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A hindered E2 ground state transition in Po207
Nuclear Physics 45 (1963) 49---53; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission trom the publisher
A H I N D E R E D E2 G R O U N D S T A T E T R A N S r F I O N I N Po 2el G. ASTNER, I. BERGSTROM, L. ERIKSSON, U. F~GERQUIST, G. HOLM and A. PERSSON Nobel Institute of Physics, Stockholm 50, Sweden and Physics Department, Royal Institute of Technology, Stockholm 70, Sweden t
Received 25 March 1963 Abstract: The half-life of the'69 keV first excited state in Po*orhas been determined to be 205 :E 10 ns using a time-to-pulse-height converter to measure alpha-electron delayed coincidences. The 69 keV E2 ground state transition, interpreted as p~ --~ft, is retarded by a factor of eight as compared to the corresponding one in Pb2°L 1. Introduction
As is well known, electromagnetic transition rates may yield detailed information about the wave functions of nuclear states. It is therefore o f importance to collect lifetime data, particularly in regions where nuclear models are most easily applicable. One region of this kind, which has been extensively studied, is the lead region close to Pb 2°8 which consists of 82 protons and 126 neutrons. Here the most useful information in this respect has so far been obtained f r o m the systematics of the i} --, ft M4 transitions 1). E2 transitions are of special interest because o f their sensitivity to collective effects. In the lead region ground state transitions of this type occur between ft and p i states. A survey of such transitions in Pb, T1 and Hg has been made by BergstrCm et al. 2). One of these transitions (Pb 2°3) proved to be retarded by a factor of 6 as compared to the corresponding transition in Pb 2°7, while all the other transitions were enhanced. In Po 2°7 a state at 69 keV has been reported by Stoner 3). He shows that it decays to the ground state by an E2 transition. In an atomic-beam resonance experiment 4) the ground state spin has been found to be ~(ft)- It seems plausible to assume that the 69 keV state is the expected p~ state which, in analogy with the situation in Pb 2°5, is expected fairly close to the ground state. It is fed by alpha particles in the decay o f Rn 21x. Since a 69 keV E2 transition is strongly converted, it should be possible to obtain the half-life of this state in an alpha-electron delayed coincidence experiment. 2. Experimental Procedure and Resnlts Rn zll was produced by irradiating ThC14 with protons in the Uppsala synchrocyclotron. In spite of the low spallation cross section for Rn 211 at the maximum t This work has been supported by the Swedish Atomic Research Council and by the Air Research and Development Command of the United States Air Force, European Office. 49
50
o . AffrNEIt et al.
available energy o f 170 MeV, adequate sources were obtained through isotope separation. This was performed in the magnetic separator of the Nobel Institute o f Physics. For that purpose the irradiated ThC14 powder was dissolved in water in a glass vessel and the radon gas brought into the water vapor phase by shaking for I
1#
L Coihcidences Y.
s.ld
10~ 50
~o
200
250
300
350
400 Channel. number
Fig. 1. Half-life o f the first excited state in Po N~ obtained by delayed alpha-electron-coincidence,s. The R n szx source was prepared by isotope separation.
los
Coincidences
i: --J~--IS ns
f
}I ,{ i
,.oo./~,
lo'
ii ,i :i I I.
lOO
2;0
~o
3;o
3.
•
4~0 Channel number
Fig. 2. Half-life o f the 8round-state in Po t~s obtained by delayed electron-alpha-coincidences in the decay of Pb tl| . The difference in slope of the prompt curve in fig. 1 and fig. 2 is due to an asymmetric prompt curve.
ten minutes. Before shaking a proper amount of xenon carrier gas was introduced into the glass vessel. Since the sources were going to be used for coincidence measuremerits only, the separation was performed at full acceleration energy (70 keV). The rate of consumption of the carrier xenon gas determined the efficient separation time,
HINDERED T R A N S I T I O N
5|
IN Po I°7
which proved to be about ten minutes. The ions were collected on 2.5 mg/cm 2 aluminium foils. The strength of the sources obtained in this way was about 0.003 ~Cur. The alpha particles in the decay of R n 211 w e r e detected in a 2 mm thick CsI crystal and the electrons in a 0.1 mm plastic scintillator. The detectors were mounted face to face and the pulses fed to a time-to-pulse-height converter 5). The time spectrum was recorded by a R I D L 400 channels pulse-height analyser. Time calibration was performed using a Tektronix 180A time marker as standard. The half-life obtained from seven different runs is 205+ 10 ns, where the uncertainty in the time calibration is estimated to be about 2 ns. A typical run is shown in fig. 1.
•
L
//I s,s7
I Stable
/ ' 7 72h zLt2" " la~+'~s
/ / /
//1
[~78 le.SY. ~S
~7~ °
//// 0.23(
o.s~
.el., Pb 207
Fig. 3. Decay scheme o f R n s~. Only details o f interest for the discussion in this p a p e r are included. F o r
details the reader is referred to ref. e). As a comparison ThB was run with the same settings. The 0.30/zs decay of Po 21~ was obtained in reverse as shown in fig. 2 because here the a-decay depopulates the delayed state. The half-life obtained (305 + 5 ns) is in good agreement with previously reported values 6). The 205 ns half-life associated with the decay of Rn 211 is attributed to the 69 keV level in Po 2°: for the following reasons. The state is observed in a-e- delayed coincidence. In the decay of Rn zl i ~-cmission is known to take place from Po 211 to Pb 2°7, from At 211 to Bi 2°~ and from Rn 211 to Po 2°~ (see fig. 3). No state populated in Pb ~°7 has a half-life of the same order of magnitude as the observed value. In the At 2tl to Bi z°7 decay on the other hand, no excited states are populated. Therefore, the isomeric state is assigned to Po 2°7. Only 0.5~o o f all Rn 2H decays lead to the 234 keV state while 17.8~o lead to the 69 keV State. The observed coincidence rate is in accordance with the assumption that the 69 keV state is responsible for the observed half-life. The best way o f testing the proposed assignment would be to select the electrons in a ]]-ray spectrometer. Using a double-focusing (r o = 15 cm) 120° sector magnet 7) a value was obtained which because of the poor statistics can only be said to be of the right order o f magnitude. However, the assignment that the 69 keV state in Po 2°7 has a half-life of 205 ns is supported.
52
O. ASTNZR e t al.
3. Discession The measured half-life of 205 ns yields a squared matrix element for the E2 transition of 0.12 relative to the ft "-' P~ transition in Pb 2°7. (A calculated conversion coefficient, u -- 39 has been used. Here as in fig. 4 a statistical factor S = 1 for ft ~ P~ and S --- 3 for p~ --, f! transitions has been included.) Thus the experimental transition rate, as in the case of Pb 2°3, is smaller than the single particle estimate which is unusual for E2 transitions. In fig. 4 the square of the matrix elements of E2 transitions where the single particle part can be interpreted as a f t ~ - P ~ neutron transition have been plotted relative to that of Pb 2°'/. ~vll 2 '
~
'lO 8
Nl~e°' s
t HOa°?
4 2
i ,Tt"ol
1
~S ~8
~2
0 pbzo~
0.1 ~08
~t05
0.02 ~01 0~08
L........•
7~
7~
~0
e~
8~
e~
e~
proton number
Fig. 4. Relative matrix elements o f E2 g r o u n d state transitions o f the type ft ~ - P~ in the lead region. F o r the sake of completeness also two eases o f odd T1 nu¢leides are included (within dashed lines) as well as one odd case in Bi teQ. I n the Tl-cases it is reasonable x,t) that these transitions are o f the same type as in the odd mass nucleides. I n the ease o f Bi tes the particle configurations o f the two states involved are n o t satisfactorily known.
The general trend of the plot is the well known enhancement of the E2 transition rate with increasing number of particles or holes outside closed shells. This can be understood in terms of the increase of collective admixture which occurs when the energy of the one phonon state decreases. The other feature of general interest is the fact that for a few transitions IMI 2 : IMip2b~O7is smaller than unity. Such a reduction in the single particle transition rate when nucleons are added to or removed from closed shells is caused by the pairing correlations. The reduction factor can be calculated for single closed shell nuclei on the basis of the work by Kisslinger and Sorensen s). However, the more general problem of treating nuclei which contain
HINDERED TRANSITIONIN Pos°?
53
both extra-core protons and neutrons has not yet been undertaken. The vibrational admixture must also be taken into account. Therefore, although there is a striking trend in the systematics of the experimental information, it is difficult to infer any numerical result from the present material. It is, in conclusion, interesting to note that there exist several retarded E2 ground state transitions in the lead region. However, more experimental evidence on this point is desirable, particularly for nuclei relatively close to Pb z°8. References I. BergstrOm and G. Andersson, Arkiv f. Fysik 12 (I 957)415 I. Bergstr0m, C. -J. Herrlander, P. Thieberger, and J. Uhler, Arkiv f. Fysik 20 (1961) 93 A. W. Stoner, Report UCRL-3471 (1956, unpublished) S. Axensten and C. M. Olsmats, Arkiv f. Fysik 19 (1961) 461 P. Thieberger, Arkiv f. Fysik 22 (1962) 127 Nuclear Data Sheets, National Academy of Sciences (National Research Council, Washington D.C.) 7) G. Asmer, I. Bergstr~m, L. Eriksson, U. Fiigerquist, and ~. Persson, to be published 8) L. S. Kisslinger andiR. A. Sorenson, Mat. Fys. Medd. Dan. Vid. Selsk. 32, No. 9 (1960)
1) 2) 3) 4) 5) 6)
A H I N D E R E D E2 G R O U N D S T A T E T R A N S r F I O N I N Po 2el G. ASTNER, I. BERGSTROM, L. ERIKSSON, U. F~GERQUIST, G. HOLM and A. PERSSON Nobel Institute of Physics, Stockholm 50, Sweden and Physics Department, Royal Institute of Technology, Stockholm 70, Sweden t
Received 25 March 1963 Abstract: The half-life of the'69 keV first excited state in Po*orhas been determined to be 205 :E 10 ns using a time-to-pulse-height converter to measure alpha-electron delayed coincidences. The 69 keV E2 ground state transition, interpreted as p~ --~ft, is retarded by a factor of eight as compared to the corresponding one in Pb2°L 1. Introduction
As is well known, electromagnetic transition rates may yield detailed information about the wave functions of nuclear states. It is therefore o f importance to collect lifetime data, particularly in regions where nuclear models are most easily applicable. One region of this kind, which has been extensively studied, is the lead region close to Pb 2°8 which consists of 82 protons and 126 neutrons. Here the most useful information in this respect has so far been obtained f r o m the systematics of the i} --, ft M4 transitions 1). E2 transitions are of special interest because o f their sensitivity to collective effects. In the lead region ground state transitions of this type occur between ft and p i states. A survey of such transitions in Pb, T1 and Hg has been made by BergstrCm et al. 2). One of these transitions (Pb 2°3) proved to be retarded by a factor of 6 as compared to the corresponding transition in Pb 2°7, while all the other transitions were enhanced. In Po 2°7 a state at 69 keV has been reported by Stoner 3). He shows that it decays to the ground state by an E2 transition. In an atomic-beam resonance experiment 4) the ground state spin has been found to be ~(ft)- It seems plausible to assume that the 69 keV state is the expected p~ state which, in analogy with the situation in Pb 2°5, is expected fairly close to the ground state. It is fed by alpha particles in the decay o f Rn 21x. Since a 69 keV E2 transition is strongly converted, it should be possible to obtain the half-life of this state in an alpha-electron delayed coincidence experiment. 2. Experimental Procedure and Resnlts Rn zll was produced by irradiating ThC14 with protons in the Uppsala synchrocyclotron. In spite of the low spallation cross section for Rn 211 at the maximum t This work has been supported by the Swedish Atomic Research Council and by the Air Research and Development Command of the United States Air Force, European Office. 49
50
o . AffrNEIt et al.
available energy o f 170 MeV, adequate sources were obtained through isotope separation. This was performed in the magnetic separator of the Nobel Institute o f Physics. For that purpose the irradiated ThC14 powder was dissolved in water in a glass vessel and the radon gas brought into the water vapor phase by shaking for I
1#
L Coihcidences Y.
s.ld
10~ 50
~o
200
250
300
350
400 Channel. number
Fig. 1. Half-life o f the first excited state in Po N~ obtained by delayed alpha-electron-coincidence,s. The R n szx source was prepared by isotope separation.
los
Coincidences
i: --J~--IS ns
f
}I ,{ i
,.oo./~,
lo'
ii ,i :i I I.
lOO
2;0
~o
3;o
3.
•
4~0 Channel number
Fig. 2. Half-life o f the 8round-state in Po t~s obtained by delayed electron-alpha-coincidences in the decay of Pb tl| . The difference in slope of the prompt curve in fig. 1 and fig. 2 is due to an asymmetric prompt curve.
ten minutes. Before shaking a proper amount of xenon carrier gas was introduced into the glass vessel. Since the sources were going to be used for coincidence measuremerits only, the separation was performed at full acceleration energy (70 keV). The rate of consumption of the carrier xenon gas determined the efficient separation time,
HINDERED T R A N S I T I O N
5|
IN Po I°7
which proved to be about ten minutes. The ions were collected on 2.5 mg/cm 2 aluminium foils. The strength of the sources obtained in this way was about 0.003 ~Cur. The alpha particles in the decay of R n 211 w e r e detected in a 2 mm thick CsI crystal and the electrons in a 0.1 mm plastic scintillator. The detectors were mounted face to face and the pulses fed to a time-to-pulse-height converter 5). The time spectrum was recorded by a R I D L 400 channels pulse-height analyser. Time calibration was performed using a Tektronix 180A time marker as standard. The half-life obtained from seven different runs is 205+ 10 ns, where the uncertainty in the time calibration is estimated to be about 2 ns. A typical run is shown in fig. 1.
•
L
//I s,s7
I Stable
/ ' 7 72h zLt2" " la~+'~s
/ / /
//1
[~78 le.SY. ~S
~7~ °
//// 0.23(
o.s~
.el., Pb 207
Fig. 3. Decay scheme o f R n s~. Only details o f interest for the discussion in this p a p e r are included. F o r
details the reader is referred to ref. e). As a comparison ThB was run with the same settings. The 0.30/zs decay of Po 21~ was obtained in reverse as shown in fig. 2 because here the a-decay depopulates the delayed state. The half-life obtained (305 + 5 ns) is in good agreement with previously reported values 6). The 205 ns half-life associated with the decay of Rn 211 is attributed to the 69 keV level in Po 2°: for the following reasons. The state is observed in a-e- delayed coincidence. In the decay of Rn zl i ~-cmission is known to take place from Po 211 to Pb 2°7, from At 211 to Bi 2°~ and from Rn 211 to Po 2°~ (see fig. 3). No state populated in Pb ~°7 has a half-life of the same order of magnitude as the observed value. In the At 2tl to Bi z°7 decay on the other hand, no excited states are populated. Therefore, the isomeric state is assigned to Po 2°7. Only 0.5~o o f all Rn 2H decays lead to the 234 keV state while 17.8~o lead to the 69 keV State. The observed coincidence rate is in accordance with the assumption that the 69 keV state is responsible for the observed half-life. The best way o f testing the proposed assignment would be to select the electrons in a ]]-ray spectrometer. Using a double-focusing (r o = 15 cm) 120° sector magnet 7) a value was obtained which because of the poor statistics can only be said to be of the right order o f magnitude. However, the assignment that the 69 keV state in Po 2°7 has a half-life of 205 ns is supported.
52
O. ASTNZR e t al.
3. Discession The measured half-life of 205 ns yields a squared matrix element for the E2 transition of 0.12 relative to the ft "-' P~ transition in Pb 2°7. (A calculated conversion coefficient, u -- 39 has been used. Here as in fig. 4 a statistical factor S = 1 for ft ~ P~ and S --- 3 for p~ --, f! transitions has been included.) Thus the experimental transition rate, as in the case of Pb 2°3, is smaller than the single particle estimate which is unusual for E2 transitions. In fig. 4 the square of the matrix elements of E2 transitions where the single particle part can be interpreted as a f t ~ - P ~ neutron transition have been plotted relative to that of Pb 2°'/. ~vll 2 '
~
'lO 8
Nl~e°' s
t HOa°?
4 2
i ,Tt"ol
1
~S ~8
~2
0 pbzo~
0.1 ~08
~t05
0.02 ~01 0~08
L........•
7~
7~
~0
e~
8~
e~
e~
proton number
Fig. 4. Relative matrix elements o f E2 g r o u n d state transitions o f the type ft ~ - P~ in the lead region. F o r the sake of completeness also two eases o f odd T1 nu¢leides are included (within dashed lines) as well as one odd case in Bi teQ. I n the Tl-cases it is reasonable x,t) that these transitions are o f the same type as in the odd mass nucleides. I n the ease o f Bi tes the particle configurations o f the two states involved are n o t satisfactorily known.
The general trend of the plot is the well known enhancement of the E2 transition rate with increasing number of particles or holes outside closed shells. This can be understood in terms of the increase of collective admixture which occurs when the energy of the one phonon state decreases. The other feature of general interest is the fact that for a few transitions IMI 2 : IMip2b~O7is smaller than unity. Such a reduction in the single particle transition rate when nucleons are added to or removed from closed shells is caused by the pairing correlations. The reduction factor can be calculated for single closed shell nuclei on the basis of the work by Kisslinger and Sorensen s). However, the more general problem of treating nuclei which contain
HINDERED TRANSITIONIN Pos°?
53
both extra-core protons and neutrons has not yet been undertaken. The vibrational admixture must also be taken into account. Therefore, although there is a striking trend in the systematics of the experimental information, it is difficult to infer any numerical result from the present material. It is, in conclusion, interesting to note that there exist several retarded E2 ground state transitions in the lead region. However, more experimental evidence on this point is desirable, particularly for nuclei relatively close to Pb z°8. References I. BergstrOm and G. Andersson, Arkiv f. Fysik 12 (I 957)415 I. Bergstr0m, C. -J. Herrlander, P. Thieberger, and J. Uhler, Arkiv f. Fysik 20 (1961) 93 A. W. Stoner, Report UCRL-3471 (1956, unpublished) S. Axensten and C. M. Olsmats, Arkiv f. Fysik 19 (1961) 461 P. Thieberger, Arkiv f. Fysik 22 (1962) 127 Nuclear Data Sheets, National Academy of Sciences (National Research Council, Washington D.C.) 7) G. Asmer, I. Bergstr~m, L. Eriksson, U. Fiigerquist, and ~. Persson, to be published 8) L. S. Kisslinger andiR. A. Sorenson, Mat. Fys. Medd. Dan. Vid. Selsk. 32, No. 9 (1960)
1) 2) 3) 4) 5) 6)