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Standardization of 133Ba by two-dimensional extrapolation
Appl. Radial. ht.
Vol. 43, No. 3, pp. 377-381, 1992
ht. J. Radiat. Appl. Instrum. Part A Printed in Great Britain.
Copyright
Standardization Two-dimensional HIROSHI Department
0883-2889/92 $5.00 + 0.00 0 1992 Pergamon Press plc
All rights reserved
of Nuclear
Engineering,
(Received
of 133Ba by Extrapolation
MIYAHARA
and CHIZUO
School of Engineering, Nagoya Nagoya 464-01, Japan 15 April
1991; in revised form
MORI
University,
8 August
Furo-cho,
Chikusa-ku,
1991)
Barium-133 has been standardized by 4 nfi(ppcky (HPGe) coincidence counting using a live-timed bi-dimensional data acquisition system. The two-dimensional efficiency function based on a computer discrimination method gave reliable results, as well as providing a useful check on the conventional efficiency extrapolation method using a wide y-gate. The estimated uncertainty was approx. 0.3% for simple mean of five combinations
al., 1977). The measured data were recorded on a 732 m magnetic tape that can store about 2 x 10’ events over 2-3 x lo3 s, including about 6 x lo5 y-ray signals. Analysis was carried out for the data on a tape, or sometimes on a few tapes to obtain enough y counts. The efficiency function was obtained by the computer discrimination (Smith, 1975) using the /Iand y-ray spectra, the /3 spectrum coincident with any y pulses, and the /I spectrum coincident with selected y-ray photopeak signals.
1. Introduction The multi-y-ray emitter ‘33Ba has well-established y-ray emission probabilities (Schiitzig et al., 1977; Yoshizawa et al., 1983; Chauvenet et al., 1983), and is preferred radionuclide for the efficiency calibration of high resolution detectors at several hundred keV. There is, however, a problem in determination of disintegration rate by the 4 IL/I - y coincidence counting, since this nuclide emits a large amount of internal conversion electrons with low energies. Actually, the results obtained from international comparison of ‘33Ba suggested that the extrapolated disintegration rate depended on the y-gate setting (Rytz, 1985). The two-dimensional extrapolation method, which has been applied to standardization of “Co (Smith and Stuart, 1975), is a powerful procedure for the nuclide which emits large numbers of conversion electrons with low energies. Funck has successfully applied this method to 20’T1 (Funck, 1987) and we have also shown good results for ls2Eu, using the 4 $I(ppc)-y(HPGe) coincidence apparatus with a live-timed bi-dimensional data acquisition system (Miyahara et ul., 1990). This report describes the standardization of ‘33Ba using the above apparatus.
3. Principle of the Counting Figure 1 shows the decay scheme of 133Ba (Schiitzig of the 80 and 81 keV are largely internally-converted. The situation is further complicated by the fact that the 53 keV transition from the 437 keV to the 384 keV level is also intemally-converted. Therefore when the source with a disintegration rate of N,, is measured, the count rate of the /I detector, NB, has to be expressed as et al., 1977). The transitions
NB=No~~+N&
-Qa,[F,+(l
-b,-c,)
x (1 - G,,) cyl + b, (1 - W x (Q + 52 - $52 +c,(l
2. Experimental
1
-G3){~,3+(1
-~,3)
x b2 kyl + 52 - q52N
All measurements were made by the 4 $(ppcky (HPGe) coincidence apparatus with the live-timed bi-dimensional data acquisition system as described in an earlier publication (Miyahara et al., 1987, 1989). The HPGe detector used in the measurements had a relative efficiency of 23% and was set at the sourcedetector distance of 9 cm. Sources were prepared by aluminium chloride treatment method (Yoshida et
+NoU
- ~1 a2F.2 + b2U - G22)
x @yl + ty2 - $52)19
(1)
where 6c represents the efficiency of the B detector to electron-capture (EC) events, a, is the i-th EC branching ratio, bi and ci are the fractions of the decays passing through the 81 (or 80) and the 53 keV 317
HIROSH,MIYAHARAand
378
CHIZUO MORI
changing cY3can be realised only by discrimination of the L Auger electrons, otherwise raising the discrimination level changes the detection efficiency for the internal conversion electrons (about 17 keV) of the 53 keV transition which changes ty3 unwantedly. All equations derived for the other y-gate-set showed the similar tendency regardless of the y-gate selection. Then, the similar two-dimensional extrapolation method to that for ‘52Eu was applied to the determination of Q. The following describes in the case of the gate set on the photopeaks of the 384 and the 356 keV y-rays. Two equations are obtained from the count rates of y and coincidence:
1 1 ‘33cs
-0
Fig. 1. A relevant decay scheme of ‘r’ Ba determined from the measurements of y-ray intensities and disintegration rate and the values in parentheses show the emission probabilities of internal conversion electrons (SchCtzig et al., 1977). transitions. The term Fi is the probability of any transitions except for the 81 (or 80) and 53 keV transition from the i-th branch where events are detected by the 4 @(ppc). The terms G,, is the probability causing a count in the /I detector by one of any transitions which feed directly or indirectly the significant level and the first number of the double suffixes indicates the EC branch and the second shows the 81, 80 and 53 keV transitions. The term cYi is the detection efficiency for the 81, 80 and 53 keV transitions with internal conversion. Considering a simple approximation that G,, = G and ey, = ty2 = cY, equation (1) is expressed as NP = N,c, + N&l - ~,)(a, F, + a,F,) +N,,a,(l
-cJ(1
-G)[(l
x b,(2
-
-c,)t,
+
$.a*)
azJ’2)+a,@,c,
+
~2)
x(l-G){(l-6,-c,)~,fb,~~(2-t~) +
ClEy3
+a,@,c,+az)(l
+
c,u
-
53)
b25(2
(4)
El
Nc(356)
cY3 obtained from equation (3), then
(5)
both
equations
= No{1 +$+
cc-
is substituted
to
+$)}y
(6)
K2 l -cy
K, = 1-(a,~, + a,)(1 - G)+(u,c,
+a,)
x(1 -G)b,c,(2-e,) K2 = -(a,~, +a,(1
+ uJ(1 - a,F, -uzF2) -G)(l
-b,
-c,)c,+u,b,(u,c,
+a,)
-G)E,
-
$11
-G)5(2-5)1.
(3)
If eYand cY3are constant for changing L, , equation (3) is approximated to be linear. Changing 6, without
- G)(a,c,
+ ~2) e,(2 - cY).
The other combinations excluding those of the 384-303 and the 356276 keV y-rays gave the similar equations to equation (6) but these two combinations cannot eliminate ty3 in calculation.
4.
(a,&
=
a2
~=~t,+(1-~t,)ey=t2 N,(356)
+a,(1 (2)
When the y-gate is set on one of the photopeaks of the 384, 356, 303, 276 and 80 plus 81 (hereafter, simply shown by 8 1) keV y-rays, the ordinary coincidence equation is obtained. A typical equation in the case of gate set on the 384 keV y-rays is the following:
x
+
x(2-c,)-(u,c,+u2)2b2Cy(2-ty)
x(1 -G)c,(2-t,).
I--a,c,53+(a,c,
Cl
x(1 -G)+u,c,b,(u,c,+a,)(1
-Q)
~,))I+ &a,(1 - 4
x
-%) 53
a,
x(1 -G)c,(2-~,)+(u,c,+u,)~
-b,
+b,Ly(2-Cy)+C,{ty3+(1
a,c,(l
N,(384) lvyo=c”+
1
Results and Discussion
Figure 2 shows a spectrum of ,33Ba obtained from the 4 $(ppc). L Auger electrons (3.6 keV) are detected up to about 50 channels, the first complex peak between about 100-250 channels shows K conversion electrons (17 keV) for the 53 keV transition and K Auger electrons (26 keV), and the second peak about 300 channels corresponds to the K conversion electrons (45 keV) for the 81 keV transition. The spectrum gated by the 356 keV y-rays (lower curve) shows a more distinguishable peak of K Auger electrons than the above. The spectra gated by the other y-rays
Standardization
of 13’Ba
379
K ConversIon
I
K Conversion
K Auger
I
100
I
I
0
I
II
I
I
I
I
400
200 Pulse
height
I
I
I
600
I channel
number
I
I
I
I
I
I
I300
I 1000
1
Fig. 2. A p spectrum (upper curve) and that coincident with the 356 keV y-rays (lower curve) which were obtained from the 4 nB(ppc). The spectrum shows L Auger electrons, K Auger electrons, K conversion electrons for the 53 keV and those for the 80 and 81 keV transitions as indicated in the figure.
showed reasonable shapes estimated from the decay scheme. Figure 3 shows a coincidence efficiency function obtained by the gate set of the 384 keV y-rays using the computer discrimination method [equation (3)]. The region of linear fitting is shorter than that of extrapolation, and then it is difficult to correctly extrapolate even by the computer discrimination method. The reason why the data deviated from a linear line was that raising the discrimination level changed the detection efficiency for the internal con-
32 ^o
30
_
26
z . 9z
o
26
L
24
2”
Fitting
region ,/**
+...d
/
22
L”
0
O.i!
0.4
0.6
0.6
1.0
( I --E,VE, Fig. 3. A coincidence efficiency function derived by the computer discrimination method for the gate set of the 384 keV y-rays.
version electrons (about 17 keV) of the 53 keV transition or .+. All results measured by a single y-gate-set showed the similar tendency regardless of the selection of the y-gate. The linear region is obtained only by the discrimination of the L Auger electrons, then the amount of the area change by the discrimination is considerably smaller than the total area of the spectrum. Therefore, it is difficult to obtain a wide fitting region. The results measured for the gate set on the 276 and the 303 keV y-rays which gave the efficiency functions with negative slopes were larger than the average, and the other results obtained from those with positive slopes were smaller. When a wide gate was set on the photopeaks from the 276 to 384 keV y-rays like the case of a NaI (Tl) scintillation detector, a small bend in the efficiency function was seen at about 0.5 of (1 - cC)/cCas shown in Fig. 4. It may be difficult to recognize the bend on the data measured by the conventional method without the computer discrimination method. The fitting using the data points between 0.3 and 2.7 of (1 - cC)/c, gave considerably lower results than the value obtained by the fitting using those between 0.3 and 0.42. When the gate was set on the energy region from the 81 to 384 keV y-rays, this tendency was remarkable. The fitting of the narrow region, however, gave nearly the same results as those in both
HIROSHI MIYAHARA and CHIZUO MORI
380
50
Fitting
region
0.30
/.’
2.70 ,# ** f
I.
40
//’ *
z” . *!
30
!
I/
22.0
z” 2 1.5
SIG
21532k34 0
I 0.5
I 1.0
I
I 1.5
I 2.5
2.0
wide y-gates. In the conventional coincidence counting, the wide fitting region cannot but be applied because of the scattering of the data points; therefore, only the computer discrimination method can give these results. The result measured with the combination shown in equation (6) gave the wide linear fitting region shown in Fig. 5, although the standard deviation of the final result was relatively large because of the low intensity of the 384 keV y-rays. Figure 6 is another example of the two-dimensional extrapolation obtained from the combination of the 81 and the 303 keV y-rays and the extrapolated result gave enough certainty. Table 1 shows the results obtained from various combinations, where the symbols 0 and x indicate suitable and unsuitable combinations judging from the calculated equation. The values in the column show the regions capable to fit linearly and the extrapolated disintegration rates with the standard deviations. Among the results excluding those with the symbol x , the values using the gate set on the 276 keV y-rays differed from the others. The Compton components of higher-energy y-rays are largely contained under the photopeak of the 276 keV y-rays, then it is incorrect to assume that the p spectrum coincident with the 276 keV y-rays would
30
-
25
-
2iG ,,’ 0
Id”“”
216462236
I I
I
I
2
3
(I --EI)/EI
Fig. 4. A coincidence efficiency function derived by the computer discrimination method for the gate set of the y-rays from the 276 to the 384 keV.
-
21636+_120
Fig. 6. Same as Fig. 5, but for the combination 81 and the 303 keV y-rays.
(I--E,)/E,
35
20;
,
I
I
I
I
2
3
4
(I_-E,)/El
Fig. 5. A coincidence efficiency function derived by the two-dimensional extrapolation for the combination of the 384 and the 356 keV y-rays [see equation (6)].
of the 80 plus
not be influenced by the conversion electrons of the 53 keV transition. Judging from ratios of the fitting regions and the extrapolation distances, five combinations, 384-356, 384-81, 81-384, 81-356 and 81-303, are suitable for practical measurement. Figure 7 shows the results by the conventional and the two-dimensional extrapolations. Considering that the extrapolated disintegration rates obtained from the narrow fitting for the measurements of the wide y-gates (81-384, 276384) agreed with that from the two-dimensional extrapolation, the broken line shows the expected disintegration rate. In the conventional extrapolation method, the most probable disintegration rate can be obtained from the narrow fitting for the wide y-gate measurement, but the measurement without the computer discrimination may systematically give a low value by about 0.5%. On the other hand, the two-dimensional extrapolations in five combinations, 384-356, 384-81, 81-384, 81-356 and 81-303, give the fitting region wider than two times of the extrapolation distance and the good result is probably obtained even by the method without the computer discrimination. When the new data of the conversion coefficients of I33Ba (Sergeenkov and Sigalov, 1986) is applied to the measurement of y-ray emission probabilities by Schiitzig et al. (1977), the emission probabilities of the conversion electrons for the 80 and 81 keV transitions increase. Therefore, the sum of the electron capture probabilities must be larger than 100% by about 1.2%. However, if the disintegration rate determined by the fitting using the ordinary wide region is smaller than the reliable value estimated from the present measurement by 0.5%, each of the y-ray emission probabilities should decrease by 0.5%. As a result, the total electron capture probabilities calculated from the emission probabilities of the y-rays and the internal conversion electrons is 99.6% and the difference of only -0.4% is contained in the uncertainty.
5. Conclusion Although the conventional efficiency extrapolation of wide y-gate has been used for standardization of
Standardization
of ‘33Ba
381
Table 1. Results obtained from the two-dimensional extrapolation in all combinations of y-gates for one of the sources used. Two values are shown in each gate combination. The upper shows fitting region and the lower extrapolated disintegration rate (Bq)
Y-axis (gate 2) (ke\;,
384
356
303
276
81
X-axis (gate I) 0.58 - 3.50 384
0
15061 ? 85
0.58 - 0.90 ’
0.33 - 0.55 356
0 ’
0
15036 f 21 15202k20
0
15294 f 31
0 x
0
15047f51
x 0
15098 + 25 16468 t 123 15057 f 73
16398 f 228
0
0
15357 f 50
0 0
15357 + 34
The symbols 0 and x show suitable and unsuitable calculation
15082 f 48 combinations
14998 f 39 0.17 -0.40 15052 f 23 0.18 - 0.26
0.98 - 3.00 0
15061 f 86 0.33 - 0.52
0.18 - 0.26
0.98 - 3.00 0
0.58 - 3.50 0
0.17-0.40
0.18-0.26
0.98 - 3.00 81
15101 k 21
15298 f I16 0.33 - 0.54
0.17 - 0.40
0.18-0.28 276
0.58 - 3.00 0
0.33 - 0.53
0.17 - 0.23 303
15187 + 119
14345 k 89
0.98 - 3.00 0
14651 + 189 from consideration
of analytical
References Two
r-ray
dimensional
gate energy tkeV1
Fig. 7. Extrapola.ted disintegration rates of a “)Ba source obtained from the computer discrimination method for various y-gate sets and two-dimensional extrapolation.
‘33Ba so far, the fitting using the data with wide efficiencies seemed to give small extrapolated result by about 0.5% as a systematic error. To avoid this there are two solutions. One of the methods is that the fitting for only the high efficiency region is applied to the data measured using the computer discrimination, and the other is standardization by the twodimensional efficiency extrapolation. Two-dimensional extrapolations on the gate set of 384356, 384-81, 81-384, 81-356 and 81-303 gave the fitting region more than twice that with conventional extrapolation, and in this context the good result is probably obtained even by the method without the computer discrimination.
Chauvenet B., Morel J. and Legrand J. (1983) An interemission-rate national intercomparison of photon measurements of X- and y-rays emitted in the decay of ‘33Ba. Int. J. Appl. Radiat. Isot. 34, 479. Funck E. (1987) A two-dimensional extrapolation for the by the 4 x/I - y coincidence standardization of “‘Tl method. Appl. Radiar. Isot. 38, 771. Miyahara H., Kitaori S. and Watanabe T. (1987) 4 n/l - y Coincidence counting using a live-timed bi-dimensional data-acquisition system. Appl. Radiat. Isot. 38, 793. Miyahara H., Kitaori S., Nozue Y. and Watanabe T. (1989) A 4 s/I @PC) - y (HPGe) coincidence apparatus using a live-timed bi-dimensional data acquisition system and its application to measurement of gamma ray emission probability. Appl. Radiat. Isol. 40, 343. Miyahara H., Nozue Y., Kitaori S. and Watanabe T. (1990) Standardisation of ‘s*Eu by two-dimensional extrapolation. Nucl. Instrum. Meth. A286, 497. Rytz A. (1985) International comparison of activity measurements of a solution of 13)Ba (March 1984). CCEMRI(II)/IS-1. Schiitzig U., Debertin K. and Walz K. F. (1977) Standardization and decay data of ‘33Ba. Int. J. Appl. Radial. Isot. 28, 503. Sergeenkov Yu V. and Sigalov V. M. (1986) Nuclear data sheets for A = 133. Nuclear Data Sheets 49, 639. Smith D. (1975) An improved method of data collection for 4 n/l - y coincidence measurements. Metrologia 11, 73. Smith D. and Stuart L. E. H. (1975) An extension of the 4 np - y coincidence technique: two dimensional extrapolation. Metrologia 11, 67. Yoshida M., Miyahara H. and WatanabeT. (1977) A source preparation for 4 np-counting with an aluminum compound. Int. J. Appl. Radial. Isot. 28, 633. Yoshizawa Y., Iwata Y., Katoh T., Ruan J. and Kawada Y. (1983) Precision measurements of gamma-ray intensities IV. low energy region: 15Se and ‘33Ba. Nucl. Instrum. Meth. 212, 249.
Vol. 43, No. 3, pp. 377-381, 1992
ht. J. Radiat. Appl. Instrum. Part A Printed in Great Britain.
Copyright
Standardization Two-dimensional HIROSHI Department
0883-2889/92 $5.00 + 0.00 0 1992 Pergamon Press plc
All rights reserved
of Nuclear
Engineering,
(Received
of 133Ba by Extrapolation
MIYAHARA
and CHIZUO
School of Engineering, Nagoya Nagoya 464-01, Japan 15 April
1991; in revised form
MORI
University,
8 August
Furo-cho,
Chikusa-ku,
1991)
Barium-133 has been standardized by 4 nfi(ppcky (HPGe) coincidence counting using a live-timed bi-dimensional data acquisition system. The two-dimensional efficiency function based on a computer discrimination method gave reliable results, as well as providing a useful check on the conventional efficiency extrapolation method using a wide y-gate. The estimated uncertainty was approx. 0.3% for simple mean of five combinations
al., 1977). The measured data were recorded on a 732 m magnetic tape that can store about 2 x 10’ events over 2-3 x lo3 s, including about 6 x lo5 y-ray signals. Analysis was carried out for the data on a tape, or sometimes on a few tapes to obtain enough y counts. The efficiency function was obtained by the computer discrimination (Smith, 1975) using the /Iand y-ray spectra, the /3 spectrum coincident with any y pulses, and the /I spectrum coincident with selected y-ray photopeak signals.
1. Introduction The multi-y-ray emitter ‘33Ba has well-established y-ray emission probabilities (Schiitzig et al., 1977; Yoshizawa et al., 1983; Chauvenet et al., 1983), and is preferred radionuclide for the efficiency calibration of high resolution detectors at several hundred keV. There is, however, a problem in determination of disintegration rate by the 4 IL/I - y coincidence counting, since this nuclide emits a large amount of internal conversion electrons with low energies. Actually, the results obtained from international comparison of ‘33Ba suggested that the extrapolated disintegration rate depended on the y-gate setting (Rytz, 1985). The two-dimensional extrapolation method, which has been applied to standardization of “Co (Smith and Stuart, 1975), is a powerful procedure for the nuclide which emits large numbers of conversion electrons with low energies. Funck has successfully applied this method to 20’T1 (Funck, 1987) and we have also shown good results for ls2Eu, using the 4 $I(ppc)-y(HPGe) coincidence apparatus with a live-timed bi-dimensional data acquisition system (Miyahara et ul., 1990). This report describes the standardization of ‘33Ba using the above apparatus.
3. Principle of the Counting Figure 1 shows the decay scheme of 133Ba (Schiitzig of the 80 and 81 keV are largely internally-converted. The situation is further complicated by the fact that the 53 keV transition from the 437 keV to the 384 keV level is also intemally-converted. Therefore when the source with a disintegration rate of N,, is measured, the count rate of the /I detector, NB, has to be expressed as et al., 1977). The transitions
NB=No~~+N&
-Qa,[F,+(l
-b,-c,)
x (1 - G,,) cyl + b, (1 - W x (Q + 52 - $52 +c,(l
2. Experimental
1
-G3){~,3+(1
-~,3)
x b2 kyl + 52 - q52N
All measurements were made by the 4 $(ppcky (HPGe) coincidence apparatus with the live-timed bi-dimensional data acquisition system as described in an earlier publication (Miyahara et al., 1987, 1989). The HPGe detector used in the measurements had a relative efficiency of 23% and was set at the sourcedetector distance of 9 cm. Sources were prepared by aluminium chloride treatment method (Yoshida et
+NoU
- ~1 a2F.2 + b2U - G22)
x @yl + ty2 - $52)19
(1)
where 6c represents the efficiency of the B detector to electron-capture (EC) events, a, is the i-th EC branching ratio, bi and ci are the fractions of the decays passing through the 81 (or 80) and the 53 keV 317
HIROSH,MIYAHARAand
378
CHIZUO MORI
changing cY3can be realised only by discrimination of the L Auger electrons, otherwise raising the discrimination level changes the detection efficiency for the internal conversion electrons (about 17 keV) of the 53 keV transition which changes ty3 unwantedly. All equations derived for the other y-gate-set showed the similar tendency regardless of the y-gate selection. Then, the similar two-dimensional extrapolation method to that for ‘52Eu was applied to the determination of Q. The following describes in the case of the gate set on the photopeaks of the 384 and the 356 keV y-rays. Two equations are obtained from the count rates of y and coincidence:
1 1 ‘33cs
-0
Fig. 1. A relevant decay scheme of ‘r’ Ba determined from the measurements of y-ray intensities and disintegration rate and the values in parentheses show the emission probabilities of internal conversion electrons (SchCtzig et al., 1977). transitions. The term Fi is the probability of any transitions except for the 81 (or 80) and 53 keV transition from the i-th branch where events are detected by the 4 @(ppc). The terms G,, is the probability causing a count in the /I detector by one of any transitions which feed directly or indirectly the significant level and the first number of the double suffixes indicates the EC branch and the second shows the 81, 80 and 53 keV transitions. The term cYi is the detection efficiency for the 81, 80 and 53 keV transitions with internal conversion. Considering a simple approximation that G,, = G and ey, = ty2 = cY, equation (1) is expressed as NP = N,c, + N&l - ~,)(a, F, + a,F,) +N,,a,(l
-cJ(1
-G)[(l
x b,(2
-
-c,)t,
+
$.a*)
azJ’2)+a,@,c,
+
~2)
x(l-G){(l-6,-c,)~,fb,~~(2-t~) +
ClEy3
+a,@,c,+az)(l
+
c,u
-
53)
b25(2
(4)
El
Nc(356)
cY3 obtained from equation (3), then
(5)
both
equations
= No{1 +$+
cc-
is substituted
to
+$)}y
(6)
K2 l -cy
K, = 1-(a,~, + a,)(1 - G)+(u,c,
+a,)
x(1 -G)b,c,(2-e,) K2 = -(a,~, +a,(1
+ uJ(1 - a,F, -uzF2) -G)(l
-b,
-c,)c,+u,b,(u,c,
+a,)
-G)E,
-
$11
-G)5(2-5)1.
(3)
If eYand cY3are constant for changing L, , equation (3) is approximated to be linear. Changing 6, without
- G)(a,c,
+ ~2) e,(2 - cY).
The other combinations excluding those of the 384-303 and the 356276 keV y-rays gave the similar equations to equation (6) but these two combinations cannot eliminate ty3 in calculation.
4.
(a,&
=
a2
~=~t,+(1-~t,)ey=t2 N,(356)
+a,(1 (2)
When the y-gate is set on one of the photopeaks of the 384, 356, 303, 276 and 80 plus 81 (hereafter, simply shown by 8 1) keV y-rays, the ordinary coincidence equation is obtained. A typical equation in the case of gate set on the 384 keV y-rays is the following:
x
+
x(2-c,)-(u,c,+u2)2b2Cy(2-ty)
x(1 -G)c,(2-t,).
I--a,c,53+(a,c,
Cl
x(1 -G)+u,c,b,(u,c,+a,)(1
-Q)
~,))I+ &a,(1 - 4
x
-%) 53
a,
x(1 -G)c,(2-~,)+(u,c,+u,)~
-b,
+b,Ly(2-Cy)+C,{ty3+(1
a,c,(l
N,(384) lvyo=c”+
1
Results and Discussion
Figure 2 shows a spectrum of ,33Ba obtained from the 4 $(ppc). L Auger electrons (3.6 keV) are detected up to about 50 channels, the first complex peak between about 100-250 channels shows K conversion electrons (17 keV) for the 53 keV transition and K Auger electrons (26 keV), and the second peak about 300 channels corresponds to the K conversion electrons (45 keV) for the 81 keV transition. The spectrum gated by the 356 keV y-rays (lower curve) shows a more distinguishable peak of K Auger electrons than the above. The spectra gated by the other y-rays
Standardization
of 13’Ba
379
K ConversIon
I
K Conversion
K Auger
I
100
I
I
0
I
II
I
I
I
I
400
200 Pulse
height
I
I
I
600
I channel
number
I
I
I
I
I
I
I300
I 1000
1
Fig. 2. A p spectrum (upper curve) and that coincident with the 356 keV y-rays (lower curve) which were obtained from the 4 nB(ppc). The spectrum shows L Auger electrons, K Auger electrons, K conversion electrons for the 53 keV and those for the 80 and 81 keV transitions as indicated in the figure.
showed reasonable shapes estimated from the decay scheme. Figure 3 shows a coincidence efficiency function obtained by the gate set of the 384 keV y-rays using the computer discrimination method [equation (3)]. The region of linear fitting is shorter than that of extrapolation, and then it is difficult to correctly extrapolate even by the computer discrimination method. The reason why the data deviated from a linear line was that raising the discrimination level changed the detection efficiency for the internal con-
32 ^o
30
_
26
z . 9z
o
26
L
24
2”
Fitting
region ,/**
+...d
/
22
L”
0
O.i!
0.4
0.6
0.6
1.0
( I --E,VE, Fig. 3. A coincidence efficiency function derived by the computer discrimination method for the gate set of the 384 keV y-rays.
version electrons (about 17 keV) of the 53 keV transition or .+. All results measured by a single y-gate-set showed the similar tendency regardless of the selection of the y-gate. The linear region is obtained only by the discrimination of the L Auger electrons, then the amount of the area change by the discrimination is considerably smaller than the total area of the spectrum. Therefore, it is difficult to obtain a wide fitting region. The results measured for the gate set on the 276 and the 303 keV y-rays which gave the efficiency functions with negative slopes were larger than the average, and the other results obtained from those with positive slopes were smaller. When a wide gate was set on the photopeaks from the 276 to 384 keV y-rays like the case of a NaI (Tl) scintillation detector, a small bend in the efficiency function was seen at about 0.5 of (1 - cC)/cCas shown in Fig. 4. It may be difficult to recognize the bend on the data measured by the conventional method without the computer discrimination method. The fitting using the data points between 0.3 and 2.7 of (1 - cC)/c, gave considerably lower results than the value obtained by the fitting using those between 0.3 and 0.42. When the gate was set on the energy region from the 81 to 384 keV y-rays, this tendency was remarkable. The fitting of the narrow region, however, gave nearly the same results as those in both
HIROSHI MIYAHARA and CHIZUO MORI
380
50
Fitting
region
0.30
/.’
2.70 ,# ** f
I.
40
//’ *
z” . *!
30
!
I/
22.0
z” 2 1.5
SIG
21532k34 0
I 0.5
I 1.0
I
I 1.5
I 2.5
2.0
wide y-gates. In the conventional coincidence counting, the wide fitting region cannot but be applied because of the scattering of the data points; therefore, only the computer discrimination method can give these results. The result measured with the combination shown in equation (6) gave the wide linear fitting region shown in Fig. 5, although the standard deviation of the final result was relatively large because of the low intensity of the 384 keV y-rays. Figure 6 is another example of the two-dimensional extrapolation obtained from the combination of the 81 and the 303 keV y-rays and the extrapolated result gave enough certainty. Table 1 shows the results obtained from various combinations, where the symbols 0 and x indicate suitable and unsuitable combinations judging from the calculated equation. The values in the column show the regions capable to fit linearly and the extrapolated disintegration rates with the standard deviations. Among the results excluding those with the symbol x , the values using the gate set on the 276 keV y-rays differed from the others. The Compton components of higher-energy y-rays are largely contained under the photopeak of the 276 keV y-rays, then it is incorrect to assume that the p spectrum coincident with the 276 keV y-rays would
30
-
25
-
2iG ,,’ 0
Id”“”
216462236
I I
I
I
2
3
(I --EI)/EI
Fig. 4. A coincidence efficiency function derived by the computer discrimination method for the gate set of the y-rays from the 276 to the 384 keV.
-
21636+_120
Fig. 6. Same as Fig. 5, but for the combination 81 and the 303 keV y-rays.
(I--E,)/E,
35
20;
,
I
I
I
I
2
3
4
(I_-E,)/El
Fig. 5. A coincidence efficiency function derived by the two-dimensional extrapolation for the combination of the 384 and the 356 keV y-rays [see equation (6)].
of the 80 plus
not be influenced by the conversion electrons of the 53 keV transition. Judging from ratios of the fitting regions and the extrapolation distances, five combinations, 384-356, 384-81, 81-384, 81-356 and 81-303, are suitable for practical measurement. Figure 7 shows the results by the conventional and the two-dimensional extrapolations. Considering that the extrapolated disintegration rates obtained from the narrow fitting for the measurements of the wide y-gates (81-384, 276384) agreed with that from the two-dimensional extrapolation, the broken line shows the expected disintegration rate. In the conventional extrapolation method, the most probable disintegration rate can be obtained from the narrow fitting for the wide y-gate measurement, but the measurement without the computer discrimination may systematically give a low value by about 0.5%. On the other hand, the two-dimensional extrapolations in five combinations, 384-356, 384-81, 81-384, 81-356 and 81-303, give the fitting region wider than two times of the extrapolation distance and the good result is probably obtained even by the method without the computer discrimination. When the new data of the conversion coefficients of I33Ba (Sergeenkov and Sigalov, 1986) is applied to the measurement of y-ray emission probabilities by Schiitzig et al. (1977), the emission probabilities of the conversion electrons for the 80 and 81 keV transitions increase. Therefore, the sum of the electron capture probabilities must be larger than 100% by about 1.2%. However, if the disintegration rate determined by the fitting using the ordinary wide region is smaller than the reliable value estimated from the present measurement by 0.5%, each of the y-ray emission probabilities should decrease by 0.5%. As a result, the total electron capture probabilities calculated from the emission probabilities of the y-rays and the internal conversion electrons is 99.6% and the difference of only -0.4% is contained in the uncertainty.
5. Conclusion Although the conventional efficiency extrapolation of wide y-gate has been used for standardization of
Standardization
of ‘33Ba
381
Table 1. Results obtained from the two-dimensional extrapolation in all combinations of y-gates for one of the sources used. Two values are shown in each gate combination. The upper shows fitting region and the lower extrapolated disintegration rate (Bq)
Y-axis (gate 2) (ke\;,
384
356
303
276
81
X-axis (gate I) 0.58 - 3.50 384
0
15061 ? 85
0.58 - 0.90 ’
0.33 - 0.55 356
0 ’
0
15036 f 21 15202k20
0
15294 f 31
0 x
0
15047f51
x 0
15098 + 25 16468 t 123 15057 f 73
16398 f 228
0
0
15357 f 50
0 0
15357 + 34
The symbols 0 and x show suitable and unsuitable calculation
15082 f 48 combinations
14998 f 39 0.17 -0.40 15052 f 23 0.18 - 0.26
0.98 - 3.00 0
15061 f 86 0.33 - 0.52
0.18 - 0.26
0.98 - 3.00 0
0.58 - 3.50 0
0.17-0.40
0.18-0.26
0.98 - 3.00 81
15101 k 21
15298 f I16 0.33 - 0.54
0.17 - 0.40
0.18-0.28 276
0.58 - 3.00 0
0.33 - 0.53
0.17 - 0.23 303
15187 + 119
14345 k 89
0.98 - 3.00 0
14651 + 189 from consideration
of analytical
References Two
r-ray
dimensional
gate energy tkeV1
Fig. 7. Extrapola.ted disintegration rates of a “)Ba source obtained from the computer discrimination method for various y-gate sets and two-dimensional extrapolation.
‘33Ba so far, the fitting using the data with wide efficiencies seemed to give small extrapolated result by about 0.5% as a systematic error. To avoid this there are two solutions. One of the methods is that the fitting for only the high efficiency region is applied to the data measured using the computer discrimination, and the other is standardization by the twodimensional efficiency extrapolation. Two-dimensional extrapolations on the gate set of 384356, 384-81, 81-384, 81-356 and 81-303 gave the fitting region more than twice that with conventional extrapolation, and in this context the good result is probably obtained even by the method without the computer discrimination.
Chauvenet B., Morel J. and Legrand J. (1983) An interemission-rate national intercomparison of photon measurements of X- and y-rays emitted in the decay of ‘33Ba. Int. J. Appl. Radiat. Isot. 34, 479. Funck E. (1987) A two-dimensional extrapolation for the by the 4 x/I - y coincidence standardization of “‘Tl method. Appl. Radiar. Isot. 38, 771. Miyahara H., Kitaori S. and Watanabe T. (1987) 4 n/l - y Coincidence counting using a live-timed bi-dimensional data-acquisition system. Appl. Radiat. Isot. 38, 793. Miyahara H., Kitaori S., Nozue Y. and Watanabe T. (1989) A 4 s/I @PC) - y (HPGe) coincidence apparatus using a live-timed bi-dimensional data acquisition system and its application to measurement of gamma ray emission probability. Appl. Radiat. Isol. 40, 343. Miyahara H., Nozue Y., Kitaori S. and Watanabe T. (1990) Standardisation of ‘s*Eu by two-dimensional extrapolation. Nucl. Instrum. Meth. A286, 497. Rytz A. (1985) International comparison of activity measurements of a solution of 13)Ba (March 1984). CCEMRI(II)/IS-1. Schiitzig U., Debertin K. and Walz K. F. (1977) Standardization and decay data of ‘33Ba. Int. J. Appl. Radial. Isot. 28, 503. Sergeenkov Yu V. and Sigalov V. M. (1986) Nuclear data sheets for A = 133. Nuclear Data Sheets 49, 639. Smith D. (1975) An improved method of data collection for 4 n/l - y coincidence measurements. Metrologia 11, 73. Smith D. and Stuart L. E. H. (1975) An extension of the 4 np - y coincidence technique: two dimensional extrapolation. Metrologia 11, 67. Yoshida M., Miyahara H. and WatanabeT. (1977) A source preparation for 4 np-counting with an aluminum compound. Int. J. Appl. Radial. Isot. 28, 633. Yoshizawa Y., Iwata Y., Katoh T., Ruan J. and Kawada Y. (1983) Precision measurements of gamma-ray intensities IV. low energy region: 15Se and ‘33Ba. Nucl. Instrum. Meth. 212, 249.