN UNITS OF S.D, FOR REJECTION OFC ISOTOPES FROM ANALYSIScC IJK= MAXIMUM NO OF ITERATIONS FOR SPECTRAL SHIFTC MR1=1 OR 2 FOR PRINT OUT OF DATAc NRK=1 FOR ANALYSIS WITH B*G AS COMPONENTcC WT=WF_iGHT FHR CALCULATE THE * V R A G E Op A SERIES Op SAMPLESc TN=-i FOR FIRST SAMPLE OF T"E AyRAGlNG SERIESC TM=1 AVERAGING CONTINUESC TNs2 LAST SAMPLE FOR AVERAGINGCC MNJi,-! roR PRINT OUT OF ALL CALCULATED VALUES FOR ITM ITERATIONc PLOT ROUTINE KG=i FOR Y LINEAR KG=2 FOR y *ND z LINEARc KG=3 FOR Y LOGRITHMIC KG=* FOR Y AND Z LOGARITHMICC KM FOR PLOTTING EVEHY KN POINTS
- 4 3 -
D (CONTINUED)
cC Si =Pi «[ ft T I rM SfTPFAT A f J * L Y S ! sC TT iLwnL , T i i : r ApF noT C n * N ^ E n FOB R E P E » T ANALYSISC NpK,i iSMT C T r . , A»T cHAN^En F Q R REPF.AT ANALYSISC
,CTS # 2 6 ° ) , D I F F
j i O l x o R i O « ; O > « E F ( 1 o l , t , , , O ) ,l N P L ' j f l ) ' ! J p U U O ) i F ( l O ) » R N l « i n ) » t R l « 1 0 | t
, (C0ntZ=6HTtRiNT) TCOM'^OM M N , i r K , X ocnM""nM K I K ? 9
3 FnRMAT«nEl3)1 2
5 FORMAT MA*)- 136 FORf'ATCSI^iOIZ) i^1 Fnnf'AT<iAAi A6»Fl0 ,2F5,4 j l? i2 ,F 'nF6«F<»'10i l ) 158 F rWATU6r5 ) 1 69 Fr>«MAT<-,AR,A6,F6) 17
12 FPi^ATlSSXiOTHKESHOLn =tt«F3«2X«»CHANNfcLS*t/) 1613 FnHMAT(?Ui^(AS,6X>J ^H FOPHATCtSX.oVOLUHEsotFB'^X^ntCAr TjME=»»F5»/) 2015 F0RM/lT{V»x«flFl/«15J 2116 FnRMAT(/,ft0X,»SnuPCF DATA«,/,^5x,"COUNTS TO ACTIylTY CONVERSION FA 22
ICTOR.so,/) 2319 F0RMAT(l'«X,T3,2X,fl( lx.E12t5») Zh17 FOHHAj (/uSSXioCn'ipTON FP ACTInNS»»/« l2< <«CRtN0*««6x«B(A6«5X) j Zb20 Fn«'AAT(F6,45 26
21 F0HHAT(49Xi«SAMPLF=e,3Afl,A65 2 7
22 FORMAT! / . 5 *X , "INPUT nATA*»»/j 2023 FORMAT U5Xt*MFASURED SAMPLE COUNTS IN»,F6»ZX, I IHIN\JTES( I«/) 2924 FfWATUXtHFfl . l ) 3025 F0H'<AT(/,4bX,3AR»A6t»lN*'Fin,l»lXi*HiNUTES»,/J 3!26 FOKMATUXtll tlX,ElO,3)) 32Z7 F0RMAT(6X«in<Fl l .3 ) ) ' 3329 F0RMATUflX,T2,lX,»ITERATIUNS-C0MPUTED yALUES«» 3^32 FORMAT(35x»nD!FFERENCE BETWEEN MEASURED AND CALCyLATED SAHPLE CftyN 3 >
I T S I N U N I T S OF S . n . « , / > 3633 FOPMAT(5oX»«GOnt!NE55 OF H T (TOTAL ) = o , F 8 , 2 J 373A FO«ViATUbX»»UNScRAMBLEn COUNTS ANN P E R CENT E"RoR°»' '»6X f H <2XtA* 36
1.1X1) 3935 F O R M A T < 6 X , 1 U ? X , A $ , 1 X ) ) <tO36 F 0 R M A T 1 6 2 X » » M A T R I X « , / J <»137 F0RMAT(58Xi*INVFRSt38 F 0 R M A T < < 5 9 X » « U N I39 F0RMAT«/,ft2X,»B(J)»,/J 4*»*tO FORMAT ( 5 1 X I » C A L C U L A T E D SAMPLE C0UNTS»»/» "5<*1 FORMAT(45Xi«8ACK6ROUND SUTBRACTEO SAMPLE COUNTS*,/> 4642 FORMAT!/,55x,#CnM(MTl*2»X)«»/> *\U3 FoRrfAT(31X,»CHANNELWlSE WEIGHTS USED F()R C A L C U L A T 1 0 N OF T H E INpUT -«6
? MATRIX*,/) ^c
^ ^ FORMAT i /.TOX,«CHANNELWISE WEIGHTS USED FOR CALCULATION OF GOO"NFS 50
IS OF FIT VALUE*,/) -!!
45 FORMAT! /,46X,»CHANNELWl5t GOODNESS OF FIT VM.UEs*,/> 5?^8 FORMAT(4OX.«ACTIVITY(MMC) CORRECTED FOR SAMPLE o«-UME *HD DECAY* 53
54
- 4 4 -
APPENDIX D (CONTINUED)
^6 run'-"«| J/^JAfVU'Miin'^tir jf '
100 FORMAT |«55x,»ANAlYSlS PARAMETERS*,/,30X,«NUMBER OF CHANNELS«,l3,21X,«NUMBER 0* ISOTOPES ANALYSEns<M3*/f42X,»ANALVSlS STAPJ5 FROM C 572HANNFL «, I3,1X,»TO CHANNEL » , I 3 , / , 3OX» «L0wER DETECTION LIMIT FOR 564 REJFCTION OF ISOTOPES(NLF) IN UNITS OF StD.s^^/ .^TX. t tMAxIHUM. 59ftNUM^Fp OF ITERATIONS«IJtC)s O , f 3 , / ,38X««FJ T DrFFtRENCE IpE/J CENT) F 60«OR TFRMtNATION OF I T E R A T I O N ! N D L ) O « , I 3 ) 61
110 Ff>RMAT(A8) 6Z121 FORMATJ/.^OX^SOURCFsOiAe^HALf LlFE»*«ElO,3tZX»»TlME OF COUNTINGB 63
1,FA,/J1003 FORMAT(^0X«»GnApH OF INPUT!,) AND CALCULATED!*) SpECTR««) 631004 F"«MAT(.10X,»C-«APH Op GAIN SHipTED XNpUT<i) ANQ CALCULATED«•> SPpCT 66
IRA«) 6766 FORMAT(16I5) 68127 FORMAT(A8.E1Z,3,F5«I2»II) 69500 FORMAT*/) 70555 FORWATUH1) 715«6 FORMAT(?X,10«1X,E11,5) ) 7Z1002 FORMATl.iaX»»0OODNESS OF FITJPHOTOI'EA^ REGlONS)B°,F8,2) 737?3 FORMAT(44X»»SHIFT CORRECTED CHANNEL NUMBER*,/) 7*722 rORMAT(nX»10FlO,2) 7b10 RFAn 110,COPE 76
1F(FOF,60) 220,330 77330 CONTiNUF 7G
IftCoDElEo.CoDElJGO TO 115 79REAn 1,N,K1,K?,MTL,MB ,TH 60READ l, (FFF(I>t 1=1,MTL) 61REAO ftb,(NPLjn»NPUU),I
al»MTL) 6ZREAD 2,FOR1»FOR3 63UO "37i jslcN 8<»
971 DKS«J)=n 85DO «»2l jIsl,MTL 8ARiTAn 127,!snT0PE(JI),Z(JI),TrME,MBK,NSMT 67REAn FOR1,(COM«J,J!)iJsliN) 66IF (MhK) g8?ii82i<5B3 g9
983 REAP g«nl,B?«fl3,B*,TTlME 90READ FOR3,(^KS(J),Jsl,N) 91
982 IF(MH-1)966,986,984 92964 PRINT 1?1, ISOTOPE<JI),Z(JI),TIME 93
PRINT 5n6,(C0MU,JI),Jsl«Nj 94IF(MHK)086,<586,g99 95
999 PRINT Z5,0lifl2,B3,B4tTTIME 96PRINT 5fl6,<mcS(I),Isl,N) 97
986 IF(MnK)986»PB7,988 98986 1)0 877 Jal,N 99
C 0 M < J , J I ) = C 0 M ( J U H / T 1 M E - B K S » J ) / T T I M . E 100lF<C0M«JtJll)969i677,877 101
989 COM(J,JI)=0 102877 CONTINUE 103667 CONTINUF 104
IF(NSMTJ921«921«923 105923 DO 922 JK al»N 1 06922 COUNTS(JK)= COM(JK,JI) 1O7
CALL SMOOT«COUNTS»NSMT> 106DO 921 JKsl.N 1 0 9
COM(JK«J1)«=COUNTS«JK) HO921 CONTINUE HI
PRINT 16 JJZ
-45-
D (CONTINUED*
PRINT ii.dSOTOPEM) tJsl»MTll 113PRINT 1«5.(EFF(I)»IB1,HTL) 114PRINT 1?, TH U 5IF<HH)6«B,6*6,94 116
94 PRINT lTi(l50T0PE(I)tIsl.MTu 117DO lfl Jal.N 118MMSJ 119PRINT lq,MH,(cOH(J»I)«Isl»MTL) 120
IB CCMTlNUF 1216B8 CONTINUE 122
ISOTOPE (MTL*Us2£^ZZ75l466445?'»B 123DO 4 1= l.MTL 1Z«»
4 Z(UsO.693/?«l> 125115 HEAD 6,Kl tK?,MT,NTl,NLF fIKJ, (N5tn,I*l,MT» 126
REAT1 ?,FOR2,FOR3 12TPRINT 500 128PPINT 100* M»HT«K1«K2*NLF»1KJ»NTL 129
11 PREAli 7"sl,52,S3,S4,vOL,TlME,TUL,MBK,MBlfNBIC,NSMT,IZR,TT,«T,TNf 111lKG.Ku,(MN<I)»Ial»lKJ) 132IF(5i;E(j.ConE?JGO TO 10 133
13<*
51 READ <}»nl,B?»P3»B4»TTlMEREAD F0R3,<«KS(DtlBl,N)FS=TIME/TTlME * F X F F
50 CONTTNUF
54PRINT 2««|CnuNT|I),!al»MJPRINT 25«Bl»B2»n3»R4»TTlMPRINT 24« «BKS(I>«tsl»N >
53 CONTINUFMTl=MTLIF«nnK)750,750*751
751 C0NT1NUF
IS(MP)= MTL+1DO 756 jnl,NCOM«J,MTL*l)sBKS(J)/TTIHEG(J)aO
756 CONTINUEZ(MTL*l»aO * EFF(MTL*l)sX«O/VOt
IKJHPsHT 135FITlsO 13*DO 47 J=1«MP I37
47 15<J1=N5(J> 138PRINT 2 1 « 5 l » S ? « S 3 » S 4 139
TF<SltFQ.CnDE3)G0 TO 53 1<|U
PRINT 2? }*1PRINT 14* VOl'TDl 14ZPRINT 23 .7!ME }«NCL=1 «*READ rOR2,(COUNT(II,ial,M) 145
GO TO »3 . ::!750 CONTINUE 170
IF(NCL)9393»193 "
- 4 6 -
APPENOIX D (CONT1NUEU)
193 i)O <»? J = 1,N 1 7 l
G(J)=RK.s(J)«Fx 1 7 2
COUNT(J)=CO'INT(J)-B|CSIJ»OTIME/TTIME 173|F<CniJNT(J))91»<»2,92 174
91 COUMT(J)=n 17592 C O N T I N U F 176
NCL=n 17793 CONTINUF !yB
224 C O N T J N U F 179
UO ??(, j = l,M i e u
W T = C O U N T ( J ) * G ( J ) iai1F ( W T - 1 . 0 ) 2 ? 7 « 2 Z 7 . 2 2 / }
227 WT=1.02?8 Wl(J)=1.0/WT ill
226 COUMTS(J)=CnuNT(J) . ngJ F ( N S M T ) 9 ? 5 » 9 2 5 9 2 6 {S
J F ( N S M T ) 9 ? 5 » 9 2 5 I 9 2 6926 CALL SHDOT(COUNTS,N5MT)925 K K 1 = K 1 * 1 $ K K ? = K 2 - 1
U^ tq J=1 ,MP<••» ISTr iPF(J)=lSOTOPEfIS(J)) ,SM
I5Tn|.f(Hp+l)=27?13U562302663R l o lI 5 T O P F ( M P + 2 > = 6 3 3 0 6 0 6 0 6 2 3 0 Z 6 % 3 B {it
lSTnPE(MP*1)s62302fi6360606330B225
UO 7q9 I=KK1tKK2
236 IF(CnijNTS(l-l)-l.0(235,235,237 ,21Z35 DCH=n
GO m 7ga237 CONTINUE
UER= -(COU"TS(U1)-COUNTS(I-1))/2.O798 CONTINUE
C O M I M T l l D E K O i /COM(I,MT1*2)=DEB
799 CONTINUFCOH(K1,MT1+1)=COM(KK1,HT1*1)C O M « l l 2 C l l
l S l P * i , S M T i * iI5(Mp+2j3HTU2M=MP*2DO 81 J = l ,NDO »! I = l , HCOMP(J,I)=Wl(j)»COH(J,IS(I))CONTINUEOMP(J,I
81 CONTINUEICK=IKJ.IJH*DO 60 J=1,HDO fto K = 1,M HIAtJtKIHO " 0DO 60 IaKl,K2 2 Z 1
A«J,K)=A(J,(f)*CoH(I,IS(J))oCoHP«I,K) If!
U(J,K)=fl(J,K) * "60 CONTINUF 2Z4
DO l?0 J=l,M Z Z S
B(JlsO,n Z 2 6
DO 120 l=Kl,K2 z|7
- 4 7 -
n jCoNTlNUED)
229120 CmjTtNUr 230
CftU. INVFRT<A«M» 231UO 10? J=l iM 2321)0 30? K=liM Z33U U * K ) = n 2341)1 30? 1=1.M 235
302 U(J,KJ=P(J»n«A«ttK>«.U<J«M 236un u n J S I , M 23?KH<J) =0.0 236DO 1/.0 I = l tM 231*R M ( J ) = A | J t n » P I I I * R N « J ) 240
140 COMTIHUF 24iSH=SH-RM(HJ 2125HT=-SH
R (&A=1.0-nN<M-l)/100.0DO 271 J=K1»K2CTSlj)=OUO ? 7 1 I = liH 2*t8
271UO 25 IC=K1»K2 251UIFF<K>=CTSfK)-COUNTS<K» 25Z
Ar,5=AnSF«COI)NTS(K|*G<K)» H53T(K)=niFF(K>/SQRTF(ABSI 25^
25 CONTmUr 255FN=O 256DO th J=K1»K2 257A B F = A * 5 F ( C T 5 U ) ) Z 5 B
WTsAHF+r, (J> 259WUlsl.O/WT 260UlFF(j)-n!FF(j>«DlFF(J)«WlJJ 261
262F P R + D ^ F F ( J >CONTJNUF 263
) 26*D 5S J l , P£R<J>=SORTF(A<J»J>«FlT>«»H)0,0/l'N(JI 266
555 CONTTMUr 267CT=O$FT=O 268
IF(NBK)135»135»136135 MPl=MP
00 To 138136 MP1=HP-1 S FtMP)=O138 DO 1000 Jsl.HPl
FU)=o t JJ=NPU(IS(J)) S KDD 1001 I = JJ»KK HI
1001 FU)=F(j)+D!FF(r) 276( " ;F(JJ=F(J)/lKK-JJ)
1000 CONTtMUfFTP=FT/CTPRINT 2O,1CKMTT=HP+3F « H 2
422 CONTtNUFPRINT 3fiPR1N7 27
- 4 8 -
A P P F N P I X D (CQNTINUEUI
- 4 9 -
D
201 MPaNx t FlTl*O
GO To 2?fc 3 f t T
CONTINUE202 3MIF(TT)444*444*449 349
445 DO 4/«6 JsltMP »501F<IS<J )#EQ,1ZR)*4T«4*6 351
446 CONTINUE 353*47 CAUL ZInCITTH.t7Ttp.NUH 353444 CONTINUF 3 5>
UO l«0 Jal,HP 35sRN(Jj=RN<J)/<VOL«TIME«EFFt!SjJM» 356
1B0 RH(J|=HM(J)«EXPF(Zll3(J>)»TDL» 35TPPIMT 5nO 358PPI«T 4fl 359PRINT 3S. ( IST0Pt ( t )» I= l9MP) 360PRINT 26t(RNtJ>«J3liMP) 3fclI N t i Z . l . Z 362
35? IF(TN)7U»712«71Z 3637 U UO 713 Jal»HT 364
E"1(JJ=O 365713 RNKjjsQ 366
NTM=o % WT1=O 367712 DO 704 js l tMP 366
RNl(TS(J))sRNl(IS(J>)«RNIJ)«WT 369704 ERl<IS<J>)aFRl(l3lj)|*(ER«J»*RN(jl»WT»0|01)##2 3 7 O
NTMsNTM+l % WTlaWTl*WT 371lf(TN-ltO>n5l,85x«7l6 37Z
716 DO 717 J=1»MT 373RNl«J)=nNlU)/WTl 374F.R1|JJ=SQRTF(ERHJ))/WT1 375
ERKJ)=FRlU)»100 iO/RNKJl 376IF DIVIDE CHECK 7 l 8 i 7 l 7 377
718 ERUj)B0 378717 CONTlNUr BJ7B
PRINT 870, NTM 379870 F°RMAT</ ,30X««AVERAGE VALOES OF L A 3 T » M X * 1 S » *X«»8A"HtS»^l 380
PRINT 35i (fSOTOPE(lJ,I«l»HT) 38lPRINT 2f>i<RNl(J>iJ=l«MT) 382PRINT 2*« ( f R l ( J ) » J e l i M T ) 383
851 IF(KG)ll«Ut853 384853 PRINT 1003 385
CALL GRAPH«KS,N,KN,COUNT»CTS» 3»7PRINT 1004 386CALL GRAPH(KG,N,KN,COUNTS»CTS> 386GO To 11 389
220 STOP 390ENU 391
SUBROUTINE SHlFY<SH,SHC»GA«CoUNT3tNI 1CCC ROUTiNE FOR GAIN AND THRESHOLD SHIFT CORRECTIONS
CDIMENSION CTS<260>«COUNTS(260>tX<260HHN(10> ?COMMON HN,1CK,X 3
- 5 0 -
A P P E N M X D (CONTINUEU)
K i ,K? *FIHST=CnUNT«i(l) 5un 2nn J = I « N &z=J IX(J)=Z»r,A*&H«(GA-l,O) 8
200 X(J)=x(J)+SHC »IF<MMI!CK))*05.205I206 10
206 CONTinUF 11205 CONTINUF 12
DO 300 jsitN 13XC=J 14UO 203 J=1«N 15xjc=xr-x(j) 1*IF(XJC) Z0l«202»ZO3 1?
202 CTS(l)=rOuNTS(J)/GA ' ItGO To 300 19
203 CONTIHUF. 20201 CTSU) = <C0UNTSU)-e0UNTS(J-ni/IXU)-X(J-l)) 21
CTS«I)=C0l)NTS«J-l)*CT3«l)»«XC-XIJ-l)) 22CT3(i)3CTS«I)/GA 23
300 CONTINUF 24C T S < l ) = l , 0 29DO ?n4 !=1«M 26
204 COUMTS(I)=CTS(I) 27CnUMTS(l)=F!R5T ZflRETIJHM 29ENU 30
SUBROUTINE 9M00T(C0UNTStNT) I
CC ROUTINE FOR SMOOTHENlNQ THE S^^TROH
cC
UIMF.NSlON CTS(260 ) ,C0UNTS(260 ) tX (260 ) ( MN( l0 ) 2COMM()H MN.ICK.X 3COMHnH K1,K? i,K3=rU2 S K<*=K2-2 5Nn=o b
451 IFINQ>NT)45Z,453,<(53 7
452 CONTINUF B
INUF B
DO t/,5 ia K3,K4 9CTS(i) = (l7.0«CoUNTS«l)*12,0»(CoUNTS(I*U*CoUMT3(l-lM-3tO»(COUNTS« 10lU2)+rOuNTS(I-2)»)/35,0 IIIF(CTS(H)4*7t<H>5»445 12CTS(i,s0
445 CONTINUE uCTS(KH=COUNTS(IC1)$ CTS(Ki*D"COUNTS(RI*IIICTSU2-I»«CO»NTSJK2-Ii 15CTS(K2)sC0UNTS«K2) • l f cDO 4<i& I S R 1 , R 2 | .COUNTS<I)=CTS(I) 11
446 CONTINUE 19N Q = N 1N Q O « 1 Zfl
GO To 4!11 2?453 CONTINUE 99
RETURN ftEND JJ
-51-
D (CONTINUEU)
7lRC(TDL,TT,ZPJ
ROUTINE FOK ESTIMATING ZR«»S PROM ZR95*NB95 COHPOSITEcc
ZRR=?. l6»( i t0-ExPF(- .009l5«TTM 2ZR=ZR/U.O*7RR) 3RETDHN *ENU 5
StiaRoilTlNE INVERT «6iN) 1CCC ROUTINE FOR DOUBl* PRECISION MATRIX iNyERSIONC ROUTINE FROM ALPHA H ORNL-3975CC
TYPE DOUBLE A,B,C»W,Y 2UIMENSlf5N A ( i o , i o ) t B ( i o ) « C { i 0 ) « L Z l l O I * 6 ( 1 0 * 1 0 l 9
DO *»0 T = 1»N *UO 41 J=1,N 5
A U . j ) s G ( I i J ) 6«1 CONTIIIUF 7«0 CONTl IUF 8
DO 10 J a l . N 910 LZ(J)=J
no ?o I = I » N l i12
Y = A ( l , n 13L=I-1 »*LP=1*1 15IF<N-LP>U,H«l l 16
11 DO 13J5LP»N ITWsAU,Jj i«IF(ABSF(W)-ABSF(Y))13.13tlZ 19
12 K=JY=W 21
13 CONTINUE14 UO 15 J = 1 . N
C(J)=A<J.K) z *A ( J , K ) s A ( J t I I H
A ( J » I J = . C ( J » / Y "2T)
15 B ( J J a A l l . j ) , .A « I » l ) S 1 . 0 D / Y z 9
2?L2(!)sL?(K)LZdfjsJDO 19 K=1«NIF(I-K»16»1
16 DO IB J=1«N
1718 CONTINUE
- 5 2 -
APPENOIX D (CONTINUED)
19 CniiTiMUT 3920 CnNTiMUE
HO ?nO I:liN HiH r<I-LZ(I)>100,200,l00 <»2
100 K=I*1N l O O J
800 l)D '•art J = K , NIr(!-LZ(J) 1500,600,500 46
600 M=L7(I>LZ(T)=L7(J) 46L7(J)=M 49Un 7nn i = l»n 50C(L)=A(I»L) 51A(I»i )=Atj»L) 52
700 A(J,i )=r(L>500 CONTINUEZOO CONTINUE
DO 42 1=1,N 96DO 03 J=1«N 57&tI.J)=A(liJ> 58
^3 CONTINUE 5942 CONTINUE 60
RETURN 61U 62
ccC ROUTINE TO PLOT CALCULATED ANn OBSERvEp rOuNTS IN SEMILOG ORC LINEAR sCALE ROUTINE TROH JAHPO UCRL-19452
cC
DIMENSION *(260)-Y<260),Z<260)»MN<10) ZACOMMON MH.ICK ,X 2 BCOMMOH K1,K? ZCUATA(jNTAPE=60) ,( IOUTAPS61),(K0UTB60I 3DATA(SCALEL=l."E+4) A
500 0000000/)*),<B=1H J,(O'lH,)•(p»lH*)«(SalHII 5A500 FORHflT</) .H5CPRINT 500 >U
PPINT 500 «EDO 200 Jsl,M -p
200 X(J)=J ,GDO ?01 J=ltK5 KM
201 Z(J)=l,0 «jDO 202 J=K6,M 5J
202 Z(J)=i,0 «YHINsY(l) 1YHAX=Y<1) 2DO 1 1=1,M ,YHIN=AMINKY(1),YHIN) q
1 YMAX=AMAX1(Y(I),YMAX) lnIF(K.EQ.l,OR.K.EQ,3)G0T03 }?DO 2 !=1,M tiYMIN-AMIN1(Z!1»,YHIN) \\
2 YMAXsAMAXHZ(I),YHAX) { |
- 5 3 -
n (CONTINUE"!
IYMAXil.OC-38)
ir(YHAX;EO.YMlN,YHAXsYHAX*l,I»"(K.r,E.,)AsALOr.ioiYMAX/Y«lN|
7 WRlTEJInUTAn(l003JYMINiYMAX SIon ro., "
8 WP.ITI (1OUTA",1OO'4)YHIN,YMAX „
T I1*un inno I=1IMH,N
11 ? . 1 . ( 7 ( U M ! N l / Y D i «:12 IO=?.+«»1.»!Y«I)-YHlNl/YniF 3?
GOTOi«?13 Al=AMAXl<7(!),YMtM)
ir-sP.+gT.eALOGlnlAl14 A2=A(<AXl<Y(!),YMlN)
. , L 6 A 2 / Y t ) A15 I M r .ro.l,On.K.EO,3»GOT01ftO !S
irCIn.liT.lP*l)GnT0ll9 43. T i H i a O 44
I»- «!o.GT.iP)OPTni30 4eIFUu.LT.IPlGOTOUO nl
100 , l J ,I 2 = " I 44
5051
110 I I = I p _ l 52l?= IO- Ip - l 5313=<»f,-ln . 54WPITC(IniJTAPflOO6)X(i) , (H, ja l« U j , p , IB* js l«I?) «Q« <Bt J»l 11 55
13>V5 .
120 Il=!n-1 5«I?=Tp-Io-l 5q13=o f l-lr 6 0WP!TF ( IniJTAPt]0nf>)X(I>,(p.J=i , I l ) ,O,(H«Jslt l2>iP,(B«Jsl«l3>tY(!)« 61
XZII) (,?ooTninnn 63
130 1 1 = I P - 1 6 *I2 6S
6f>6T
140 l l = T n - l 6ft12="f.-If« 6<»
T 70717?
-54-
APPENDIX 0 (CONTINUED)
T3
&OTO1000 T5160 Il»lo-1 Tft
l?a«)6-n 77WRITE (IOUTAP, 10061 X (II, (BtJ'it I D«Of (8,^1,12)1 Y{!) 70
1000 CONTiNUr 79HBITElIOUTAP.10051 (SiJal^Z* 00RETURN 61
1001 FORHATMX. 9HX *4**£l3,5i 27n»YHjN LlNE«R 5CAl£ ,36X, 62X 5HVMAXa,Cl3,5, <»H V) 63
1008 FoRHAT^X, JHX t4X«El3,S« 47H« HlN LINEAR SCALE V • V 6*X * z I «12H • a MATCHi<iXi 5H MAX=,E13;=,, U H Y 85
1303 FORMAT(^X. 5HX ,ftX,El3i5i Z7H«"HJN LOOARJTHHIC 5ACLCt36X% 6*X 5HYHAX,,El3f5, 4H Yl 68
1004 P0RHAT1.1X. 5HX «<»X,E13,5, *'H HIN L°GARITHHIC SCAUE • Y 89X • s Z «12H • • NATCH'**' 5H MAX«,E13,3, 1*H Y ¥0X 7) 91
1005 F0BMAT«l«.XO2Alj 9?1OO FORMflT(lX,tlO,3»2H t96Al«2E10<3> 9«
ENU 94
Table E.l»
PHOTOPEAK CHANNEL LIMITS AND MINIMUM DETECTAULE LEVELS OF THE MEASURED ISOTOPESIN TWO GAMMA SPECTROMETER SYSTEMS; AIR FILTER AND PRECIPITATION SAMPLE STUDIES
7.5 x T.5 eras Nal (Tl) - 100 channel analyser 12.5 x 10 cms NaS (Tl) - 256 channel analyserIsotope Photbpeak Area of Background Minimum4
channel photopeak (cpm) detectablelimits scanned level
fl (uuo)
Photopeak Area ofchannel photopeaklimits scanned
Background(cpm)
22.3
26.1
20.8
18.1
12.1
9.3
Minimum*detectablelevel(uuc)
7.0
2.6
7.3
5.2
1.1
1.1
Ce
Sb
144
125
Ru106
137CB
Zr95+Nb
95
Mn54
4-8
26-33
31-36
34-40
46-52
53-61
61-66
92
75
89
87
65
86
78
19.5
13.8
9.9
10.9
6.9
7.3
4.5
5.2
3.2
7.6
5.0
1.5
1.3
1.2
15-19
57-68
66-75
72-80
95-105
110-120
Bl
80
82
85
76
77
IenenI
*For 1000 minutes background oount taking into aocount gamma abundance
Table E.2
PUOTOPEAK. EFFICIENCIES W VARIOUS ISOTOPES FOR DIFFERENT SAHPLE GEOMETRIES; AIttFIL'fliR AND PRECIPITATION SAMPLE STUDIES
FacTors for converting ciim in photopeak region scanned to u u c activity*I 8 o t o e 7.5 x 7.5 cms Nal(Tl) - 100 channel analyser 12.5x10 cms Nal(Ti) - 256 channel analyser
2.5 cms diam. 5 cms diam. Daily Monthly 2.5 cms diam.perspex disc, perspex pressed pressed perBpex disc,
disc. filter filter
15.7
5.5I
16.9 gI
12.8
3.0
3.7
2.4
•Factors include gamma abundances.
Ce 1 4 4
s*125
Be 7
Ru 1 0 6
C s 1 3 7
zr 9 5+ m, 9 5
Mn54
12.3
9 . 0
25.6
16.0
5 . 5
5 . 0
5 . 8
13.9
10.2
29.0
18.1
6 . 2
5 .7
6 . 6
14.4
10.5
29.9
18.7
6 . 4
5 . 9
6 . 8
15.1
11.1
31.4
19.7
6 .7
6 . 2
7 . 2
Table E.3
ACTIVITY CONVERSION FACTORS AND MINIMUM DKTECTAULE LEVELS FOR TUP-BA.T CONTAINERS;5"x4" Nal(Tl) - 256 CHANNEL ANALYSER - SOIL STUDIES
Isotope Channel Energy regionregion
Minimum Detectable LevelConcentration percpra in the region Total sample Per gr&m of soil sample
act ivity
jrium-144i
-imony-125
Ruthenium-106
Ceaium-137
Manganese-54
Thorium-232
Uranlura-238
Potassium
14 -
56 -
69 -
94 -
122-
134-
160-
216-
20
67
81
105
13S
157
190
235
0.115 -
0.389 -
0.470-
0.630 -
0.810 -
0.385 -
1.050 -
1.400 -
0.150
0.456
0.550
0.700
0.880
1.030
1.240
1.520
8.14
'J.38
28.12
8.24
7.50
0.048
0.034
0.154
uuc
uuo
uuc
uuc
uuc
•B
ng
g
8.9 uuc
8.9 uuc
26.4 uut
5.6 uuc
4.1 uuc
35.1 ug
25.0 ug
98.6 ng
—34.45 x 10 uuc
—34.45 x 10 uuc-21.32 x 10 uuc
—32.8 x 10 uuc
Q
2.1 x 10" uuc
1.75 x 10"2 ug
1.25 x 10"2 ug4.93 x 10" 2
- S B -
• I I i ! • =;
• i l ' . i ; ' :T ••, -;—-'••-• —4-r-'
\ A i i r r j r U i m iiiiiiiiii.i.•:.:•;•• ^ &M L " H ! i jTTf f i i ^ i i i l i .liwiliJifeMjl!r f, l b l 4 i;tiIa^ILi ;l!lii:;i!31ii|ili
FIGURE . E l THEORETICAL TOTAL EFFICIENCIES FOR POINT SOURCE ON AXIS 2 1 / Z D I A 2 Vg THICKN a l C T | ; CRYSTAL. ( R E F . 6 )
E - 5 0 4 4 - G - 2 1 6 3
- S 9 -
FIGURE E 2 . THEORETICAL TOTAL EFFICIENCIES FOR POINT SOURCE ON AXIS 3 OIA 3 THICK
N a l C T | ) CRYSTAL . ( REF . S )E-S044-C-Z164
- 6 0 -
r^-4--~Li:_..;......;:...,.:.iT.i
FIGURE:E3 THEORETICAL TOTAL EFFICIENCIES FOR POINT SOURCE ON AXIS s"r»IA 4"THiCK N a l ( T OCRYSTAL. CREF.6)
E-5044-G-1138
- 6 1 -
1.0
ENERGY CMcV)
FIGURE :E4. PEAK/TOTAL RATIOS FOR A 2*D!A.x 2*THICK N a l CT l )
CRYSTAL. SOURCE DISTANCE! 10cmi, POINT SOURCE
10.0
- 6 2 -
1.0
1.0
ENERGY (MeV)
FIGURE.E5. PEAK TOTAL RATIOS FOR A 2.5*D1A. x 2.5*THICK
N a l ( T l ) CRYSTAL. SOURCE DISTANCE 1 10cmi,
POINT SOURCE.
- 6 3 -
s
I
1.0
ENERGY CM<V)
FIGURE:E6. PEAU/TOTAL RATIOS FOR A 3*DIA. x 1* THICK N a l
CRYSTAL. SOURCE DISTANCE. lOcmi, POINT SOURCE.
10.0
- 6 4 -
sOB
ol 1.0
ENERGY CM«V)
10.0
FIGURE.E7. PEAK/TOTAL RATIOS FOR A 3*DIA.x 3*THICK N a l
CRYSTAL. SOURCE DISTANCE! 10cm«, POINT SOURCE.
- M -
POtNT SOUnCf AT 1Ot.«
TO* HAT CONTAINER
FIGURE: E9 .RESOLUTION or S'OIA 4"THICK Nai (TI) CRYSTALFOR POINT SOURCE AND TOP HAT CONTAINER SOURCES.
- 6 5 -
CC
0.3
0.2
0.1
0o.i
;
1
'' ii : " : ;!
: 1 • .;,
• I
1.0
ENERGY (McV)10.0
FIGURE-.E8. PEAK/TOTAL RATIOS FOR A 5*DIA.« 4*THICK N o l ( T l )
CRYSTAL. SOURCE DISTANCE! lOcmi, POINT SOURCE.
- 8 7 -
10
E
to
u
m
10
: \
•• *
1 1 1 1
1 1 1 I
\
i i i i
i t l i
POINT SOURCE AT 1e»
TOP-HAT COKTAIHER
•
1 l l f
0.5 1.0 i.sEMEKCT CM<«3
FIGURE. E 10.PHOTOPEAK EFFICIENCY OF 5*DIA. 4*THICK
Nal CTl) CRYSTAL FOR POINT SOURCE AND
TOP-HAT CONTAINER SOURCE.
