- Email: [email protected]
Spectrum shape measurement of two beta transitions in 111Ag
I
4.E
I
Nuclear Physics A98 (1967) 273--277; (~) North-Holland Publishing Co., Amsterdam
I
Not to be reproduced by photoprint or microfilm without written permission from the publisher
SPECTRUM SHAPE MEASUREMENT OF T W O BETA T R A N S I T I O N S IN 11lAg J. L E H M A N N *
Centre d'Etude de l'Energie Nucldaire, Mol, Belgique Received 13 F e b r u a r y 1967
Abstract: The spectrum shape factors of the 685 keV and 1028 keV beta transitions in the decay of ntAg have been measured. The results are: C(W) = CSt[I--(0.023±0.04)W] and C(W) ~ C~t[1--(0.0±0.01)W], respectively. The experimental results are compared with the predictions of the extreme single-particle shell model. E
RADIOACTIVITY: 24Na, mAg; measured E//, fl-spectrum shape.
]
1. Introduction
When analysing the first-forbidden beta transition in the decay of 1t tAg , Delabaye et al. 1,2) found a good agreement between the predictions of the extreme singleparticle shell model and experimental results, except for the spectrum shape of the f13 transition measured by Langer el al. 4) (see fig. 1). Consequently, we decided to remeasure the spectrum shape of the transition f13 with another type of spectrometer than the one used by Langer et al. We measured also the spectrum shape of the fil branch. 2. Experimental methods We have studied the two spectra of the 171 and/73 transitions (see fig. 1) with an intermediate image ]~-ray spectrometer of the Siegbahn-S15.tis type *t modified so as to permit measurements of 3-7 coincidences. The 3-detector is an anthracene crystal (1 cm diam and 0.5 cm thick) and the y-detector is a Nal(T1) crystal (2.54 cm x 2.54 cm). The influence of the spectrometer magnetic field on the photomultipliers is reduced by the use of lucite light pipes (30 cm long) and by three concentric #-metal shields. For the maximum magnetic field strength used in this study, no change higher than 0.5 ~ was detected on the pulseheight from the photomultipliers. The fast-slow coincidence circuit resolution time was adjusted at 50 nsec. The general controls and tests performed are described elsewhere 7). ,+ N o w at L o u v a i n University, Hdverl6-Louvain, Belgium. tt M a n u f a c t u r e d by L.K.B., Sweden. 273
274
J. LEHMANN
As a final test of our method, we have measured the allowed fl-spectrum shape factor of the 1.394 MeV/?-transition in the decay of 24Na in coincidence with the 4.12, 2.75 and 1.368 MeV ,,-ray lines. The results are shown in fig. 2. From this figure, one can conclude that the apparatus does not introduce an error larger than 1% in the measurement of a spectrum shape factor above 300 keV. 11lAg 64
47
A
i
B
54 418 '3
1/2 -
0,5'/.
685
8 '/.
log ft=7,3
"~2 785
1%
[og.f t = 8,8
~1 1028
91 '/.
Iogtt =7,8
5/2+ 610
[mo
419
£
I
343 5/2+ 243
\
1/2+ 111 Cd 48 63
[ I T (key)
Fig. 1. Decay scheme 10) o f m A g . The energies of the transitions (A) and levels are indicated in keV. The intensities (B) of the fl-transitions are from ref. lo).
N/p2F(Z,W)(W-Wo) 2
21 20
--o --o
.__0
"--0
0
--0
--
__
0
__
0---
0---
°
o
_0
1-
)
o
19 W(rne 2) i.5
2
2,5
3
Fig. 2. Spectrum shape factor of the 1393 keV/3-transition of 24Na.
The isotope ltXAg in the form of A g N O 3 was obtained t as a solution in HNO3; it was deposited by evaporation on an aluminized mylar film of about 500/,g/cm z. The resulting source had a diam of 2 m m and thickness of about 150 pg/cm 2. + Obtained from Amersham, England.
BETA
275
TRANSITIONS
3. Experimental results 3.1. T R A N S I T I O N O F 685 keV (/~3)
We have measured the 685 keV fl-transition in coincidence with the 343 keV 7-ray whose photopeak was selected by a single-channel pulse-height analyser (window width of 30 keV). As the//-branch under study amounts to only 8 % of the total fl-intensity, particular care had to be taken to determinate the random coincidences. The result of the measurements is presented in fig. 3 where we have plotted the quantity N
C ( w ) = P 2 F ( Z E ) ( W o - rV)2 ; [ Wo= 2.325
/
N / p2F(Z,W)(Wo-W) 2
/
/ / w0=2.33 200
// / / 180
_L_L_,_
/-
~
Wo =2,335
/ /
j
_
160 \ Wo=2.345 140
I
t4
1.5
1
I
1
I
I
I
I
1.6 1.7 1.8 1,9 2 Zl 22 Fig. 3. Spectrum shape factor of the 682 keV/33 transition of m A g .
I
2.3
W(mc 2)
C ( W ) is the spectrum shape factor, N the number of counts per unit momentum interval, F ( Z E ) the Fermi function, W o the end-point energy in mc 2 units, p the electron momentum in me units and W the electron energy in rnc a units. Restricting the possible variation of Wo to values yielding a physical behaviour of C(W) in the endpoint region 9), we obtain Wo = 685+_3 keV; the 3 keV error does not take into account possible calibration uncertainties irrelevant for the determination of C ( W ) [ref. 8)] and estimated to be about 10 keV. Fig. 3 shows C ( W ) for different values of W o. The spectrum shape factor obtained by this analysis can be described by the equation C ( W ) = C~t[1-(0.023-t-0.03)W]. 3.2. T R A N S I T I O N O F 1028 keV (/31)
Because of the influence of the//3 and flz transitions, the pure fll spectrum can only be measured at electron energies above 785 keV. It is possible, however, to extend the
276
J. LEHMANN
m e a s u r e m e n t s to lower energies if the results are corrected for the c o n t r i b u t i o n s o f the/73 and/72 transitions using a g r a p h i c a l m e t h o d . W e have studied in this w a y the /?-spectrum shape factor f r o m 500 k e V u p w a r d s . I n fig. 4 are shown the raw results (curve A ) a n d the same results corrected for the influence o f the lower-energy b e t a N I p2F(Z.W )(Wo-W )2
~
17C
~_
150
CURVE A CURVE B
"---e ---e
:z:~ ~
o __
Q.,..,_ o'~
0
0
0 __0 - - 0 - -
O--
0---
-0
130
W(mc 2) I
I
2.1
I
22
2,3
214
2'5
2r6
I
2~7
2B
Fig. 4. Spectrum shape factor of the 1024 keV/3t transition of mAg. o o o
14 I
o
o
131
o
o
o
o
o
o
o
o
o o
oo
o
o
o
o
o
o
o
o
o
o
o
o o
Wo=233
o
•
o
o o
12 [
o
o o
o
o
o
o
o
o
o o o
.I
o
13 [
o
o
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o
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o o
o
o o
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o
o
o °
o
o
0
o
o
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o
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o
o
o
-,y
o
o
o
- -
o o
o
o
o o
%o2 3z,
o o
o
12!
o
o
o
13
o
o
o %
o
o o
°
o
o
o
o
o
o
c~
o
o
°o
o o o °°
o o
o
o
o
o
o
Wo=
o o C{W)
o °
oo
o°
o o
o
o o
o o
o
o
o o
o
o o
o
o o
o
o
o
o
l
W(mc2)
o
o o
I Ii|F
2.347
o
o o
12~
o
o
12 j
Wo=2,36 oo
o
Fit. 5. Spectrum shape correction factor of the 682 keV fla transition of t11Ag for different values of I1~, after Langer et al. 4).
BETA TRANSITIONS
277
groups (curve B). F o r this correction, we have assumed that the spectrum shape factors o f the 685 keV/33 transition is allowed and that the 785 keV/32 transition has a unique shape; the errors which m a y be introduced by these simplifications are negligible within the accuracy of the experiment. The spectrum shape factor o f the 1.024 keV transition can be described by the equation
C ( W ) = C S t [ 1 - ( 0 . 0 0 + 0 . 0 1 ) W ] for W o = 1 0 2 8 + 3 keV.
4. Discussion of the P3 transition The spectrum shape factor for the 685 keV beta transition has already been investigated by Langer et al. 3) and f o u n d to be o f the f o r m C ( W ) = C S t ( 1 - 0 . 1 7 W ) . We have studied the variation of the best fit to their experimental results as a function of the end-point energy; the resulting curves are shown in fig. 5 for four particular choices o f Wo. In order to restrict the variation of W o, most authors reject the W o values giving unphysical behaviour of C ( W ) near the end-point energy. As Langer et al. 3) did not measure close to this end-point energy, their experimental result does not give firm restrictions u p o n Wo. As a consequence, any of the four sets of data presented on fig. 5 can be accepted on the basis of these data alone, and neither the linear slope stated by Langer et al. 3) nor the correction factor is unique. Moreover, one cannot find a value o f W o which gives an experimental correction factor in agreement with the model prediction 2), which is C ( W ) ~ C st. Our measurement gives a fit very close to this prediction. We can thus conclude that the new experimental situation gives a very good agreement with the extreme single-particle shell-model calculations.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
M. Delabaye, Ph.D. thesis, University of Louvain (1965) M. Delabaye, J. P. Deutsch and P. Lipnik, Nuclear Physics 80 (1966) 385 J. H. Hamilton, B. G. Petterson and J. M. Hollander, Ark. Fys. 18 (1960) 273 L. M. Langer and R. L. Robinson, Phys. Rev. 112 (1958) 481 P. Lipnik and J. W. Sunier, Nuclear Physics 53 (1964) 305 H. Daniel, C. Engler, G. Th. Kaschl and S. A. A. Zaidi, Phys. Lett. 12 (1964) 337 S. Andr6, J. Phys. Rev. 26 (1965) 161A F. T. Porter, F. Wagner and M. S. Freedman, Phys. Rev. 107 (1960) 135 P. Depommier and M. Chabre, J. Phys. Rad. 22 (1961) 657 V. V. G. Sastry, V. Lakshminarayana and S. Jwanananda, Nuclear Physics 56 (1964) 140
4.E
I
Nuclear Physics A98 (1967) 273--277; (~) North-Holland Publishing Co., Amsterdam
I
Not to be reproduced by photoprint or microfilm without written permission from the publisher
SPECTRUM SHAPE MEASUREMENT OF T W O BETA T R A N S I T I O N S IN 11lAg J. L E H M A N N *
Centre d'Etude de l'Energie Nucldaire, Mol, Belgique Received 13 F e b r u a r y 1967
Abstract: The spectrum shape factors of the 685 keV and 1028 keV beta transitions in the decay of ntAg have been measured. The results are: C(W) = CSt[I--(0.023±0.04)W] and C(W) ~ C~t[1--(0.0±0.01)W], respectively. The experimental results are compared with the predictions of the extreme single-particle shell model. E
RADIOACTIVITY: 24Na, mAg; measured E//, fl-spectrum shape.
]
1. Introduction
When analysing the first-forbidden beta transition in the decay of 1t tAg , Delabaye et al. 1,2) found a good agreement between the predictions of the extreme singleparticle shell model and experimental results, except for the spectrum shape of the f13 transition measured by Langer el al. 4) (see fig. 1). Consequently, we decided to remeasure the spectrum shape of the transition f13 with another type of spectrometer than the one used by Langer et al. We measured also the spectrum shape of the fil branch. 2. Experimental methods We have studied the two spectra of the 171 and/73 transitions (see fig. 1) with an intermediate image ]~-ray spectrometer of the Siegbahn-S15.tis type *t modified so as to permit measurements of 3-7 coincidences. The 3-detector is an anthracene crystal (1 cm diam and 0.5 cm thick) and the y-detector is a Nal(T1) crystal (2.54 cm x 2.54 cm). The influence of the spectrometer magnetic field on the photomultipliers is reduced by the use of lucite light pipes (30 cm long) and by three concentric #-metal shields. For the maximum magnetic field strength used in this study, no change higher than 0.5 ~ was detected on the pulseheight from the photomultipliers. The fast-slow coincidence circuit resolution time was adjusted at 50 nsec. The general controls and tests performed are described elsewhere 7). ,+ N o w at L o u v a i n University, Hdverl6-Louvain, Belgium. tt M a n u f a c t u r e d by L.K.B., Sweden. 273
274
J. LEHMANN
As a final test of our method, we have measured the allowed fl-spectrum shape factor of the 1.394 MeV/?-transition in the decay of 24Na in coincidence with the 4.12, 2.75 and 1.368 MeV ,,-ray lines. The results are shown in fig. 2. From this figure, one can conclude that the apparatus does not introduce an error larger than 1% in the measurement of a spectrum shape factor above 300 keV. 11lAg 64
47
A
i
B
54 418 '3
1/2 -
0,5'/.
685
8 '/.
log ft=7,3
"~2 785
1%
[og.f t = 8,8
~1 1028
91 '/.
Iogtt =7,8
5/2+ 610
[mo
419
£
I
343 5/2+ 243
\
1/2+ 111 Cd 48 63
[ I T (key)
Fig. 1. Decay scheme 10) o f m A g . The energies of the transitions (A) and levels are indicated in keV. The intensities (B) of the fl-transitions are from ref. lo).
N/p2F(Z,W)(W-Wo) 2
21 20
--o --o
.__0
"--0
0
--0
--
__
0
__
0---
0---
°
o
_0
1-
)
o
19 W(rne 2) i.5
2
2,5
3
Fig. 2. Spectrum shape factor of the 1393 keV/3-transition of 24Na.
The isotope ltXAg in the form of A g N O 3 was obtained t as a solution in HNO3; it was deposited by evaporation on an aluminized mylar film of about 500/,g/cm z. The resulting source had a diam of 2 m m and thickness of about 150 pg/cm 2. + Obtained from Amersham, England.
BETA
275
TRANSITIONS
3. Experimental results 3.1. T R A N S I T I O N O F 685 keV (/~3)
We have measured the 685 keV fl-transition in coincidence with the 343 keV 7-ray whose photopeak was selected by a single-channel pulse-height analyser (window width of 30 keV). As the//-branch under study amounts to only 8 % of the total fl-intensity, particular care had to be taken to determinate the random coincidences. The result of the measurements is presented in fig. 3 where we have plotted the quantity N
C ( w ) = P 2 F ( Z E ) ( W o - rV)2 ; [ Wo= 2.325
/
N / p2F(Z,W)(Wo-W) 2
/
/ / w0=2.33 200
// / / 180
_L_L_,_
/-
~
Wo =2,335
/ /
j
_
160 \ Wo=2.345 140
I
t4
1.5
1
I
1
I
I
I
I
1.6 1.7 1.8 1,9 2 Zl 22 Fig. 3. Spectrum shape factor of the 682 keV/33 transition of m A g .
I
2.3
W(mc 2)
C ( W ) is the spectrum shape factor, N the number of counts per unit momentum interval, F ( Z E ) the Fermi function, W o the end-point energy in mc 2 units, p the electron momentum in me units and W the electron energy in rnc a units. Restricting the possible variation of Wo to values yielding a physical behaviour of C(W) in the endpoint region 9), we obtain Wo = 685+_3 keV; the 3 keV error does not take into account possible calibration uncertainties irrelevant for the determination of C ( W ) [ref. 8)] and estimated to be about 10 keV. Fig. 3 shows C ( W ) for different values of W o. The spectrum shape factor obtained by this analysis can be described by the equation C ( W ) = C~t[1-(0.023-t-0.03)W]. 3.2. T R A N S I T I O N O F 1028 keV (/31)
Because of the influence of the//3 and flz transitions, the pure fll spectrum can only be measured at electron energies above 785 keV. It is possible, however, to extend the
276
J. LEHMANN
m e a s u r e m e n t s to lower energies if the results are corrected for the c o n t r i b u t i o n s o f the/73 and/72 transitions using a g r a p h i c a l m e t h o d . W e have studied in this w a y the /?-spectrum shape factor f r o m 500 k e V u p w a r d s . I n fig. 4 are shown the raw results (curve A ) a n d the same results corrected for the influence o f the lower-energy b e t a N I p2F(Z.W )(Wo-W )2
~
17C
~_
150
CURVE A CURVE B
"---e ---e
:z:~ ~
o __
Q.,..,_ o'~
0
0
0 __0 - - 0 - -
O--
0---
-0
130
W(mc 2) I
I
2.1
I
22
2,3
214
2'5
2r6
I
2~7
2B
Fig. 4. Spectrum shape factor of the 1024 keV/3t transition of mAg. o o o
14 I
o
o
131
o
o
o
o
o
o
o
o
o o
oo
o
o
o
o
o
o
o
o
o
o
o
o o
Wo=233
o
•
o
o o
12 [
o
o o
o
o
o
o
o
o
o o o
.I
o
13 [
o
o
o
o
o o
o o
o
o o
Oo
o
o
o
o °
o
o
0
o
o
o
o
o
o
o
o
o
-,y
o
o
o
- -
o o
o
o
o o
%o2 3z,
o o
o
12!
o
o
o
13
o
o
o %
o
o o
°
o
o
o
o
o
o
c~
o
o
°o
o o o °°
o o
o
o
o
o
o
Wo=
o o C{W)
o °
oo
o°
o o
o
o o
o o
o
o
o o
o
o o
o
o o
o
o
o
o
l
W(mc2)
o
o o
I Ii|F
2.347
o
o o
12~
o
o
12 j
Wo=2,36 oo
o
Fit. 5. Spectrum shape correction factor of the 682 keV fla transition of t11Ag for different values of I1~, after Langer et al. 4).
BETA TRANSITIONS
277
groups (curve B). F o r this correction, we have assumed that the spectrum shape factors o f the 685 keV/33 transition is allowed and that the 785 keV/32 transition has a unique shape; the errors which m a y be introduced by these simplifications are negligible within the accuracy of the experiment. The spectrum shape factor o f the 1.024 keV transition can be described by the equation
C ( W ) = C S t [ 1 - ( 0 . 0 0 + 0 . 0 1 ) W ] for W o = 1 0 2 8 + 3 keV.
4. Discussion of the P3 transition The spectrum shape factor for the 685 keV beta transition has already been investigated by Langer et al. 3) and f o u n d to be o f the f o r m C ( W ) = C S t ( 1 - 0 . 1 7 W ) . We have studied the variation of the best fit to their experimental results as a function of the end-point energy; the resulting curves are shown in fig. 5 for four particular choices o f Wo. In order to restrict the variation of W o, most authors reject the W o values giving unphysical behaviour of C ( W ) near the end-point energy. As Langer et al. 3) did not measure close to this end-point energy, their experimental result does not give firm restrictions u p o n Wo. As a consequence, any of the four sets of data presented on fig. 5 can be accepted on the basis of these data alone, and neither the linear slope stated by Langer et al. 3) nor the correction factor is unique. Moreover, one cannot find a value o f W o which gives an experimental correction factor in agreement with the model prediction 2), which is C ( W ) ~ C st. Our measurement gives a fit very close to this prediction. We can thus conclude that the new experimental situation gives a very good agreement with the extreme single-particle shell-model calculations.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
M. Delabaye, Ph.D. thesis, University of Louvain (1965) M. Delabaye, J. P. Deutsch and P. Lipnik, Nuclear Physics 80 (1966) 385 J. H. Hamilton, B. G. Petterson and J. M. Hollander, Ark. Fys. 18 (1960) 273 L. M. Langer and R. L. Robinson, Phys. Rev. 112 (1958) 481 P. Lipnik and J. W. Sunier, Nuclear Physics 53 (1964) 305 H. Daniel, C. Engler, G. Th. Kaschl and S. A. A. Zaidi, Phys. Lett. 12 (1964) 337 S. Andr6, J. Phys. Rev. 26 (1965) 161A F. T. Porter, F. Wagner and M. S. Freedman, Phys. Rev. 107 (1960) 135 P. Depommier and M. Chabre, J. Phys. Rad. 22 (1961) 657 V. V. G. Sastry, V. Lakshminarayana and S. Jwanananda, Nuclear Physics 56 (1964) 140