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Measurement of the activity concentration of a solution of 75Se
Nuclear Instruments and Methods in Physics Research A 339 (1994) 408-413 North-Holland
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH S(?c*,lorl A
Measurement of the activity concentration of a solution of
755e
Guy Ratel Bureau International des Poids et Mesures. Par'ilion de Breteuil, F-92312 Skt'res Cedex, France
The activity concentration of a solution of 75Se has been measured at BIPM as part of an international comparison organised on behalf of Section II of the CCEMRI. Two methods were used: the traditional 4~r[5-~, coincidence technique and the selective sampling method. The results agree, however the values have to be corrected because of the presence of a long-lived intermediate state at 304 keV. The beta spectrum has a complicated structure, and therefore the extrapolation to a beta efficiency of I is not straightforward. Different threshold settings are discussed for perlorming the extrapolation. The measured correction is compared with the values obtained by a calculation which uses tabulated data.
I. Introduction It is well known that the coincidence m e t h o d gives g(x~d results in the m e a s u r e m e n t of activity if applied to the decay of a radioactive source. If the excited nucleus decays by successive, nearly simultaneous emissions there is no p r o b l e m in the use of the coincidence m e t h o d and the results o b t a i n e d arc usually of high quality, as can be shown by comparison with results o b t a i n e d by o t h e r means. Because of the I(~v 13 efficiency in the proportional counter, which a p p r o a c h e s only 70% in the most favourable case, an extrapolation m e t h o d has to be used in o r d e r to estimate the activity which would c o r r e s p o n d to 100% efficiency. No particular problems result from this procedure, but the uncertainty in the final value of the activity is inevitably larger than would be the case if the cfficiencies were greater. Serious difficulties arise, however, when o n e of the excited levels is a metastable state from which decay by 13 emission is possible. In this case, some events originating from the metastable state arc registered in the 13 c h a n n e l and added to the truly coincident events in this channel. It is then necessary to correct for the n u m b e r of delayed events following the decay of the metastable state. T h e correction can be o b t a i n e d in two different ways: an experimental m e t h o d like the correlation t e c h n i q u e [1,2] can be applied, or it may be calculated from the data characterizing the decay of the nuclide u n d e r consideration - such as emission probabilities of g a m m a s or conversion electrons in Tables [3,4].
T h e nuclide 75Se is of this class and is difficult to standardize because of the p r e s e n c e of a long-lived i n t e r m e d i a t e state (sec Fig. 1). Section II of the C C E M R I (Comit6 C o n s u l t a t i f pour lcs Etalons de M e s u r e des R a y o n n e m e n t s Ionisants) has decided to e m b a r k on a full-scale international comparison of this radionuclide after the e n c o u r a g i n g results [5,6] of the trial comparison, but it is evident that i m p r o v e m e n t s in the m e a s u r e m e n t of 75Se can only be achieved if an investigation leading to a b e t t e r u n d e r s t a n d i n g of the extrapolation technique, or to a more precise value for the correction for delayed events, is carried out. This is not a small task. This report deals with the extrapolation proccdurc. T h e results of the full-scale comparison of activity of 7SSc are not p r e s e n t e d here, a l t h o u g h this study is a by-product of the comparison, the results of which will be published later.
2. Experimental conditions and theoretical features From the nuclear data of 75Se (see for instance ref. [4]) it can be seen that energy levels above 400 keV: are not converted, are fed at a low rate, have a low emission probability and have energies too high to give a significant signal in the proportional counter. For these four reasons it is usual and legitimate to t r u n c a t e the decay scheme, for example at the 400 kcV level, and to consider only its lower part. All transitions in this reduced decay scheme are converted. U n d e r these
0168-9(~)2/94/$07.00 .© 1994 - Elsevier ,Science B.V. All rights reserved SSDI 01 6 8 - 9 0 0 2 ( 9 3 ) E 0 7 0 8 - Z
G. Ratel / Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
~:Se4t
409
Table 1 Intensity of the various emissions in 75Se
TI/2 .1119.8-* 0.1 )d
s~ //I
~;"
/
I
/
'
I
"~, ,Y, .k . . . / 'I % ~,y~, co : % ~ c
5/2 ÷
"
,
/
J ;
/
/
, , ~
1,~ " ,L,3 c% J,72c'2 [~
--
-
V,,
¥,
Y,o
!¢,
Y,
c°12
cell
celo
ce9
ce7
0.303 7 0.279 5
I
XKa XK), "Yt
10.53 I 1.8 24.38
72
66.06
I
,
74
80.92 96.73
76
136.00
-y~' *
198.60
78 ~
264.66 3(13.92
7~o*
0.19o s
' :
Y ~I
'I I
I
cetK
#
ce ~,l. c e ~M
a s s u m p t i o n s the e q u a t i o n s for the c o u n t rates in the t h r e e different c h a n n e l s can b e expressed easily. In the p r o p o r t i o n a l counter, for c o n v e n i e n c e called the 13 c h a n n e l in what follows, the n u m b e r of collected events N o is given by [ £~t 6ce,
CCzK CC21.M ce.~K* CC4K Ce4L cesK CCSLM ce6K cct, l.M ce ~'K* ce~)~ CC91M CO" "*IOK*
** Cel01.M
+ .~-,,ece, 1 + r
Or'r
(1)
N , = N,)ate~;.
ce*tK
151.4 23.0
48.6 +_3.7 7.4 + 0.6 0.035 + 0.006 1.14 +_0.02 0.008 _+0.002 3.48 + 0.117 17.3 +0.2 59.(I + 0.8 1.47 _+0.02 59.1 _+0.8 25.2 + 0.4 1.34 _+0.02 11.56 _+0.02 31.2 9.8 1.0 5.8 +_ 1.2 1.3 +0.3 0.25 -+0.01
8.75 to 9.10 10.12 to 10.52 11.44 to 11.8
100 31.4 3.3
13.50 22.85 to 23.06 24.18 to 24.34 54.193 + 0.(X17 64.53 to 66.02 69.05 + 0.02 84.867 -+0.002 95.20 to 95.41 109.252 + 0.003 119.59 to 121.08 124.135 + 0.003 134.47 to 135.96 186.729 _+0.006 252.739 -+0.004 263.12 to 264.61 267.671 _+0.(X13 278.01 to 279.13 292.057+ 0.003
0.40 + 0.01 0.059± I).002 (1.012 -+0.(~)3 2.7 +0.1 0.36 +0.01 0.64 + 0.02 (1.1183+ 0.003 1.56 _+0.02 0.189-+0.003 0.029 __+().(~)1 0.38 -+0.02 0.044 _+0.1X)3 0.18 +0.01 0.025 z 0.002 0.063 _+1).(~3
One star is shown in this column if the emission is delayed, and two stars if the emission is partially delayed.
"
For the ~t c h a n n e l it is c o n v e n i e n t to choose a window, set in a particular ~'-cnergy range, which encloses a given a n d well-separated 7 peak. U n d e r this assumption, the n u m b e r of registered events N.~ for the level l is
Absolute intensity/%
4(X).66
e KLI, eKI-X CKX Y
Fig. 1. Simplified decay scheme of VSSe (from ref. [3]). All energies are given in MeV.
Relative intensity
279.54
;
33 $42
'~r )
Energy/ kcV
7t *
0.2646
o
75A
Type of emission "
0.SSSMeVi
0.400 5
/
~ !
N
I
I
I
I
x . . 1o.s~ v ~ s , ~ ) A
---7- ~
I P = 0 8 MPB
~(x 2Ol
"
(2) b
¢,,~= 24.3 key (0.~P4)
T h e n u m b e r of coincident events is t h e r e f o r e given by U, = Noatevte ~.
(3)
In these t h r e e e q u a t i o n s N O refers to the activity of the source, the coefficient a, is the b r a n c h i n g ratio of the energy level i, % is the d e t e c t i o n efficiency of coincident events, ec~ the detection efficiency of conversion electrons a n d ce, is the total conversion coefficient for b r a n c h i. It is s u p p o s e d t h a t all c o u n t rates have b e e n corrected for d e a d times, decay, resolving times and background.
0
0
5
10
15
20
25
Energy / k e V
Fig. 2. Expanded proportional counter spectrum. The letters a, b and c show the positions of the threshold used. V. STANDARDS, 75Se AND I'21r
410
G. Ratel /Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
before
T
after
T
Colnold.
'~
after
T
before
T
NOVELEC SCALERS
Fig. 3. Experimental arrangement used for the measurements described in this article.
A n explanation of events in the 13 c h a n n e l is necessary. Here, the c o u n t rate may be s e p a r a t e d into two parts: the first characterizes events which are not delayed a n d may be d e t e c t e d in coincidence, the second
refers exclusively to delayed events. (In the energy range of the events d e t e c t e d by the proportional counter, and written as ece, the efficiency can be considered as constant.)
before
T
after
T
Colncld.
~"
after
T
"~ before
T
NOVELEC SCALERS
Fig. 4. Experimental arrangement used for conventional coincidence measurements.
411
G. Ratel //Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
The equations lead to an estimate for the value of the activity concentration by forming the well-known expression N~N. t Nc; -
g~
=
ffi~:ce
=N,, 1+ •
]
E i;-g,
-
(1 + a , l E c '
(4)
J
with E i ~ r a i = 1.
1 650
I
I
If, by varying the experimental conditions, the detection efficiency can be changed, it is obvious from Eq. (4) that a linear extrapolation to the condition (1 - e c) = 0 provides an estimate of the activity. It is also clear that a precise knowledge of the fraction of delayed events is essential for this determination. The coefficients which appear in Eq. (4) can be evaluated from nuclear data tables. Table 1, which is taken from ref. [3], gives the required data for evaluation of these coefficients. As may be seen from the pressurized proportional counter spectrum shown in Fig. 2, the delayed conversion electrons (CC~K) emitted by the metastable state at 304 keV, the energy of which is about 13.5 keV, cannot be separated from the other prompt events. However, the second peak contains no prompt events. This distinction leads to a possibility for the experimental elimination of the conversion electrons which produce
I
I
G
1 600
E
I
1 550
O"
1 500
f, o, ,/
¢~ 1 450
/[3//
_/,,
4/
"
C~
._g =
1 400
C
8 <"~
1 350 //,/ .-"
1 300
0
0.5
1.0
1.5
2.0
2.5
3.0
(1 - '~'c)/~c
Fig. 5. Extrapolated curves obtained for six different threshold settings. The numbers refer to Table 2. V. STANDARDS, 75Se AND 192Ir
412
G. Ratel /NucL bzstr, and Meth. in Phys. Res. A 339 11994) 408-413
the second peak (Ce~L and CC~M), and so to a determination of the emission intensity of these delayed events. If, by some experimental means, the contributions of ceu. and Ce~M electrons are eliminated from the count rate, only Nt~ is affectcd, N.~ and N,. remaining constant. Thus, the slope of the extrapolated straight line given by Eq. (4) does not change, but the intercept of the activity axis is lowered by the n u m b e r of delayed electrons ceu. and CelM.
3. Experimental procedure 3.1. Source preparation To perform these m e a s u r e m e n t s , a source, of mass 40.913 mg, was chosen from those p r e p a r e d for the international comparison. Drops from a 75Se solution were deposited on metal-coated VYNS foils which, in turn, were sandwiched b e t w e e n two gold-coated VYNS foils. This reduces the efficiency of the proportional c o u n t e r slightly, but makes the source more able to resist pressure changes. Ludox was a d d e d to spread the metallic precipitate uniformly.
3. 2. Detector systems 3.2.1. Electron detectors A pressurized proportional counter operating with a voltage of 6.7 kV, in a 4~v geometry, was used. A flow of a r g o n / m e t h a n e , at a mixing ratio of 9:1 and a fixed pressure of 0.8 MPa, was maintained in the counter. A lower threshold was set to eliminate electronic perturbations in the range 0 to 2 keV. Three o t h e r thresholds, labelled a, b and c in Fig. 2, were set in the electron spectrum. Threshold c is the u p p e r limit of the window set to eliminate delayed electrons and the lower limit, n a m e d b, was movable. For each width of the window characterized by thc pair of thresholds b and c. the threshold a was set at seven positions in the range from approximatively 2 to 10 keV. The count rates varied between 281X1 s ~ and 5900 s - t, with a background rate lower than 5 s - t. The highest 13 efficiency achieved was 58°~.
3.2.2. Gamma-ray detectors Two 3 in. X 3 in. NaI(TI) detectors werc used, onc on cach side of the proportional counter, to incrcase the "v-detection efficiency. A value of about 5% was obtained. A fixed window, close to the 400 kcV peak, was chosen for the m e a s u r e m e n t s . A typical count rate was 5011 s - i against a background rate of 3 s - l ; the counting time was as long as 180 s.
3.3. Fxperimental arrangement The experimental setup is shown in Figs. 3 and 4. The signals from the photomultipliers are a d d e d and
Table 2 Linear extrapolation of the activity concentration in the form A[(I-- e~)/,..]+ B. for reference and 21 runs. The runs corrcSl:xmd to different settings of the threshold a
1 2 3 4 5 6 7 8 9 111 11 12 13 14 15 16 17 18 19 20 21 22
A/(Bq/mg)
B /(Bq/mg)
101.7+_ 1.5 "
1335.1 ~ 1.6
83.5+ 1.3 811.2 + 1.4 76.7 +-2.3 78.4 + 2.2 77.4+11.9 811.4 &2.3 84.5 _+.1.8 90.5 + 3.0 85.6 _+3.(1 87.11 -,-3.2 87.3-3.2 81.7+2.6 87.1 ±2.1 91.4 +_2.2 93.6_+. 1.9 87. I + 3.1 98.0± 1.11 105.8 +-11.9 106.4 + 2.9 1111.2 ± 2.6 116.0 ± 1.t,~
1298.3+_ 1.7 1293.4 +- 1.9 1299.9 +-3.2 131111.5+ 2.9 13112.1 +- 1.1 1311tl.3 + 3.3 1298.0 +-2.2 1294.6 +-3.3 1307.1 +_4.2 13119.4 +_4.11 1311.8+4.2 1321.9+-3.4 13119.6+-2.5 1307.5 +_2.5 13111.3+_2.11 1318.11 +_3.8 1313.8+ 1.3 1318.9 z 1.(1 1322.3 +_3.2 1325.1 _+2.9 1332.11 + 2.1
" This is the reference value, called A. in the text.
scnt directly to the c o u n t e r through a numerical dcad time of 10 Its. The corrected signals arc also dircctcd to a coincidence unit in which a resolving time of 1.5 ~xs was used.
4. Results and discussion To obtain a reliable result, the usual extrapolation was p e r f o r m e d in a first step. In o r d e r to do so in the electron channel, the system was o p e r a t e d with a single-channel analyser as shown in Fig. 4. After these initial m e a s u r e m e n t s the amplifier was c o n n e c t e d to the sum circuit, as indicated in Fig. 3. The results of the different extrapolations can be seen in Table 2 (for the reference dale). Table 2 shows that the elimination of the contributkm of the delayed conversion electrons celL and ce ~M produces drastic changes in the slope A and intercept B of the extrapolated straight lines. If the window width is too large, some coincident events go undetected, which leads to a significant decrease in the value of the slope. If the slope A reaches the reference value A o one can assume that all coincident events have been taken into account. W h e n the uncertainties are included, the slopes obtained for extrapolations (1) and 118) are very similar
G. Ratel / Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
and the above condition can be considered as fulfilled: the difference betwccn the two intercepts can thus be assumed to give a value for the emission probability of the conversion electrons ce~. and ce~M. Some of the experimental data are shown in Fig. 5 with the corresponding extrapolated values. Thc experimental values noted above yield an emission probability of (1.593 + 0.002)%, while a calculation based on Tablc 1 yields (1.55 _+ 0.03)%. These values are very similar so, although the method used in this work seems to be rather simple, the result it provides is quite reasonable. The uncertainty quoted for the experimental value is low because it includes only statistical contributions and those duc to the extrapolation procedure.
5.
Conclusion
From this study, somc general conclusions can be drawn: first, a good discrimination between given events can be achieved with the use of a pressurized proportional counter operated under high pressure; second, the change in the slope of the extrapolated straight line versus the variablc [ ( 1 - e ) / e ] is vcry sensitive to a decrease in coincident events, a property which has bccn used in order to determine the overall emission probability of the delayed conversion electrons c e l l and Ce~M. It is clear, however, that this method is not sensitive enough to allow a separate determination of the single-emission probability of these conversion electrons. This is mainly because the very small energy difference between these decay processes cannot be separated with a pressurized proportional counter. Nevertheless, it should bc possible to improve the
413
method and so obtain more reliable results. Experimental changes which would help are: a better pressure regulation system to ensure higher stability of the spectrum and, consequently, the repeatability and reliability of the threshold settings; a peak follower to keep the spectrum stable; a reduction of the threshold setting increments to make them as small as possible, in the region where the slopes of the extrapolated curves are nearly equal, a change which would make evaluation of the critical threshold more precise. This work cxmfirms the emission probabilities fl)und by Lagoutinc ct al. [3] for the conversion electrons Cell and CeIM, SO it is reasonable to suppose that the value (7.35 + 1.24)% for the total emission probability of thc conversion electrons CelK,L,M , deduced from the same table, is also reasonable. This raises the question of whether the value (5.4 + 0.35)% reported by Lewis et al. [1], based on a correlation method and often used for the correction of experimcntal data for delayed conversion electrons, is too low.
References
[1] V.E. Lewis, D. Smith and A. Williams, Metrologia 9 (1973) 14. [21 H. Janssen, Nucl. Instr. and Meth. A 299 (1990) 292. [3] F. Lagoutine, N. Coursol and J. Legrand, Table des Radionucl~ides, CEA-LMRI, Gif-sur-Yvette (1982). [4] C.M. Ledercr and V.S. Shirley, Tables of Isotopes (Wiley, New York, 1978). [5] G. Ratel, Trial comparison of activity measurements of a solution of 755e, Rapport BIPM-90/8, BIPM, S~:vres (1990). [6] G. Ratel, Nucl. Instr. and Meth. A 312 (1992) 201.
V. STANDARDS, 75Se AND 1921r
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH S(?c*,lorl A
Measurement of the activity concentration of a solution of
755e
Guy Ratel Bureau International des Poids et Mesures. Par'ilion de Breteuil, F-92312 Skt'res Cedex, France
The activity concentration of a solution of 75Se has been measured at BIPM as part of an international comparison organised on behalf of Section II of the CCEMRI. Two methods were used: the traditional 4~r[5-~, coincidence technique and the selective sampling method. The results agree, however the values have to be corrected because of the presence of a long-lived intermediate state at 304 keV. The beta spectrum has a complicated structure, and therefore the extrapolation to a beta efficiency of I is not straightforward. Different threshold settings are discussed for perlorming the extrapolation. The measured correction is compared with the values obtained by a calculation which uses tabulated data.
I. Introduction It is well known that the coincidence m e t h o d gives g(x~d results in the m e a s u r e m e n t of activity if applied to the decay of a radioactive source. If the excited nucleus decays by successive, nearly simultaneous emissions there is no p r o b l e m in the use of the coincidence m e t h o d and the results o b t a i n e d arc usually of high quality, as can be shown by comparison with results o b t a i n e d by o t h e r means. Because of the I(~v 13 efficiency in the proportional counter, which a p p r o a c h e s only 70% in the most favourable case, an extrapolation m e t h o d has to be used in o r d e r to estimate the activity which would c o r r e s p o n d to 100% efficiency. No particular problems result from this procedure, but the uncertainty in the final value of the activity is inevitably larger than would be the case if the cfficiencies were greater. Serious difficulties arise, however, when o n e of the excited levels is a metastable state from which decay by 13 emission is possible. In this case, some events originating from the metastable state arc registered in the 13 c h a n n e l and added to the truly coincident events in this channel. It is then necessary to correct for the n u m b e r of delayed events following the decay of the metastable state. T h e correction can be o b t a i n e d in two different ways: an experimental m e t h o d like the correlation t e c h n i q u e [1,2] can be applied, or it may be calculated from the data characterizing the decay of the nuclide u n d e r consideration - such as emission probabilities of g a m m a s or conversion electrons in Tables [3,4].
T h e nuclide 75Se is of this class and is difficult to standardize because of the p r e s e n c e of a long-lived i n t e r m e d i a t e state (sec Fig. 1). Section II of the C C E M R I (Comit6 C o n s u l t a t i f pour lcs Etalons de M e s u r e des R a y o n n e m e n t s Ionisants) has decided to e m b a r k on a full-scale international comparison of this radionuclide after the e n c o u r a g i n g results [5,6] of the trial comparison, but it is evident that i m p r o v e m e n t s in the m e a s u r e m e n t of 75Se can only be achieved if an investigation leading to a b e t t e r u n d e r s t a n d i n g of the extrapolation technique, or to a more precise value for the correction for delayed events, is carried out. This is not a small task. This report deals with the extrapolation proccdurc. T h e results of the full-scale comparison of activity of 7SSc are not p r e s e n t e d here, a l t h o u g h this study is a by-product of the comparison, the results of which will be published later.
2. Experimental conditions and theoretical features From the nuclear data of 75Se (see for instance ref. [4]) it can be seen that energy levels above 400 keV: are not converted, are fed at a low rate, have a low emission probability and have energies too high to give a significant signal in the proportional counter. For these four reasons it is usual and legitimate to t r u n c a t e the decay scheme, for example at the 400 kcV level, and to consider only its lower part. All transitions in this reduced decay scheme are converted. U n d e r these
0168-9(~)2/94/$07.00 .© 1994 - Elsevier ,Science B.V. All rights reserved SSDI 01 6 8 - 9 0 0 2 ( 9 3 ) E 0 7 0 8 - Z
G. Ratel / Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
~:Se4t
409
Table 1 Intensity of the various emissions in 75Se
TI/2 .1119.8-* 0.1 )d
s~ //I
~;"
/
I
/
'
I
"~, ,Y, .k . . . / 'I % ~,y~, co : % ~ c
5/2 ÷
"
,
/
J ;
/
/
, , ~
1,~ " ,L,3 c% J,72c'2 [~
--
-
V,,
¥,
Y,o
!¢,
Y,
c°12
cell
celo
ce9
ce7
0.303 7 0.279 5
I
XKa XK), "Yt
10.53 I 1.8 24.38
72
66.06
I
,
74
80.92 96.73
76
136.00
-y~' *
198.60
78 ~
264.66 3(13.92
7~o*
0.19o s
' :
Y ~I
'I I
I
cetK
#
ce ~,l. c e ~M
a s s u m p t i o n s the e q u a t i o n s for the c o u n t rates in the t h r e e different c h a n n e l s can b e expressed easily. In the p r o p o r t i o n a l counter, for c o n v e n i e n c e called the 13 c h a n n e l in what follows, the n u m b e r of collected events N o is given by [ £~t 6ce,
CCzK CC21.M ce.~K* CC4K Ce4L cesK CCSLM ce6K cct, l.M ce ~'K* ce~)~ CC91M CO" "*IOK*
** Cel01.M
+ .~-,,ece, 1 + r
Or'r
(1)
N , = N,)ate~;.
ce*tK
151.4 23.0
48.6 +_3.7 7.4 + 0.6 0.035 + 0.006 1.14 +_0.02 0.008 _+0.002 3.48 + 0.117 17.3 +0.2 59.(I + 0.8 1.47 _+0.02 59.1 _+0.8 25.2 + 0.4 1.34 _+0.02 11.56 _+0.02 31.2 9.8 1.0 5.8 +_ 1.2 1.3 +0.3 0.25 -+0.01
8.75 to 9.10 10.12 to 10.52 11.44 to 11.8
100 31.4 3.3
13.50 22.85 to 23.06 24.18 to 24.34 54.193 + 0.(X17 64.53 to 66.02 69.05 + 0.02 84.867 -+0.002 95.20 to 95.41 109.252 + 0.003 119.59 to 121.08 124.135 + 0.003 134.47 to 135.96 186.729 _+0.006 252.739 -+0.004 263.12 to 264.61 267.671 _+0.(X13 278.01 to 279.13 292.057+ 0.003
0.40 + 0.01 0.059± I).002 (1.012 -+0.(~)3 2.7 +0.1 0.36 +0.01 0.64 + 0.02 (1.1183+ 0.003 1.56 _+0.02 0.189-+0.003 0.029 __+().(~)1 0.38 -+0.02 0.044 _+0.1X)3 0.18 +0.01 0.025 z 0.002 0.063 _+1).(~3
One star is shown in this column if the emission is delayed, and two stars if the emission is partially delayed.
"
For the ~t c h a n n e l it is c o n v e n i e n t to choose a window, set in a particular ~'-cnergy range, which encloses a given a n d well-separated 7 peak. U n d e r this assumption, the n u m b e r of registered events N.~ for the level l is
Absolute intensity/%
4(X).66
e KLI, eKI-X CKX Y
Fig. 1. Simplified decay scheme of VSSe (from ref. [3]). All energies are given in MeV.
Relative intensity
279.54
;
33 $42
'~r )
Energy/ kcV
7t *
0.2646
o
75A
Type of emission "
0.SSSMeVi
0.400 5
/
~ !
N
I
I
I
I
x . . 1o.s~ v ~ s , ~ ) A
---7- ~
I P = 0 8 MPB
~(x 2Ol
"
(2) b
¢,,~= 24.3 key (0.~P4)
T h e n u m b e r of coincident events is t h e r e f o r e given by U, = Noatevte ~.
(3)
In these t h r e e e q u a t i o n s N O refers to the activity of the source, the coefficient a, is the b r a n c h i n g ratio of the energy level i, % is the d e t e c t i o n efficiency of coincident events, ec~ the detection efficiency of conversion electrons a n d ce, is the total conversion coefficient for b r a n c h i. It is s u p p o s e d t h a t all c o u n t rates have b e e n corrected for d e a d times, decay, resolving times and background.
0
0
5
10
15
20
25
Energy / k e V
Fig. 2. Expanded proportional counter spectrum. The letters a, b and c show the positions of the threshold used. V. STANDARDS, 75Se AND I'21r
410
G. Ratel /Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
before
T
after
T
Colnold.
'~
after
T
before
T
NOVELEC SCALERS
Fig. 3. Experimental arrangement used for the measurements described in this article.
A n explanation of events in the 13 c h a n n e l is necessary. Here, the c o u n t rate may be s e p a r a t e d into two parts: the first characterizes events which are not delayed a n d may be d e t e c t e d in coincidence, the second
refers exclusively to delayed events. (In the energy range of the events d e t e c t e d by the proportional counter, and written as ece, the efficiency can be considered as constant.)
before
T
after
T
Colncld.
~"
after
T
"~ before
T
NOVELEC SCALERS
Fig. 4. Experimental arrangement used for conventional coincidence measurements.
411
G. Ratel //Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
The equations lead to an estimate for the value of the activity concentration by forming the well-known expression N~N. t Nc; -
g~
=
ffi~:ce
=N,, 1+ •
]
E i;-g,
-
(1 + a , l E c '
(4)
J
with E i ~ r a i = 1.
1 650
I
I
If, by varying the experimental conditions, the detection efficiency can be changed, it is obvious from Eq. (4) that a linear extrapolation to the condition (1 - e c) = 0 provides an estimate of the activity. It is also clear that a precise knowledge of the fraction of delayed events is essential for this determination. The coefficients which appear in Eq. (4) can be evaluated from nuclear data tables. Table 1, which is taken from ref. [3], gives the required data for evaluation of these coefficients. As may be seen from the pressurized proportional counter spectrum shown in Fig. 2, the delayed conversion electrons (CC~K) emitted by the metastable state at 304 keV, the energy of which is about 13.5 keV, cannot be separated from the other prompt events. However, the second peak contains no prompt events. This distinction leads to a possibility for the experimental elimination of the conversion electrons which produce
I
I
G
1 600
E
I
1 550
O"
1 500
f, o, ,/
¢~ 1 450
/[3//
_/,,
4/
"
C~
._g =
1 400
C
8 <"~
1 350 //,/ .-"
1 300
0
0.5
1.0
1.5
2.0
2.5
3.0
(1 - '~'c)/~c
Fig. 5. Extrapolated curves obtained for six different threshold settings. The numbers refer to Table 2. V. STANDARDS, 75Se AND 192Ir
412
G. Ratel /NucL bzstr, and Meth. in Phys. Res. A 339 11994) 408-413
the second peak (Ce~L and CC~M), and so to a determination of the emission intensity of these delayed events. If, by some experimental means, the contributions of ceu. and Ce~M electrons are eliminated from the count rate, only Nt~ is affectcd, N.~ and N,. remaining constant. Thus, the slope of the extrapolated straight line given by Eq. (4) does not change, but the intercept of the activity axis is lowered by the n u m b e r of delayed electrons ceu. and CelM.
3. Experimental procedure 3.1. Source preparation To perform these m e a s u r e m e n t s , a source, of mass 40.913 mg, was chosen from those p r e p a r e d for the international comparison. Drops from a 75Se solution were deposited on metal-coated VYNS foils which, in turn, were sandwiched b e t w e e n two gold-coated VYNS foils. This reduces the efficiency of the proportional c o u n t e r slightly, but makes the source more able to resist pressure changes. Ludox was a d d e d to spread the metallic precipitate uniformly.
3. 2. Detector systems 3.2.1. Electron detectors A pressurized proportional counter operating with a voltage of 6.7 kV, in a 4~v geometry, was used. A flow of a r g o n / m e t h a n e , at a mixing ratio of 9:1 and a fixed pressure of 0.8 MPa, was maintained in the counter. A lower threshold was set to eliminate electronic perturbations in the range 0 to 2 keV. Three o t h e r thresholds, labelled a, b and c in Fig. 2, were set in the electron spectrum. Threshold c is the u p p e r limit of the window set to eliminate delayed electrons and the lower limit, n a m e d b, was movable. For each width of the window characterized by thc pair of thresholds b and c. the threshold a was set at seven positions in the range from approximatively 2 to 10 keV. The count rates varied between 281X1 s ~ and 5900 s - t, with a background rate lower than 5 s - t. The highest 13 efficiency achieved was 58°~.
3.2.2. Gamma-ray detectors Two 3 in. X 3 in. NaI(TI) detectors werc used, onc on cach side of the proportional counter, to incrcase the "v-detection efficiency. A value of about 5% was obtained. A fixed window, close to the 400 kcV peak, was chosen for the m e a s u r e m e n t s . A typical count rate was 5011 s - i against a background rate of 3 s - l ; the counting time was as long as 180 s.
3.3. Fxperimental arrangement The experimental setup is shown in Figs. 3 and 4. The signals from the photomultipliers are a d d e d and
Table 2 Linear extrapolation of the activity concentration in the form A[(I-- e~)/,..]+ B. for reference and 21 runs. The runs corrcSl:xmd to different settings of the threshold a
1 2 3 4 5 6 7 8 9 111 11 12 13 14 15 16 17 18 19 20 21 22
A/(Bq/mg)
B /(Bq/mg)
101.7+_ 1.5 "
1335.1 ~ 1.6
83.5+ 1.3 811.2 + 1.4 76.7 +-2.3 78.4 + 2.2 77.4+11.9 811.4 &2.3 84.5 _+.1.8 90.5 + 3.0 85.6 _+3.(1 87.11 -,-3.2 87.3-3.2 81.7+2.6 87.1 ±2.1 91.4 +_2.2 93.6_+. 1.9 87. I + 3.1 98.0± 1.11 105.8 +-11.9 106.4 + 2.9 1111.2 ± 2.6 116.0 ± 1.t,~
1298.3+_ 1.7 1293.4 +- 1.9 1299.9 +-3.2 131111.5+ 2.9 13112.1 +- 1.1 1311tl.3 + 3.3 1298.0 +-2.2 1294.6 +-3.3 1307.1 +_4.2 13119.4 +_4.11 1311.8+4.2 1321.9+-3.4 13119.6+-2.5 1307.5 +_2.5 13111.3+_2.11 1318.11 +_3.8 1313.8+ 1.3 1318.9 z 1.(1 1322.3 +_3.2 1325.1 _+2.9 1332.11 + 2.1
" This is the reference value, called A. in the text.
scnt directly to the c o u n t e r through a numerical dcad time of 10 Its. The corrected signals arc also dircctcd to a coincidence unit in which a resolving time of 1.5 ~xs was used.
4. Results and discussion To obtain a reliable result, the usual extrapolation was p e r f o r m e d in a first step. In o r d e r to do so in the electron channel, the system was o p e r a t e d with a single-channel analyser as shown in Fig. 4. After these initial m e a s u r e m e n t s the amplifier was c o n n e c t e d to the sum circuit, as indicated in Fig. 3. The results of the different extrapolations can be seen in Table 2 (for the reference dale). Table 2 shows that the elimination of the contributkm of the delayed conversion electrons celL and ce ~M produces drastic changes in the slope A and intercept B of the extrapolated straight lines. If the window width is too large, some coincident events go undetected, which leads to a significant decrease in the value of the slope. If the slope A reaches the reference value A o one can assume that all coincident events have been taken into account. W h e n the uncertainties are included, the slopes obtained for extrapolations (1) and 118) are very similar
G. Ratel / Nucl. Instr. and Meth. in Phys. Res. A 339 (1994) 408-413
and the above condition can be considered as fulfilled: the difference betwccn the two intercepts can thus be assumed to give a value for the emission probability of the conversion electrons ce~. and ce~M. Some of the experimental data are shown in Fig. 5 with the corresponding extrapolated values. Thc experimental values noted above yield an emission probability of (1.593 + 0.002)%, while a calculation based on Tablc 1 yields (1.55 _+ 0.03)%. These values are very similar so, although the method used in this work seems to be rather simple, the result it provides is quite reasonable. The uncertainty quoted for the experimental value is low because it includes only statistical contributions and those duc to the extrapolation procedure.
5.
Conclusion
From this study, somc general conclusions can be drawn: first, a good discrimination between given events can be achieved with the use of a pressurized proportional counter operated under high pressure; second, the change in the slope of the extrapolated straight line versus the variablc [ ( 1 - e ) / e ] is vcry sensitive to a decrease in coincident events, a property which has bccn used in order to determine the overall emission probability of the delayed conversion electrons c e l l and Ce~M. It is clear, however, that this method is not sensitive enough to allow a separate determination of the single-emission probability of these conversion electrons. This is mainly because the very small energy difference between these decay processes cannot be separated with a pressurized proportional counter. Nevertheless, it should bc possible to improve the
413
method and so obtain more reliable results. Experimental changes which would help are: a better pressure regulation system to ensure higher stability of the spectrum and, consequently, the repeatability and reliability of the threshold settings; a peak follower to keep the spectrum stable; a reduction of the threshold setting increments to make them as small as possible, in the region where the slopes of the extrapolated curves are nearly equal, a change which would make evaluation of the critical threshold more precise. This work cxmfirms the emission probabilities fl)und by Lagoutinc ct al. [3] for the conversion electrons Cell and CeIM, SO it is reasonable to suppose that the value (7.35 + 1.24)% for the total emission probability of thc conversion electrons CelK,L,M , deduced from the same table, is also reasonable. This raises the question of whether the value (5.4 + 0.35)% reported by Lewis et al. [1], based on a correlation method and often used for the correction of experimcntal data for delayed conversion electrons, is too low.
References
[1] V.E. Lewis, D. Smith and A. Williams, Metrologia 9 (1973) 14. [21 H. Janssen, Nucl. Instr. and Meth. A 299 (1990) 292. [3] F. Lagoutine, N. Coursol and J. Legrand, Table des Radionucl~ides, CEA-LMRI, Gif-sur-Yvette (1982). [4] C.M. Ledercr and V.S. Shirley, Tables of Isotopes (Wiley, New York, 1978). [5] G. Ratel, Trial comparison of activity measurements of a solution of 755e, Rapport BIPM-90/8, BIPM, S~:vres (1990). [6] G. Ratel, Nucl. Instr. and Meth. A 312 (1992) 201.
V. STANDARDS, 75Se AND 1921r