UNCLASSIFIED
ORNL





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DETERMINATION Q MUCLIDE CONCENTRATIONS IN SOLUTIONS CONTAINING LOW LEVELS OF
RADIOACTIVITY BY LEAST-SQUARES RESOLUTION OF THIS GAMU-RAY SPECTRA"
E. Schonfeld A. &. Kibbey
W. Davis, Jr.
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To be presented at the "Sighth Conference on Analytical Chemistry in Nuclear
Technology," to be held at Gatlinburg, Tennessee, October 6-8, 1964.
Research sponsored by the 0.8. Atanic Energy Commission under contract with
the Union Carbide Corporation.
2
7
!
T
.
ABSTRACT
Carmen-ray spectrun resolution, « rapid, cheap pothod for determining the
ndionuclide content of solutions, was tested for use in studies of processes
concerned with the decontamination of waste water containing only 102 to 10%
wuc of radionuclides per liter. Tosta, with two multichannel spectrometers, and
Assocated data analyses by the method of least squares, were made with solutions
of boco, 855r, lice, and 144ce added as tracero to water containing gºer, 95zr-Mo,
LORu, 134cs, and 137C8. The lowest concentration of radioactivity was about one-
tenth of the lovest value previously determined by this technique. Some of the
solutions were concentrated by evaporation by factors up to 20 to evaluate this
feature for improving accuracies of analyses.
For comparison, the solutions were also analyzed by standard radiochemical
Dethode. Agreement between the two methods was excellent for con sr
for concentrations down to about 500 muc/11ter (scatter of t5 to 20%).
Agreement between the two methods was good for C8 at activities down to 3000
to 4000 muc/liter comparative values from the two methods difered by factors of
5 to 10 for 4*ce except at activities above 5000 wc/liter. More dilute solutions
were successfully analyzed only if they were first concentrated by evaporation.
Because of large statistical fluctuations at "U Ru concentrations no bigb 18 1000
to 2000 vuc/liter, no particular significance can de given to the data for this
nuclide.
Several contributions to the
thematical techniques of govery spectrum
resolution are reported. These include: data showing that gaib süifts up to 5$,
and threshold shifts of two cišannels, can be accurately handled by a computer
program; resolution of the errors of concentration estimates into contributions
by various kind and the various radioactive species present; and use of chi-square
to test the ovenll relability of the multichannel spretrunter.
page 3 deleted - was ristred for
* table of contents.
INTRODUCTION
1
.
One by-product of some nuclear-energy installations 18 slightly radioactive
process water, produced in such large volumes (hundreds of thousando to millions
of gallons a day) that disposal to the environment is an economia neccosity.
However, such disposal can be permitted only if the concentrations of biologically
hazardoue auclides (such as posr and +31Co) do not exceed certain maximum permis-
ofble values defined by the V.8. Public Health Service. To quote, for example,
"When 220Ra and Sofr concentrations do not exceed 3 and 10 wuc/liter, water supplies
shall be approved without consideration of other sources of intake of these radio-
active materials." If these maximum permissible concentrations are exceeded, then
the water must be decontaminated to a level that permite safe disposal. At CRNL
buch decontamination 18 partly achieved by a conventional line-soda process fol.
loved by dilution in the Clinch River, which further serves to reduce the concen-
tration of contaminants.
The goal is to decontaminate such waste water to extremely low levels prior
to its disposal, not depending on dilution by surface or ground water. Thus, the
new processes for decontaminating large volumes of blightly radioactive water
have been under study at CRNL for a number of years. These methods include sorp-
tion of the radioactivity on naturlly occurring ion exchange materials,' on organic
ion exchangers in fixed-bed", and moving-bedº processes, and by foam separation.'
The test water may be tap water to which radioactive tracers are added, or actual
proce88 vaste water to which tracers may or may not be added.
The efficiency of a process for removing a radioactive auclide frou water 18
calculated from aumerical values of the concentration of this radioactivity entering
and leaving the process. In common with most process development work, then, the
rate at and the extent to which the process variables are tested will depend on
the speed and cost of the analytical results -- in this case, ndiochemical analyses,
which can in some instances be replaced by a faster and cheaper wethod.
The first purpose of the present report is to describe the results of multi-
channel gamma-ray spectrometry and associated spectrum-resolution tachniques for
"WYTYT T
WICE
determining the concentrations of cach of five to eight nuclides when individual
concentrations are in the range 10% to 105 wo/liter. Canna-ray spectrometry 15
Past and cheap for such activity levels because counting times are only 5 to 20 min,
and sample handling is limited to concentrition hy evaporation. Radionuolide con-
centrations obtained with standard, yet costlier and more tedious, radiochemical
methods used at CRNL are also presented to show the probable absence of bias in
the spectrum-resolution calculations.
The second purpose de to describe extensions we have made to existing mathe-
matical techniques for estimating the uncertainties of concentratioüs of gamma-
ray emitters by spectral resolution. These extensions, particularly to the work
of Salmon, "º include further study of the effects of the following: gain and
threshold shifts, the presence of unexpected nuclides, and the prerence of short-
lived nuclidee. The extensi.one also include a
method for estimating
the contribution of background and the activity of all other nuclides to the un-
certainty of the activity of a selected nuclide, and the use of chi-square as
an overall equipment test.

EXPERIMENTAL
Procedure and Description of Sanyoles
The procedure for obtaining • gamma-ray spectrum consisted in placing 100 ml
of the radioactive solution in a pint-size polyethylene bottle, in turn placing
the bottle in a polyethylene bag, and thence on top of a 3- X 3-in. NaI crystal.
After closing the lead shield in which the crystal was contained, the sample was
counted for 5 to 20 min with a 200- or 256-channel gamma-ray spectrometer. An
additional step with many of the samples (because much of the radioactivity was
removed from the water in the sludge and foam columo) was evaporation of 500 to :
2500 ml of solution down to 100 ml, this 100 ml then being placed in the polyethylene
bottle for counting. Concentration by evaporation 18 a cheap way of further 10-
creasing the accuracy of estimates of radioactivity.
Ivo types of aqueous solution were used in these studies: (1) samples takea
1 during operation of a laboratory unit (for decontaminating actual process waste
water) consisting of a suspended-bed sludge column followed by a town separation

column', and (2) synethtic aqueous solut tops. Solutions from the laboratory
equipment consisted of the feed water, unfiltered and f!lterod water from the
sludge column, and unfiltered and filtered water from the town column. The radio-
chemical content of the food water, made by adding tracer nuclides to process
waste water, 16 given in Table in
The second type of onlution was syrithesized from tap water and radioactive
tracers. These solutions, also as 100-mal volumes in pint polyethylene bottles,
were used to study several of the variables associated with multichannel garma-
ray spectrometer operation and the subsequent results of spectrum resolutia. A
solution containing boco, JUORU, 237C8, and 144ce, cach approximately at the level
of 0.5 uc/11ter, was used to study the effects of threshold and gain shifts on
subsequent spectrum resolution. Spectra from this solution were used to study
the computational consequences of assuming that only three of the four puclidee
were present. Four solutions, whose radiochemical content are given in Table 2, que
were used in studies of spectrum resolution of short-lived auclides.
1
Radiochemical Analyses Used for Calibrating Spectral Resolution
As mentioned previously, evaluation of the spectral resolution method 18
based partly on a comparison with results of other methods that are more or less
standard at ORNL. Thus, boco, 098r, and 137C8 activities were obtained by compari-
son of areas under the gamma-ray photopeake for the samples at 1.33, 0.51, and 0.66
Mev, respectively, with those for standards of equal or greater activity. These
calculations (manual stripping) involved manual estimation of areas and corrections
for contributions by the other nuclides in a manner such as that described by
Heach. 11
Zirconium, ruthenium, and cerium were determined by beta counting after ap-
propriate chemical separations. Zirconium was precipitated as the mandelate and
counted after drying instead of being precipitated with cupferron and counted
arter ignition to Zroz, as described in the standard procedure. .
Table 1. Radioactivity in Process Waste Water from the Laboratory-Tost Equipment'
Activity
Activity in Added 48
Waste Wate
Tracer
(818 min 2-1) (ais min2-2)
Final Feed
Activity
(tuc/liter)
Lovest
Activity
(wc/liter)
Nuclide
360
6000
85.gr :
9528-NO0
106Ru :
13466
3 to 10
N11
to 0.6
0 to 3
50 to 1000
None
None
3,000 to 5,700
20,000 to 450,000
0 to 300
0 to 1400
100
1,400 to 6,000
2,000 to 9,000
9,000 to 30,000
1.5
None
100
137 cm
3 to 14
1000
14tce
None
None
5 to 20
20 to 70
24th ce
Trace
Table 2. Activities in Solutions Containing Short-lived Nuclides
Half-
ble
Initial
Activity
(uc/liter)
No. of
Photopeaks
Nuclide
0.04 to 0.09
60 co
12 Go
1301
15.05 kr
5.3 yr
14.1 hr
12.5 hr
30 yr
64.8 bir
0.02 to 0.04
0.6
0.13
0.01 to 0.02
0.04
13708 •
198 au
*
.
.
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.
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.
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..
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....
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RESULTS Q SPECTRUM RESOLUTION COMPARED WITH THOSE FROM UBUAL RADIOCHEMICAL ANALYSES
The primary results of the first phase of this work are presented in Fig. 1
through 4 and in Table 3. In each of the figures, the concentration of a nuclide
calculated from resolution of a gamma-ray spectrum is plotted against the concentra-
tion obtained from the more usual radiochemical analyson, as described above.
There
are more than 80 pairs of points for each of these nuclides. Numerical values are
for solutions as counted--that 18, after concentration by evaporation 18 such
evaporation was performed. For the sake of clarity, standard deviations of results
of spectrum rosolution (to be described below) are not plotted in these figures.
Cobalt-60
From Fig. 1 it 18 apparent that agreement between the two methods for obtain-
ing bºco activities 18 excellent for activities from 100 down to 1 die miami ?
(45,000 to 450 wuc/liter). At the upper end of this range, the two methods agree
within 5 to 10%; at the lower end, ponagreements are in the range of 10 to 30%.
Strontium-85
Comparative data for $58r (Fig. 2) extend from more than 6000 down to about
0.4 dis min m2? (or down to about 200 wuc/liter). Agreement between the two
methods for activities above 100 de min-m12 18 better (+2 or 3%) than we might
have expected. In the activity range 10 to 100 dis minº-m2the spectrum resolu-
tion values are about 10% below those obtained by manual-stripping comparison with
09gr standards, while for activities below about 3 di8 min 21 the spectrum-
resolution values are about 15% above those obtained by manual stripping. We do
not believe these differences need explanations beyond those residing in the un-
certainties of the manual-stripping method (which are unknown) and the calculated
· uncertainties of values from spectrum resolution.
Cesium-137
Activities of 137C8 varied from about 200 to 7 d18 min-ba1-2 (F1g. 3). Agree-
ment between spectrum-resolution values and those from manual-visual comparison
(stripping) with standard solutions 18 good at activities above 20 dis min-m1°+;
at lover activities the spectru resolution values are lover by about 50% than
those obtained by stripping. Although this discrepancy has not been analyzed in
1.-
-..
.-
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.
CO. FROM SPECTRUM RESOLUTION, counts minimi
ACTIVITY OF 6°C FROM SPECTRUM RESOLUTION, dis min-mi"!
.
=
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ACTIVITY OF
.
+
1
:
4
0
2x
ACTIVITY OF O CO BY MANUAL-STRIPPING COMPARISON WITH STANDARDS, dis minº'mi"!
Fig. 1. Comparison of Two Methods for Estimating the
Content of a Solution.
Co
.
.
.
..
...
!
4,6
.
L
i
.
.
mini
..
.
.

ACTIVITY OF ST FROM SPECTRUM RESOLUTION, dis min' mla!
ACTIVITY OF ST FROM SPECTRUM RESOLUTION, counts min-'m1!
·
!
proseso ..
ACTIVITY OF 885r BY MANUAL-STRIPPING COMPARISON WITH STANDARDS, dis minimi
rogramowanie
na..
.... .....................
.
. cream ever........
Fig. 2. Comparison of Two Methods for Estimating the
Sr Content of a Solution.
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ACTIVITY OF 13 CS FROM SPECTRUM RESOLUTION, dis minimal
.:: ACTIVITY OF WCS FROM SPECTRUM RESOLUTION, counts min min
42
'
.
I
ACTIVITY OF 13% GO BY MANUAL-STRIPPING COMPARISON WITH STANDARDS, dis minimio!
. ei
.-
112
Fig. 3. Comparison of Two Methods for Estimating the
Content of a Solution. .
püs
ta
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.
ACTIVITY OF "CO FROM SPECTRUM RESOLUTION, dis min
mla!
2016
.
C
2
.
..
with
..
Content of a Solution.
Fig. 4. Comparison of Two Mothods for Estimating the co
ACTIVITY OF MA CO BY BETA COUNTING, dis mind mind
Urs
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.
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; ACTIVITY OF 144 CFROM SPECTRUM RESOLUTION, counts min. 'mt

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Table 3. The Estimated Standard deviation of the Isotopic Ratio is
Consistent by Two Different Methods
Average
Average
Ratio. . Standard Standard Ratie. Standard
13700/136C8 Deviation 1* Deviation 26 lkce/lce Deviation 1
8.92
2.45 2.26 2.7 2.1
standard deviation of each measurement.
Average standard deviation of the isotopic ratio.
Standard
Deviation 26
2.6
......
detall, it is probable that it is due in part to the large interference by the
0.51-Mev photopeak of Ssr in the manual-visual estimation of the counting site
at the 0.66-Nev photopeak of 137cs.
Cerium-;
Activities of luce extended from 500 down to about 0. dis nou (Fig. 4).
Here, agreement between the radiochemical beta-counting estimates of activity and
1
those from gamma-ray spectrum resolution are not entirely satisfactory. In most
cases, the value of 1*ce activity from spectrum resolution 18 higher than that
fron beta counting. The ratio of the two values 18 about 1.2 at the high end of
the activity range, but it increases to about 5 at the low end. Uatil solutions
of known radiochemical content have been analyzed by the two method, it will not
be possible to explain these results with 144ce. Such comparisons are now in progress.
Other Radioactive Elements
Four other radioactive nuclides or nuclide pairs were present in these
solutions, namely, 952r-Mo, 100 Ru-Rh, 134c8, and 141ce. With the exception of
134c8, none of these could be determined with much accuracy by spectrum resolution,
nor by beta counting after radiochemical separation in the cases of 95zr-ND and
LoRu-Rh. Thus, the results are primarily of use indicating the magnitude of activities
that are too low to measure.
Activities of >2r-Mo (arter concentration by evaporation) were in the range
0 to 2.6 dis nine-2 according to beta counting and 0 to 3.7 als un 21-2 according
2
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.
.
.
.
DYN
*
2.
- 19
1
to spectrum resolution. In all cases this muclide combination contributed 2088
than 5% of the total activity; in many 1t contributed less than 0.1%.
Generally speaking, there was agreement (a factor of 2 or more) between the
düd ethods of analysis even at the upper end of the activity range. On this
basis, values of activities of 95zr-Nd below about 3 d1s mio ?, in solutions
described in this report, should not be given serious consideration, whether
determined by beta counting after radiochemical separation or by gamma-ray-
spectrum resolution, 1f this activity constitutes only a few percent of the
total.
The situation is much the same for to Ru, which contributed a maximum of
12% of the total activity, although this was at most 15.5 dis ma-n10% according
to beta counting after radiochemical separation. At these levels of concentra-
tion and activity, the uncertainty of the value of LºRu 18 at least as large as
110 die min 22%
Two nuclides, 234C8 and 141ce, were determined by spectrum resolu-
tion Bence, the meaning of a value of the concentration of one of these can be
discussed only in terms of a ratio, such as +37C8/134c8 and 14*ce/14-ce. These
ratios, which should be the same for all samples of each of the three laboratory
experiments, are 8.9 and 2.7, respectively (Table 3). The uncertainty of the
S1C8/+s4C8 ratio 18 about 25% of the value. This 18 a reasonably low value in
view of the fact that 134c8 contributes only about 11% as much activity as does
137C8. By comparison with Fig. 3 it may be seen that activities of 134cs in
these solutions were as low 48 1 die miami. .
The uncertainty of the ratio +ce/14-ce 18 nearly as large as the ratio
Itself (Table 3). Since the 14-ce activity 18 only 1/2.7 of that of 144ce, compari-
son with Fig. ' shows that 14-ce contributed only a few disintegrations per minute
per mill1liter to the total activity, or only a few percent of the total activity.
Thus, the available data indicate that the lower limit of +4dce activity that
can be estimated with an uncertainty less than the estimate 18 2 to 5 dis nin 222,
or 1000 to 2500 wc/1$ for solutions such as we have tested.
.
WWW.
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14
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Pirut
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22
KATY
***
V
16
DATA AMLYSIS
Basic Concepts and Equations
The mathematical equations used in spectrum resolution by the methods of
least-squares have been presented many times. Since we will be extending the
techniques of error analysis, it 18 first necessary to summarize the basic concepts
and equations.
Consider a standard sample (of solution, in our studies) containing a known
quantity of the gamma-ray emitter ] (10 disintegrations per minute per milliliter,
for example). We mount the sample appropriately in a lead shield that contains
a scintillation detector that is connected to a multichannel analyzer. During
an elapsed time interval ®, we collect $y counts on channel 1, Say counts on :
channel 2, and, more generally, $ counts on channel 1. These counts are
contributed partly by the sample and partly by background radiation. Before or
after collecting counts from this standard we count the background during an
elapsed time on (which may or may not differ from @y) and collect counts
on channel 1. Similarly, we mount and count separately the standard samples of
all gamma-ray-emitting nuclides in which we are interested. Finally, we mount
and count (under conditions identical with those used for the standards) a sample
that contains unknown quantities of some or all of the standard nuclides. This
sample of unknown composition 18 counted for an elapsed time t, during which za
counts are collected on channel i. The corresponding background counting interval
18 t, and the number of background counts on channel 1 18 z.
If there have been no changes in the background radiation intensity or in
the operating characteristics of the electronic components of our multichannel
gamma-ray spectrometer during the time required to perform all these counting
operations2 - specifically, if gamma-ray energy vs channel number and sensitivity
ve channel number bave remained invariant -- then the counting rate (counts per
unit time) due to standard j on channel 1 18 :
Ca.
.."
16:19
!
v
MLA YA
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.
LES
1
....
KL.
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.
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18
Similarly, the counting rate due to radioactive puclides in the sample of unknown
composition is :
2
.
The tern X, 18 the sum of counting rates of all radioactive buclides that can
activate the detector (NoI crystal); that 16,
(3)
..
where x,, is the counting rata in channel 1 due to radiation from nuclide 3. One
requirement of the following least-squares analys18 18 that the relative uncertainty
10 au 18 less than that of x.
Whether we really know the absolute activity of the standard samples or not,
the process of resolving a spectrum requires that we express the quantity of
nuclide j in a sample of unknown composition in terms of the standard for
puclide j. Thus, the resolution process reduces to calculating the quantity :
mi the ratio of concentration of nuclide 3 in the unknown to the concentration
in the standard J. This applies to all channels 15 15a of the spectrometer.
By combining Eqs. (3) and (4) we obtaio o equations in he unknown quantities me,
where o vill generally be 100 (channels) or greater, and h will be in the range
I to 20 (nuclides).
.
*114,3 + 0,202 + €133 +...+15* ,
*214 * 222 +233 + ... + detay
+ baths + 42363 +...+ and the en
(5)
............
..
.
.
...
...
TY
,
.
als
:.
.
in med
Here, f, 18 the expected value of xj,and, more generally, f4 18 the expected
value of xq :
Sources of Error
Equation (5) applies only to the ideal case wherein the electronic equipment
of the gamma-ray spectrometer remains perfectly stable during the whole period
required to perform a series of countings. In terms of the familiar plot of the Le
energy of maximum 1.ntensity of a photopeas vs channel number( Fig. 5) this
perfect stability corresponds to the situation wherein both intercept and slope
remain constant. The intercept of the line through the data with the "channel
a umber" axis (that 18, the threshola) need not be at channel number 0.
Unfortunately, the electronic equipment does not have this ideal stability
Instead there are changes in the threshold and in the variation of energy with
channel number. One instrument we used showed a 40.5 channel change in threshold,
and a 10.5, gain (percentage change in energy per channel), during wf-day period.
We consider these to be indicative of very good stability. The spectrometer used for
counting the eighty-odd process water samples showed threshold changes of +0.5 .
channels and +1.5% gain shift during an 8- hr period; a spectrometer used for counting
solutions containing short-lived nuclides showed threshold changes of #1.5 channels
and +1.5% gain shift in 8 br. All these values were calculated as part of the
resolution of the various spectra.
In addition to these small gain and threshold shifts, for which, as described
below, we make appropriate corrections in the computer program, there are several
mechanical problems involved in the transfer of counting data from the spectrometer
memory to magnetic tape for use in the computer. There 18 also the problem of
determining whether there are short-term instabilities in the electronic equipment.
18
Fig. 5. Gamma-Ray Energy vs. Channel Number (RCL Spectrometer and a 1/4-in. Beryllium Absorber
----..................................................... ....... ----------...--........
A

..
isotope
Sr-85
Cs-137
Cs-134
Peak
% Efficiency
Channel Energy Channels
No. (mev) 16 to 200)
52.2 0.51 12.40
66.6 0.667 9.50
61.0 0.601 22.1
80.6 0.794
118.5 1.17
17.5 ..
· 133.8 1.33
52.2
4.42
14.1 0.134. 3.195
15.2 0.145 8.07
75.5 0.75 9.88
Co-60
Ru-106
Ce-144
Co-141
Zr-Nb-95
--
.
.
.
GAMMA-RAY ENERGY
Zr-Nb
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CHANNEL NUMBER
OMBER..
.
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Short-Term Instabilities. The chi-square test++ provides a quantitative statement »
concerning the short-term stability of a multichannel analyzer, although there is a
lapse of several hours from the end of the counting operation until computer output
18 available. To use this test, we take 15 successive counts of the same sample and
then for each channel calculate the quantity,
! ops ..
..!
x?
malam •
· Both this and the summation of x over all channels provide quantitative
information on instrument stability at the time of measurement.
Mechanical Problems with Paper Tape At present, our most serious problems are
associated with the transfer of data from spectrometer to computer. This transfer
involves several steps. First, the spectrometer controls a paper punch whereby
the channel-by-channel counting data are listed as bloctal punches on a (black)
paper tape. Second, a master paper tape (MPT)+) of the CDC 160-A assembly system
(OSAS-A) and then the tape of counting data are fed into the 160-A assembly system.
This operation generates a magnetic tape and a paper listing of the data (channel
by channel) and printed statements giving channel numbers and the natures of any
errors in the paper tape. These might be parity errors or mis-punch errors. An
example of the latter would be a punch of 10675 counts when the correct value 18
00675 counts. If there are no errors, the magnetic tape is ready for use in the
spectrum-resolution program. However, our present experience shows that there will
be an error in the punching of data on paper tape in at least channel of 1 to 10%
& card deck of the data, in binary-coded decimal (BCD). Any card containing erroneous
data, as shown by error statements on the printed list, 18 reproduced, manually,
where correct and punched correctly where incorrect. The resulting corrected data
deck is inserted appropriately into the binary or FORTRAN deck of the spectrum -
resolution program, which 18 then executed.
.
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Correcting for Gain and Threshold Shifts A geometrical representation of gamma-ray
energy channel number with greatly exaggerated shifts in threshold and gain
18 shown in Fig. 6 , wherein the superscript s refers to standard samples. This
figure shows the energy for channel 1 to be Es, the energy for the channel of highest
number (n) to he E, the energy of any channel 1 to be E, and the threshold channel
to be nø, However, when the sample 18 counted, the let and oth channels correspond to
energies E, and E., the threshold has shifted to channel n, and the channel corresponding
to energy Bhas shifted from 1 to 1, and the gain, instead of remaining 1.0000, bas
become :
al
·
The definitions above.
Abe summarized by the two linear equations, one for
: sample and one for standard;
788234
ра
(9)
From a straight-forward application of Eq8. (8) and (9) we obtain an expression
for the shift in the number of channels at channel i in terms of. F and the two
threshold channels, n and nº, namely;'
.(06) - (F - 1) (
1
40-1.90 4-mythe
79) + (n - )%.
deceased
(10)
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A
"
W
..die mond os..
..
.......
...
..

Fig. 6. Schematic Representation of Gamma-ray Energy vs. Channel Number
Under Conditions of Different Threshold and Gain.

.
-
-
--
MDPOINT ENERGY OF CHANNEL (mev)
ma.com
-
CHANNEL NUMBER

The time interval between counting a standard and its background, or between
counting a sample and its background, was small. Therefore, we
assumed that there
and its background. This assumption need not be ade 11 it is not reasonable since the
geometry described above can be used to make any necessary corrections. In our studies
the only necessary corrections were between standards and suples in many cases
several days, between counting standards and counting Bemples.
The effect of gain and threshold shifts on counting rates in specific channels
can be expressed by terms represented in Fig. Thus, the set counting rate
(background subtracted) observed for a sample la channel 1 is y, (Eq. (2)), whereas
18 do gala and threshold shirts had occurred it would have been xg, which we may
express as :
1707
24 48
nel com
(11)
Now the term (6-1) has already been given 1o Eq. (10), while the derivative
ter of Eq. (u) 18 approximated, numerically, o
28 :
Equation (u) then becomes :
***Todas las comp
23
Flo. 7. Change in Location of Gamma-ray Spectrum Due to Threshold and Goin Changes
themises
(ben)
COUNTING RATE, BACKGROUND SUBTRACTED

Observed
Expected if no :)
poln or threshold
shifts occur
1.
! CHANNEL NUMBER
This equation contains thrve unknown parameters, namely, P, n, and n'. We evaluate
go by sitting data od standards for photopouk onerky ve channel number EA. (9),
w shown in Figs. 5 and 6, and then calculate
(14)
With threshold and said shifts, the expected value of x0 novely to 18 no
longer given by Eq. (15). Instead, by combining Eqs. (5) and (13) ve obtalo :
ya ... [14) (46) #2) cofin)-4)
spoty a oy our family me" +62 9
was....[lefty) is a 1 * * *
. For convenience in writing and in computer programming we define the (n+1)
variable and parameter as
(16)
(17)
ve define the (2+2)
Variable and parameter as
"i(2+2)
(18)
and
(hee) - ches.
(19)
Thus, Eq8. (15) become of the same form ab Eq • (5) but contain a summation of
k (equal to h+2) terms instead of h, whure h 18 the number of different gamma-ray-
emitting nuclides in the sample under consideration.
These n equations (n channels) in the k (equal to h42) unknown quantities
(b auclides plus gain and threshold shirts) are expressed in the same terminology
48 used by Cramér." Thus, the expected value of x, 16 :
E (x) .fi
(20)
and the variance
Bay)
(21)
r
.
.
.....
where p, 18 a weighting factor for the counts collected on channel 1, and of
and I, are unknown. As shown by Rainwater and Wy, the weighting factor for a
single term such as $29 18 simply equal to $4.. Since ay is a difference in
counting rates, we have:
WALL-
(22)
The limitation is that the probability that any particular atau vill disintegrate
during the counting period io very small.
12
Equations used in the analysis of data to obtain maximum likelihood estimates
of , and other parameters are, from Cronér,7 m follower
minimum.
where r and 8 may take all values 1, 2, ..., ko
The normal equations of the problem are :
$11% + bl2m2 + ... + ban than
a
.......
(25)
" + bretz + ... + bung
The determinant B 1o defined as:
pu $22... by
bki oka ... Pick
(26)
1
:
Bro 18 the cofactor of element Drone
Then the maximum likelihood estimate of m, 18 unbiased :
The variance of * 16:
.
and the maximum likelihood estimate o
and the maximum likelihood estimate c*? of the variance of fit, of, 10 :
pamo,
** 3,247
variance of fit,
where
The true value of m at the standard confidence level 18 then :
and the variance
D? (wa) - orzec
.
.
4
EVALUATION OF ACCURACY AND ERRORA
Many tests wore made with solutions of known and unknown radiochanical com
position (EXPERIMENTAL section) in attempts to evaluste the accuracy with which
gamma-ray spectra are renolved according to equations presented above. These
equations woro programmed for excoution with a CDC-1604 computer. In the fol-
lowing paragraphs we present examples of the speed of convergence of the computer
program, of the accuracy of analysis, of the use or the chi-square tost, and of
errors that result from not correcting for gain and threshold shifts.
.
Convergence of the Computer Prosram
The normal equations, EqN. (25), are linear in the parameters. For this
reason, values of my thay, o .., are obtained very readily with a computer.
However, the fact that Eq. (12) 16 only approximately correct means that the
first-order approximation. As a result, the first computed values of the m,'s
may be in error, in which case successive iterations are necessary. The first
iteration consists in calculating a first-approximation spectrum from the ob-
served spectrum by use of the first estimates of gain and threshold shifts. By
comparison with the standards, this first-approximation spectrum is used to obtain
a second estimate of gain and threshold shifts.
The possibility of error in Eq. (12) was tested by counting a sample con-
taining 60co, 200 Ru, 237C8, and "*ce (paragraph of EXPERIMENTAL) five times.
The first count data (on a 256 channel analyzer) were taken with gain and threshold
at reference values; the succeeding four counts were taken without threshold
shift but with -7.3%, -4.0%, +3.0%, and +6.7% gain changes. The chi-square values
for each spectrum :) show that the best estimates of parameters were not
obtained on the first iteration. The shift of +3.04 required a second iteration, and
the shift of -7.3% e fifth iteration. It may be noted that for +3.0 and 4.0%
salo-shifts, the final viulue of x2 16 about 250, namely, approximately equal to the
.......
Whe
r
wereld.
Fig. 8. Gain and Throshold Shift Correction by Successivo Approximation,
ki

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.
...
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number of channels, as it should be, however, with shifts as large as 16.7% and
-7.3%, A and not get below about 350. Thus, 17 gada shifto exceed about 15%,
there'will be at least a small dies in the final (seventh) ostinates of paramotors.
Cain and threshold-shift Corrections
When gain' and threshold-shirt corrections are not included in the computer
program, the effects on ye orx®/(*) are very dramatic, fig. • 'The quantity
*lcalfi) should be about 1 1f there 18 no shifting of threshold or gain in the
interval between ccunting standards and counting a sample. The spectrometer
used in these tests yielded spectra withx 2/(-E) of about 500, with gain shirts
of 15% for threshold shifts of -2 or +2 channels, the corresponding x®/(**)
values were 37 and 90, respectively. Such large numbers indicate that the count-
ing data do not fit the equations Eq. (5)] very well.
The quantitative estimates of errors due to gain shifts are shown for one /
solution in Fig. The spectrometer gain was shifted by -5% to +6%, after
which the spectra were resolved three ways: (1) with no shift correction for gain;
(2) with just the first approximation of moky) and in Eq. (25); (3) with ab .
many iterations (a maximum of 5) in Eq. (25) as were' necessary to yield two suc-
cessive values of xa that differed by less than 5%. It may be seen that computed
values are in error by 10 to 60% when no correction is made for gain shift; when
successive iterations are made (to a criterion, in this case, that Xe change by
less than 5% on successive iterations), the error in the estimated quantity of
nuclide present 18 less than 4% in the worst case (STCs at -5% gain, Fig. .
lig
10.
.
.
.
.
Reducing Uncertainties by_Increasing Counting Time
. The variance of an estimate of a parameter me
. 18 calculated according
to Eq. (33); the standard deviation of mo namely 0(2), 18 obtained simply by
taking the square root of DP (n). This uncertainty can be reduced by increasing
the counting time, as shown in 718. for one of the samples of water from the
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33
-
Fig. 11. Variation of the Standard Deviation of Each of the Components of a
Soven-Isotope Mixture With Counting Time.
..
.
.
--
Conditions Sample counting rate/Background counting rato = 1.3
Vol. = 100 ml in l-pt. polyethylene bottle
-
.
.

NUCLIDE ACTIVITY
T
ito Isr
(dis min-1 me!)
lo 106
4.5
+ 141ce-144 Co(50-50) (<0.1)
p . 137 C.
E
9.1
1x 95 2r-no
0 134cs
1060 Co
DXO 0
0.6
0.9
1.6
1.
Slope : 5
STANDARD DEVIATION (dis min-mi-h
-ooooo
to sol
4
to je to
.
mantener
croce,
..........................
COUNTING TIME (min)
1
laboratory test imit. The activities of the nuclides are averages from spectrum
resolution and conventional analyses. This figure shows the wcertainties that
are typical for conting times of 5 to 20 ming the times used with samples
shown in Figs. 1 The figure also shows a familiar reduction 10 standard
deviation proportional to the square root of counting time.
L
......
.
.........
..
...,
drømmen mit Naistening
hollowin
2K
g
sekiant nobis
RESOLUTION OF ERRORS
The amount of nuclide e in a sample per unit of this nuclide in standard 8
is calculated according to Eq. (32); the absolute amount of this auclide in the
sample 18 ans, where ag 18 the activity of nuclide s in its standard in whatever
units we wish-to use. Whereas the variance of m 18 given by Eq. (33), the
variance of a m
18 :
8
8
$10,) -3°(.) +
b(0,).
(34)
Now we have already assumed that the channel-by-channel counting-rate data for
each standard are much more accurate than the corresponding data for a sample.
Mathematically, this 18 equivalent to dropping the second term on the right of
Eq. (34), in which case we use :
p2(,me) - 6332(m.).
(35)
We would like to able to express this variance of the activity a , in
terms of the counting rates of the various gamma-ray emitters in the sample. For
this purpose we combine Eq6. (33) and (35) to obtain':
pºs = ). * * 12
2
-
)
pe
D2(x)
(36)
wawi
where we define:
D2(x,) .
.
(37)
As defined below Eq. (3), xij is the counting rate in chanel i due to muclide
3. The total counting rate (in all channels) due to muclide j 11, then:
.
.
. .
(38)
.
.
.
Similarly, the total background counting rate 18:
--]
(39)
The total counting rate of all nuclides (excluding background) 18, from Eq8. (3)
and (38):
(40)
By substituting Eq. (2) into (22) and then bumming over all channels, we obtain:
PoE CHAT
(41)
By substituting Ege. (39) and (40) 1nto (41) we obtain:
È )****;;*****..
(he)
Finally from Eq8. (37), (42), and (36) ve obtain the desired expression for the
variance of a , in terms of the counting rates of the various buclides plus
background.
8
:{**** ****,5].
(3)
A very extensive analysis of Eq. (43) 18 beyond the scope of this report.
However, we do wish to point out several features of significance. First,
except for the multiplying factor a, the counting rates of the various puclides
are simply additive in their contributions to the variance of the activity of a
specific nuclide. Second, the background counting rate appears twice in the
contribution to variance. Third, 18 a.? 18 constant, then the variance of the
activity is inversely proportional to counting time a (18 pl = 7), in which case
the inverse effect of the square root of a would be expected; as shown in Fig.
this inverse effect of Vi 18 observed, suggesting that a ? 18 constant.
The last feature of Eq. (43) that we wish to discuss briefly 16"ą, some
values of which are given in Table 4 for water (first two colums) and for solu-
Men
tions containing total activity of the nuclides corresponding to counting rates
in which were particularly interested. Values of a were calculated from
two types of Least-squares resolution of gamma-ray spectra: first, by using
PA = 1 in Eq. (23); second by using a weighting factor 1/02(x), where DP (x) 18
defined in Eq. (22). By comparing values of a 10 1 and 2, or 3 and the
we see that the two calculations do not differ much. We also see from Prowo
2, 6, 8, 10, and 12 that the value of a 18 nearly independent of sample activity
(from o activity in sample to 3 timee background activity), provided the two
nuclide groups 1 Ru-Rh and 95zr-No are assumed to be absent. These two are
present in very low and very uncertain concentrations. As stated under RESULTS
OF SPECTRUM RESOLUTION ,the spectral-resolution values for activities of Ru-Rb
and »2r-No should not be taken seriously.
Samole Concentration by Evaporation
There are several ways to improve the accuracy of estimates of nuclide
activities in solutions such as those described in F188. 1. These include 10-
creasing the counting time, decreasing the background activity, and increasing the
*
******
etiam
.
-.
Table 4. Values of a. Do Not Change Much with Type of Weighting Factor, Mixture Activity level,
and Number of Isotopes (unless they have similar Energies).
-
Number of a weighting
Activity
Ratio
Sample
Background
Values of
Components Weighting
Assumeda Factor
13708
Co
100Au
celo)
9527-N
858r
0.40
0.39
1
0.49
0-2(x)
0.43
0.59
0.60
2.6
0.44
0.444
D-2(x)
2.9
0.54
0.44
0.64
0.72
0.61
0.59
0.77
0.89
0.47
1.20
0.56
0.54
0.54
0.65
0.62
0.61
0.60
0.47
1.6
0.50
0.50
1.6
0.14
0.21
0.55
0.34 0.42
0.24 0.74
0.37
0.36 0.52
0.36mm -
0.40
0.37 .
0.40
0.37
0.45 0.37
0.42
134C.
0.65
0.60
1.27
1.13
0.80
0.73
1.2
0.78
1.16
0.77
0.80
0.52
0.30
0.6
0.64
.
0.47
-
'
0.74
2.9
0.6
31
.
..
.
.
0.30
0.63
.
.
..
1.6
0.47
1.32
0.68
3.0
2.4
.
..
0.52
0.42
.
.:-*-
3.0
0.46
:;
Although the nuclide groups were present, computations were made on the basis that all á or only
or were present. À dash in a column of values of age corresponds to a calculation in which the
auclide was assumed to be absent.
$50% of each of 141ce and 144ce.
T
201
CTS
L
'A
IN
.
.
NA
:4
.
SC
.
39
sample specific activity by evaporation of the solvent (water, in our studies).
Economically, the evaporation process 18 the most satisfactory since the cost
of evaporation 18 much less than a pro rated cost of gamma-ray spectrometer
use. The effect of volume reduction, VR, which varied from 1 to 25 10 our tents,
on the standard deviation of an 18, from Eq. (22) and if a remains constant,
.
.
1/2
.
Draguay Pesten w). 71. *-*73):
Dla od (atment wa) * * * .5:
Dam) (with VR)
D(ams? (without VR)
too.
If the background counting rate 18 small compared with sample counting rate, then
the relative uncertainty in the value of a m 18 decreased by VVR ?
86
SUMMARY AND CONCLUSIONS
Gamma-ray spectrum resolution by least-squares methods, programmed for a
high-speed digital computer, has been used to calculate the amounts of each of
4 to 10 nuclides present in aqueous solutions containing 500 wc/1 to 0.5 pc/liter
of each nuclide. The nuclides in the solutions of lowest activity were "co,
8557, 952r-ND, 106Ru-Rh, 134c6, 137c6, 143ce, and 144ce. 9 The main basis for a
conclusion concerning the accuracy of the spectrum-resolution technique at the
lowest activity levels was a comparison with parallel analyses of the same solu-
tions by conventional methods used at ORNL, namely beta counting or manual strip-
ping. On this basis, 60co, 85sr, and 137cs can be determined very satisfactorily
(t5 to +20% scatter) at activities from 50,000 down to 500 ppc/, 24*ce was deter-
mined somewhat le88 satisfactorily (+20% uncertainty at 50,000 pc/v to uncer-
tainties of 5 to 10 at 500 pc/w, perhaps because this buclide contri-
buted only 10% to less than 0.1% of the total counting rates of the solutions.
Activities of 952r-No, which were less than a few disintegrations per minute per
.xora
WWW
XWTA
TUM
TIN
.
h
.
1
milliliter and less than 5% of the total activity, could not be determined ac-
curately by gamma-ray spectrum resolution or beta counting. Similarly,
LLORu activities could not be determined satisfactorily at levels of 15 dis min
m2? (.12% of the total activity).
This cheap, lapid method for determining the amount of each of a number of
gamma-ray emitters in a sample is not a cure-all for the high cost of analyses of
radioactive materials; yet the potential for savings in time and money are great
at activities as low as 1 dis min -m2, and this potential increased as the
activities increase to 10 to 100 dis min--m2-2. Some of this potential can be
realized simply by concentrating the solution by evaporation; in other cases,
particularly when one or two nuclides contribute most of the activity, some
chemical separation steps can be used to remove those nuclides that are causing
the most uncertainty in other calculated activities.
The statistical equations used in this report include corrections for gain
and threshold shifts. From tests with solutions of known radiochemical composition,
these equations lead to accurate estimates of individual activities if the gain
shift 18 as large as 5% and the threshold shift as large as + 2 channels. Such
large shifts are greater than we encountered with two gamma-ray spectrometers
and are apparently greater than those encountered with most reasonably well-
maintained instruments. Thus, accurate corrections for these shifts can be
made in a computer program.
..........
....
..
..
..
.
.........37,47,574"mtina
;'
2
ACKNOWLEDGEMENT
The authors thank 1. A. Parker and E. I. Wyatt, of the CRNL Analytical
Chemistry Division, for conducting the radiochemical and manual-stripping analyses
and for measuring the gamma-ray spectra of the low-activity solutions from the
laboratory decontamination unit. Credit 18 also due f. L. Miller of the Mathe-
matics Division and J. Halperin of the Chemistry Division for their advice and
comments.
42
REFERENCES
1. W. G. Belter, "Radioactive Wastes," Intern. Sci. Technol. (12), pp 42-7 (1962).
2. U. S. Public Health Service, Public Health Service Drinking Water Standards 1962,
Publication No. 956, Washington D. c., 1962.
3. K. E. Cowser and T. Tamura, "Significant Results in Low-Level Waste Treatment
at CRNL," Health Physics 9, 687 (1963).
?
Oc.
4.
J. T. Roberts and R. R. Holcomb, A Phenolic Resin Ion-Exchange Process for
Decontaminating Low-Radioactivity-Level Process Water Wastes, ORNL-3036
(May 22, 1961).
5. R. E. Brooksbank, F. N. Browder, R. R. Holcomb, and W. R. Whitson, Low Radio-
activity-Level Waste Treatment. Part II. Pilot Plant Demonstration of the
Removal of Activity from Low-Level Process Wastes by a Scavenging-Precipita-
tion Ion-Exchange Process, ORNL-3349 (May 13, 1963).
6.
I. R. Higgins and A. F. Messing, Development of a continuous Ion Exchange
Process for the Removal and Recovery of High-Purity Cesium from Alkaline
Waste, ORNL-2491 TOctober 1958).
7.
E. Rubin, E. Schonfeld, and R. Everett, Jr., The Removal of Metallic Ions by
Foaming Agents and Suspensions: Laboratory and Engineering Studies, RAI-104
(October 1962).
8. R. E. Druschel, "Zirconium Activity in Aqueous or Organic Solutions," Method
No. 2 21981, March 8, 1954. ORNL Master Analytical Manual, sec. 2. TID-7015
(November 1957).
R. R. Rickard and E. I. Wyatt, "Ruthenium Activity in Aqueous Solutions, Non-
Distillation Method," Method No. 2 21733, June 13, 1960. ORNL Master Analytical .
Manual, Sec, 2. TDD-7015 (suppl. 3, June, 1961).
E. I. Wyatt and D. K. Smith, "Low Concentration & Cerium and Trivalent Rare-
Earth Element Activities in Water," Method Nos. 2 211.82 and 2 21994, July 28,
1958. ORNL Master Analytical Manual, Sec 2. TID-7015 (suppl. 1, November 1959).
9. G. D. O'Kelley, ed., Proceedings of the Symposium on Applications of Computers
- to Nuclear and Radiochemistry, held at Gatlinburg, Tennesse, (October 1962),
U. S. Atomic Energy Commission Monograph NAS-NS 3107 (March 1963).

10. L. Salmon, Computer Analysis of Gamma-Ray Spectra from Mixtures of Known
Nuclides by the Method of Least Squares, pp 165-83, NAS-NS 3107 (see ref 9).
11. R. L. Heath, Scintillation Spectrometry, Gamma-Ray Spectrum Catalos, IDO-
16408 (July 1, 1957), TID-4500, p 20.
12. R. L. Heath, Scintillation Spectrometry - The Experimental Problem, pp 93-107,
NAS-NS 3107 (see ref 9).
13. V. P. Guinn and J. E. Lasch, Gamma-Ray Spectrometry Requirements for Spectrum
Stripper and Computer Calculations in Activation Analysis Studies, pp 243-54
In NAS-NS 3107 (see ref 9).

en reception
le monde
en perym
14. G. D. Chase and J. L. Rabinowitz, Principles of Radioisotope Methodology,
Burgess Pub. Co., Minneapolis, Mi
A. A. Jarrett, Statistical Methods used in the Measurement of Radioactivity,
MonP-126 (July 1946).
L. Cziffra and M. J. Moravsik, A Practical Guide to the Method of least
Squares, UCLA-8523 Rev. (June 1959).
15. Control Date Corporation, OBAS-A, Minneapolis, Minn. 1962.

.
17. 1. Cramer, The Elements of Probability Theory, pp 235-42, Wiley, New York, 1955.
18. L. J. Rainwater and C. 8. Wu, "Applications of Probability Theory to Muclear
Particle Detection," Mucleonics 2 (2), 60 (1947).
DATE FILMED
11/ 25 / 164




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