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Core-excitations in 209 Po
Nuclear Physics A 665 Ž2000. 318–331
Core-excitations in 209 Po A.R. Poletti a,1, G.D. Dracoulis b, A.P. Byrne b,2 , A.E. Stuchbery b, B. Fabricius b, T. Kibedi ´ b, P.M. Davidson b b
a Department of Physics, UniÕersity of Auckland, PriÕate Bag 92019, Auckland, New Zealand Department of Nuclear Physics, Research School of Physical Sciences and Engineering, Australian National UniÕersity, Canberra, ACT 0200, Australia
Received 27 April 1999; received in revised form 12 July 1999; accepted 11 October 1999
Abstract The properties of high spin states in 209 Po have been investigated using the 204 Hg Ž9 Be,4n. Po reaction at a bombarding energy of 62 MeV. Decay properties for states in 209 Po up to an excitation energy of 8392 keV and spins up to J s Ž47r2. have been deduced. The mean life of the level at 4266 keV was determined as 172Ž5. ns and a limit of - 15 ns was determined for that at 5504 keV. The level scheme is compared with predictions of multi-particle shell model calculations. The lowest core excited state is confirmed to be the 31r2y state at 4266 keV. Another core excited state lies at 5356 keV, while above 5.5 MeV the yrast line is exclusively composed of such excitations. q 2000 Elsevier Science B.V. All rights reserved.
209
Keywords: NUCLEAR REACTIONS 204 HgŽ9 Be,4n.209 Po, E s 55–65 MeV; Measured gg Ž t ., Eg , Ig Ž u ., Ig Ž E,t .; Linear polarisation; 209 Po deduced high spin levels J, p , T1r2 ; Enriched target; Pulsed beam; Compton suppressed detectors; Ge hyper pure detectors in linear polarimeter; NUCLEAR STRUCTURE 209 Po; Calculated levels; Semi-empirical shell model
1. Introduction Over twenty years ago the Stockholm group established the high spin level scheme of Po up to an energy of 4354 keV, provided a shell model interpretation of the scheme and showed that the 31r2y isomer at 4266 keV was a core excited state ŽBergstrom ¨ et al., Rensfelt et al. w1,2x.. Since that time, there has been no further attempt to investigate 209
1 2
Visiting Scientist, Laboratori Nazionali Legnaro, 1998. Joint appointment, Department of Physics, Faculties, Australian National University.
0375-9474r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 Ž 9 9 . 0 0 4 2 1 - 2
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319
the scheme to higher excitation energies and establish the positions of other core excited states. This is surprising because 209 Po, with two protons and one neutron hole outside the doubly closed shell 208 Pb126 core is a particularly simple system and the results of multiparticle shell model calculations are readily compared to the experimental data. The magnetic moment of the 17r2y and 31r2y isomers were determined by Hausser et al. ¨ w3x, and Rensfelt et al. w2x respectively, while the quadrupole moment of the 17r2y state was measured by Dafni et al. w4x. Martin w5x summarises all nuclear structure information on 209 Po as known up to 1991. No reports relevant to the subject of the present work have been published since. In this paper we report the extension of the high spin level scheme of 209 Po to an excitation energy of 8391 keV and a spin of Ž47r2y. . The results have been interpreted in terms of the multi particle shell model and the role played by core excited states along the yrast line has been determined. The data relevant to 209 Po has been obtained by analyses of experimental results from an investigation of the high spin states of 208 Po. That work has already been published w6x as have the results for the nuclei 205,206 Pb and 204,205 Hg Žsee Refs. w7,8x. which were obtained from the same data set.
2. Experimental procedure Details concerning the different experiments are summarized in the first paper in this series w7x. The prime aim of the experiments had been to investigate the high spin structure of 208 Po using the 204 HgŽ9 Be, 5n.208 Po reaction. Following an excitation function measurement, a bombarding energy of 62 MeV, which optimized the population of 208 Po, was chosen for all subsequent experiments. Pulsed beam– g-timing and g – g-time measurements using the CAESAR array w9x were carried out as well as angular distribution measurements using a single moveable detector and a linear polarization measurement using a three crystal polarimeter. Although 209 Po was weakly populated compared to 208 Po with only 9% of its intensity, the high bombarding energy increased the relative population of the high spin levels in 209 Po. Despite its relative weakness at the energies used, the Ž9 Be, 4n. reaction is nevertheless the best fusionevaporation reaction for the population of these high spin levels.
3. Results and level schemes The level scheme deduced from our work is given in Fig. 1 in which level energies are given to the nearest keV. For completeness, Table 1 lists all electromagnetic transitions Žinvolving high spin states. assigned to 209 Po from the present and previous work w1,2x, together with their assigned position and precise energies. Relative intensities observed in the present work together with the a 2 coefficient in the Legendre polynomial expansion describing the angular distribution of each gamma ray transition are presented. In cases where they could not be extracted reliably from the angular distribution data, intensities have been inferred from coincidence spectra. The deduced
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
320
Fig. 1. The high spin structure of 209 Po as observed in this and previous work.
energy levels are listed in Table 2, together with branchings deduced from this and previous works. All of the levels above 4500 keV are new. The results of the linear polarization measurements are given in Table 3. The bases of spin-parity assignments are discussed in Section 3.6 below. 3.1. The
209
Po leÕel scheme
Ten nuclei were populated to a significant extent in this study w7x, hence cross contamination of coincidence spectra has been an especially severe problem. In Fig. 2, however we present three spectra which between them clearly show all of the transitions which we ascribe to 209 Po and which lie above the 17r2y isomer at 1472.9 keV. The upper panel shows the spectrum of transitions which are early with respect to the 782 keV gate: all transitions assigned as feeding the 17r2y isomer are clearly seen. In the middle panel is the spectrum of transitions which are early with respect to the 1289 keV gate. The prominent peaks in this spectrum arise from transitions which ultimately feed
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331 Table 1 Electromagnetic transitions observed in
209
Po in the
Energy ŽkeV.1
g-ray intensity
Initial level
Final level
54.9 Ž88.6. 90.9 Ž92.1. 96.9 137.1 148.0 161.5 176.8 185.6 206.5 265.6 275.2 299.9 420.1 440.3 444.7 465.1 467.1 519.9 545.1 548.0 557.2 574.6 603.0 643.9 654.0 694.3 729.4 752.8 782.0 824.6 953.8 1028.7 1108.6 1231.3 1238.0 1289.0 1297.3 1304.1 1377.6 1771.2
– – – – 70 350 47 35 109 300 470 27 120 30 52 26 40 25 30 40 1000 215 450 40 670 260 60 190 80 50 980 145 45 50 80 25 110 230 90 27 30 95
1472.9 4354.2 1418.0 2030.1 4265.6 2167.2 5503.6 6464.1 4531.1 4354.2 2976.7 4531.1 6739.3
1418.0 4265.6 1327.1 1938.0 4168.6 2030.1 5355.7 6302.6 4354.2 4168.6 2770.2 4265.2 6464.1
7159.4 7247.8
6739.3 6807.5
1938.0
1472.9
1938.0 545.1 4168.6 2030.1 6807.5 2770.2 3620.6
1418.0 0.0 3620.6 1472.9 6233.0 2167.2 2976.7
2167.2 6233.0
204
321
Hgq9 Be reaction at 62 MeV 100= a2
100= a4
Multipolarity 2 E2 M1 E2 M1 M1 M1 E1 E2 M1 E1 M1 ŽM1. M1
y03Ž22.
05Ž01. y24Ž11. y12Ž04. y02Ž12. y26Ž07.
ŽM1rE2. ŽM1rE2. 01Ž05.
ŽM1.
28Ž03. y26Ž04.
E2 E2 M1rE2 M1rE2 ŽM1. E1 M1rE2
1472.9 5503.6
y46Ž12.
E2 M1
1327.1 5355.7 7693.1
545.1 4531.1 6739.3
00Ž01. y12Ž07. 10Ž36.
E2 M1 ŽE2.
6464.1 8390.7 5503.6 4265.6 2770.2 6807.5 4354.2 6302.6
5355.7 7159.4 4265.6 2976.7 1472.9 5503.6 2976.7 4531.1
y03Ž02. y29Ž05. y32Ž03.
y16Ž22. 10Ž07. 09Ž18.
00Ž17.
y18Ž10. y30Ž26.
ŽE3. ŽE1. E3 E3 E3 ŽE2. E3 ŽE3.
1 Uncertainties on transition energies are "0.1 keV Ž"0.2 keV. for lines less than Žgreater than. 1 MeV and an intensity of greater than 50. For weak lines the corresponding uncertainties are "0.2 keV and "0.4 keV respectively. 2 See text for discussion of the bases for these assignments.
the 31r2y isomer at 4265.6 keV. Although the spectrum in coincidence with the prompt gate at 644 keV in the lower panel is dominated by transitions lower in the scheme, the
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
322 Table 2 Energy levels in this work.
209
Po excited in the
204
Level
Jp
0.0 545.1 1327.1 1418.0 1472.9 1938.0
1r2y 5r2y 9r2y 13r2y 17r2y 17r2y
2030.1
19r2y
2167.2
21r2y
2770.2
23r2q
2976.7 3620.6 4168.6 4265.6
25r2q 27r2q 29r2q 31r2y
4354.2
31r2y
-10 ns
4531.1
33r2y
-10 ns
5355.7 5503.6
35r2y 37r2q
- 5 ns -15 ns
6233.0 6302.6 6464.1
39r2q Ž39r2q . Ž41r2q .
6739.3 6807.5
Ž43r2q . Ž41r2q .
7159.4 7247.8 7693.1 8390.7
Ž45r2q . Ž43r2q . Ž47r2q . Ž47r2y .
Hgq9 Be reaction at 62 MeV. An asterisk signifies a new level from
Mean-life
a
36Ž1.ns 134Ž7.ns
; 3.6 ns
-10 ns 172Ž6. ns
-10 ns
Transitionsb 545.1 782.0 90.9 54.9 465.1 38Ž8.% 92.1c 16Ž2.% 137.1 65Ž4.% 603.0 88Ž2.% 206.6 643.9 548.0 96.9 c 30Ž5.% 88.6 c 37Ž3.% 176.8 80Ž4.% 824.6 148.0 30Ž4.% 729.1 1771.2 161.5 27Ž5.% 275.2 574.6 60Ž5.% 420.1 440.3 953.8 1231.2
519.9 62Ž8.% 557.2 c 84Ž2.% 694.3 35Ž4.% 1297.3 12Ž2.%
1289.0 c 70Ž5.% 185.6 c 58Ž3.% 265.6 20Ž4.% 1238.0 70Ž4.%
1108.6 73Ž5.% 1304.1 40Ž5.%
1377.6 c 5Ž2.% ) ) ) ) ) ) ) ) ) ) ) )
a Limits on mean lives are from the present work. Mean lives are from Ref. w5x, except for that of the 4265.6 keV level which is an average of the present result and that given in Ref. w1x. b Percentages refer to gamma ray branchings except where specified. c The branchings refer to the total transition intensity for each branch.
presence of many lines placed above 4300 keV demonstrates that a substantial fraction of the decay intensity bypasses the 31r2y isomer. ŽGamma ray energies shown in Figs. 2 and 3 are given to the nearest keV.. 3.2. LeÕels up to the 4354 keV state We confirm the level scheme as reported in Refs. w1,2x. Coincidences observed between the 137.1 keV and 519.9 keV lines demonstrate that the 17r2y level at 1938.0
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331 Table 3 Linear polarization measurements in
209
323
Po
Energy
100= a 2
100= Pex
100= Ptha
265.6 275.2 545.1 548.0 557.2 643.9 729.4 782.0 824.6 953.8 1289.0 1297.3
y02Ž12. y26Ž07. y03Ž02. y29Ž05. y32Ž03. y26Ž04. y46Ž12. 00Ž01. y12Ž07. 10Ž36. 10Ž07. c 09Ž18. e
y71Ž60. y83Ž26. y08Ž08. y19Ž23. 15Ž08. y46Ž17. y86Ž27. 05Ž05. y14Ž24. y37Ž116. 48Ž34. 41Ž83.
y03Ž18. y35Ž08. y04Ž03. y38Ž06. y41Ž03. y35Ž05. y56Ž12. 00Ž02. y17Ž09. 15Ž60. 62Ž32. d 100Ž89. d
Assignment M1 E2 b M1rE2 M1rE2 M1rE2 M1 E2 b M1
Mixing ratio
q0.53Ž05. b or 1.67Ž16. b
E3 E3
a
If a4 is neglected, Pth s 3 az 2 rŽ2y a 2 . for pure M1 or E2 transitions while Pth sy3a 2 rŽ2y a 2 . for pure E1 or M2 transitions. If a6 is neglected, Pth s Ž2 a 2 y5a4 .rŽ2y a 2 q0.75a 4 . for pure E3 transitions. The values given in this column are for pure M1 or E2 transitions except for the 1289.0 and 1297.3 keV transitions which are for pure E3. b Bergstro¨ m et al. c 100= a 4 sy18Ž10.. d E3 transition. e 100= a4 sy30Ž26..
keV is fed from the 2030.1 keV level via a 92.1 keV transition which is obscured by the 92.4 keV polonium X-ray line. There is no evidence of direct feeding of the 1938.0 keV level from either the 2167.2 or 2770.2 keV levels. 3.3. The leÕels associated with the 1238.0 keV transition Transitions coincident with a prompt gate at 1238 keV are shown in the middle panel of Fig. 3 and show the major feeding transitions. The 1238.0 keV transition which directly populates the 31r2y isomer defines a level at 5503.6 keV which is in turn populated by transitions of 729.4 and 1304.1 keV, defining levels at 6233.0 and 6807.5 keV respectively. The latter level populates that at 6233.0 keV via a transition of 574.6 keV and is in its turn populated by a transition of 440.3 keV. 3.4. The 4531.1 keV leÕel and associated transitions and leÕels The major branch from the level at 4531.1 keV is the 176.8 keV transition to the level at 4354.2 keV. The strongest transition, of 185.6 keV, from this latter level bypasses the 31r2y isomer at 4265.6 keV. In addition to the 1238.0 keV transition, the 31r2y isomer is however populated by weak transitions from the 4354.2 and 4531.1 keV levels with energies of 88.6 and 265.6 keV respectively. ŽThe existence of an 88.6 keV transition is inferred from coincidence relationships.. A strong 824.6 keV transition Žsee the lower panel of Fig. 3. defines a level at 5355.7 keV which is fed in parallel by transitions of 148.0 keV and 1108.6 keV. The former transition provides a connecting path to transitions which feed the 5503.6 keV level, while the latter defines a level at 6464.1 keV. This level is also de-excited by a transition of 161.5 keV which populates a
324
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
Fig. 2. Representative coincidence spectra illustrating the decay of the high spin states in 209 Po. The top panel shows the transitions which lie above the isomeric levels at 1418 and 1473 keV. Middle panel: all of the transitions placed above the 31r2y isomer at 4266 keV are labelled, as are six others. Although we were unable to place the following transitions: those of 654, 752 and 1029 keV predominantly feed the isomer, while those of 300, 444 and 467 keV largely bypass it. Bottom panel: for the transitions lying high in the scheme, this shows those which populate the levels at 4531 and 4354 keV, thereby largely bypassing the 31r2y isomer at 4266 keV.
level at 6302.6 keV which in turn is de-excited by a transition of 1771.2 keV to the level at 4531.1 keV. The upper panel of Fig. 3 displays the spectrum of gamma rays in prompt coincidence with a gate set on the 1771.2 keV transition. A cascade of three transitions which feed the 6464.1 keV level defines higher states at 6739.3, 7159.4 and 8390.7 keV which are respectively de-excited by transitions of 275.2, 420.1 and 1231.3 keV. A transition of 953.8 keV in coincidence with that of 275.2 keV defines a level at 7693.1 keV. All four transitions are seen in the prompt gate set on the 824.6 transition Žlower panel, Fig. 3.. 3.5. Mean life of the 4265.6 keV leÕel, lifetime limits We confirmed the measured mean life of the 4265.8 keV level. This was determined as t s 172Ž5. ns from a weighted average of fits to the time spectra of the 1289, 603 and 207 keV transitions, in excellent agreement with the mean life of 170Ž4. ns determined
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325
Fig. 3. Spectra further illustrating the decay of the high spin states of 209 Po. Middle panel: the 1238 keV transition directly populates the 31r2y isomer at 4266 keV. Its major feeding transitions are labelled. The 109 keV line arises from the 109–1236 keV cascade in 19 F. Top and bottom panels: the 1771 and 825 keV transitions carry a major part of the decay flux from the high lying levels.
by Bergstrom ¨ et al. w1x. The time spectrum of the 1289 keV transition is illustrated in Fig. 4. A limit on the mean life of the level at 5503.6 keV was determined as t - 15 ns from the time spectrum of the 825 keV gate. The gates set on the 1238.0 and 148.0 transitions immediately depopulating the isomer were heavily contaminated. Limits on mean lives of other transitions and present and previous measurements of mean lives are given in Table 2. 3.6. Spin and parity assignments Spin-parity assignments are based on the results of several different measurements. 1. Angular distributions of gamma rays ŽTables 1 and 2.. 2. Linear polarizations of gamma rays with energies greater than approximately 250 keV ŽTable 3..
326
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
Fig. 4. Time spectrum of the 1289 keV transition.
3. Mean lives and lifetime limits ŽTable 2.. 4. Intensities and intensity balances of gamma rays ŽTable 1 and intensities obtained from relevant coincidence spectra.. In addition to confirming several previous multipolarity assignments, multipolarities were obtained for the newly placed transitions of 148.0, 161.5 and 176.8 keV from total conversion coefficient measurements. The total conversion coefficient, a T s 1.7Ž6., of the 176.8 keV transition is consistent only with M1. ŽFor 176.8 keV, a T ŽM1. s 2.34 and a T ŽE2. s 0.75.. This and the lack of any transitions to states of spin less than 31r2 implied a spin-parity assignment of 33r2y for the level at 4531.1 keV. Linear polarization and angular distribution measurements showed the 824.6 keV transition to be stretched and M1, fixing the level at 5355.7 keV as 35r2y. For the 148.0 keV transition, a T - 0.37 and hence it is E1. ŽFor 148.0 keV, a T ŽE1. s 0.17, a T ŽM1. s 3.85 and a T ŽE2. s 1.46.. This E1 assignment and the upper limit on the mean life for the 5503.6 keV level of t - 15 ns are consistent with a spin-parity assignment of 37r2q to this level and an E3 character for the 1238.0 keV transition. The measured linear polarization and angular distribution of the 729.4 keV transition, consistent with stretched M1, further imply the spin-parity of the 6233.0 keV level is 39r2q. For the higher lying levels, assignments are less certain. The total conversion coefficient, a T s 1.4Ž5., for the 161.5 keV transition is consistent with M1rE2. ŽFor 161.5 keV, a T ŽM1. s 3.01 and a T ŽE2. s 1.05.. This is consistent with spin-parity assignments of Ž41r2q. and Ž39r2q. to the levels at 6464.1 and 6302.6 keV respectively and E3 assignments to both of the 1771.2 and 1108.6 keV transitions. The linear polarization data suggests that the 275.2 keV transition is stretched and M1. The 6739.3 keV level is thus likely to Ž43r2q. . For the remaining five high lying levels the suggested spins and parities are consistent with the decay scheme which has been established, but definitive information on spins and parities is lacking. 4. Discussion 4.1. Empirical Shell Model (ESM) calculations The Empirical Shell Model Žsee for instance, Refs. w6,7,10x. has been used to interpret the observed nuclear structure of 209 Po. Calculations were carried out for two
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327
Fig. 5. The single-particle orbits used in the ESM calculations.
classes of states: those arising from the valence particles alone and those which occur as a result of core excitation. Fig. 5 illustrates the orbitals which were considered, while Table 4 lists the theoretical levels identified with those experimentally observed. Fig. 6 gives an overview of the calculated level energies together with their spins and parities and compares these properties to those of the experimentally determined levels. 4.1.1. Valence particle states All configurations in which the two protons were in any of the three lowest proton particle orbitals outside the 208 Pb closed core were considered. These were the 1h 9r2 , 2f 7r2 and 1i 13r2 orbitals. The neutron hole was allocated to any of the four neutron-hole orbitals, that is to the 3p1r2 , 2f 5r2 , 3p 3r2 and 1i 13r2 orbitals. ŽThe calculations did not include mixing between configurations containing different orbitals.. 4.1.2. Core excited states Table 4 shows that there are a relatively small number of configurations involved in the lowest core excited states. These entailed the excitation of a neutron across the energy gap to the 2g 9r2 or 1j15r2 orbitals and involved just one proton configuration which was p Žh 9r2 i 13r2 .. For the levels above that at 6233.0 keV, the spins and parities are those of the corresponding theoretical levels. Their association with the experimental levels can only be tentative. 4.1.3. Comparison of the ESM calculations with the leÕel scheme The levels arising from the valence configurations are all well reproduced by the ESM calculations which are in good agreement with those of Refs. w1,2x where the two calculations overlap. The ESM calculation also give a good account of the ground state and first excited state energies and also agrees well with the energy of the 33r2y state found to lie at 4531.1 keV. Bergstrom ¨ et al. w1,2x had already shown that the lowest lying core excited state Ž J p s 31r2y . which entered the yrast line at an energy of 4266 keV arose from the . Ž . Ž y2 . Ž . n Žpy2 1r2 g 9r2 p h 9r2 i 13r2 configuration. The n p 1r2 j15r2 p h 9r2 i 13r2 configuration
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
328
Table 4 Experimental and theoretical level energies in Energy ŽkeV. experiment
J
p
209
Po Configurationa
Energy ŽkeV. theory present y
0.0 545.1 1327.1 1418.0 1472.9 1938.0 2030.1 2167.2 2770.2 2976.7 3620.6
1r2 5r2y 9r2y 13r2y 17r2y 17r2y 19r2y 21r2y 23r2q 25r2q 27r2q
4168.6 4265.6 4354.2 4531.1 5355.7
29r2q 31r2y 31r2y 33r2y 35r2y
5503.6 6233.0 6302.6 6464.1 6739.7 6807.5 7159.4 7247.8 7693.1 8390.7
37r2q 39r2q Ž39r2q . Ž41r2q . Ž43r2q . Ž41r2q . Ž45r2q . Ž43r2q . Ž47r2q . Ž47r2y .
y51 558 1351 1384 1455 1912 2048 2131 2758 2977 3713 3860 4164 4281 4356 4572 5263 5526 5441 6317 6349 6551 6660 6363 7228 7201 7750 8319
b
previous
1338 1372 1443 1901 2036 2119 2787 2965 3684 4153 4700 4371
c
n Žpy1 .p Žh2 . n Žfy1 .p Žh2 . n Žpy1 .p Žh2 . n Žpy1 .p Žh2 . n Žpy1 .p Žh2 . n Žfy1 .p Žh2 . n Žfy1 .p Žh2 . n Žfy1 .p Žh2 . n Žpy1 .p Žhi. n Žiy1 .p Žh2 . n Žfy1 .p Žhi. n Žiy1 .p Žh2 . n Žiy1 .p Žh2 . n Žpy2 g.p Žhi. n Žiy1 .p Žhi. n Žiy1 .p Žhi. n Žpy1 fy1 g.p Žhi. n Žiy1 .p Žhi. n Žpy2 j.p Žhi. n Žpy1 fy1 j.p Žhi. n Žpy1 iy1 g.p Žhi. n Žpy1 fy1 j.p Žhi. n Žpy1 iy1 g.p Žhi. n Žpy1 iy1 g.p Žhi. n Žfy1 iy1 g.p Žhi. n Žpy1 fy1 j.p Žhi. n Žfy1 iy1 g.p Žhi. n Žiy2 g.p Žhi.
a For neutrons Ž n ., i s i 13 r 2 , ps p1 r 2 , f s f 5 r 2 , g s g 9 r 2 js j15 r 2 . For protons Žp ., h s h 9 r 2 , i s i 13 r 2 . b Present work. c Bergstrom ¨ et al. w1x, Rensfelt et al. w2x.
™
gives rise to the 37r2q state at 5503.6 keV. Its major decay is via an E3 transition y1 . Ž . n Ž j15r2 g 9r2 . to the 31r2y state at 4266 keV. The n Žpy1 1r2 f 5r2 g 9r2 p h 9r2 i 13r2 y configuration gives rise to the 5355.7 keV level, although a 35r2 valence particle state is predicted to lie 170 keV above it at 5526 keV. The levels at 6233.0, 6464.1 and y1 . Ž . 7247.8 keV arise from the n Žpy1 1r2 f 5r2 j15r2 p h 9r2 i 13r2 configuration, while the level y1 . Ž at 6302.6 keV is assigned to the n Žpy1 i g p h 9r2 i 13r2 . configuration. This 1r2 13r2 9r2 latter configuration also gives rise to the levels at 6739.3 and 6807.5 keV. Three further levels demand the complete filling of the n Žp 1r2. shell. Those at 7159.4 and 7693.1 keV y1 . Ž . arise from the n Žfy1 5r2 i 13r2 g 9r2 p h 9r2 i 13r2 configuration, while the highest lying . Ž . level at 8390.7 keV is identified with the n Žiy2 13r2 g 9r2 p h 9r2 i 13r2 configuration. 4.1.4. E3 transitions in 2 0 9Po Table 5 summarises the experimental information on the transition strengths of four E3 transitions. The strength of these may be understood in terms of the configuration
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
329
Fig. 6. Comparison of the experimental level scheme with the ESM calculations. The valence particle states are indicated by triangular symbols in both panels. In the left hand panel, core excited states are indicated by square symbols. All transitions are also shown. In the right hand panel, the configurations of the core excited states are indicated: I n Žp y 2 g .p Žhi. ( n Žp y 1 fy 1 g .p Žhi. I n Žp y 2 j.p Žhi. en Žp y 1 fy 1 j.p Žhi. , n Žpy1 iy1 g.p Žhi. v n Žfy1 iy1 g.p Žhi. en Žiy2 g.p Žhi.. In the above, we have used the following abbreviations for neutron states: ps p1 r 2 , f s f 5 r 2 , i s i 13 r 2 , g s g 9 r 2 , js j15 r 2 . For the proton states, the abbreviations are: h s h 9 r 2 , i s i 13 r 2 . Transitions which require configuration mixing are shown dashed Žsee text..
assignments given in Table 4 and the mixing between the two 31r2y states which was previously proposed by Bergstrom ¨ et al. w1x. The transitions and configurations involved may be written in terms of the core excitation Žce. or valence Žv. configurations:
™ 1238 ™ <31r2 ce ™ Ž 1. <31r2 ce ™ 1289 ™ <25r2 n Ž i Ž 2. . p Žh . ™ <31r2 v ™ 1378 ™ <25r2 n Ž i Ž 3. . p Žh . ™ <23r2 n Ž p . p Ž h i Ž 4. . ™ 1297 ™ <17r2 n Ž p . p Ž h . ™ Here as proposed in Ref. w1x, we take the mainly core excited 31r2 state as <31r2 ce ™s0.922 <31r2 n Ž p g . p Ž h i . q 0.387 <31r2 n Ž i . p Žh i . ™ , while the 31r2 state which arises mostly from the valence particle configuration is <31r2 v ™sy0.387 <31r2 n Ž p g . p Ž h i . q 0.922 <31r2 n Ž i . p Žh i . ™ . <37r2q n Ž py2 1r2 j15r2 . p Ž h 9r2 i 13r2 . y
q
y q
2 9r2
y1 13r2
q
y1 1r2
y
2 9r2
y1 13r2
y
9r2 13r2
y1 1r2
2 9r2
y
y
y
y2 1r2
y
9r2
y1 13r2
9r2 13r2
9r2 13r2
y
y
y
y
y2 1r2
y1 13r2
9r2
9r2 13r2
9r2 13r2
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
330 Table 5 E3 strengths in Transition q
209
Po
3
™ ™ ™ ™
y
37r2 31r2 ce 31r2y ce 25r2q 31r2yn 25r2q q 23r2 17r2y 3 4
Eg ŽkeV.
1238 1289 1378 1297
)7 0.47Ž3. ) 0.36 ; 3.6
The 31r2y states are mainly core excited Žce. and valence particle Žv. states respectively, see text. Strength in Weisskopf single particle units ŽW.u...
™
The limit of ) 7 W.u. on the strength of transition Ž1. is consistent with that expected for the non-spin flip transition Žj15 r 2 g 9r2 . and can be compared to the directly related transition ŽMcGoram et al. w11x. in 211 Po: <37r2q n Ž j15r2 . p Ž h 9r2 i 13r2 .
™ 1308 ™ <31r2 n Ž g y
9r2
. p Ž h 9r2 i 13r2 .
9r2
. p Ž h29r2 ,0q .
and in the same nucleus, the transition w11x <15r2y n Ž j15r2 . p Ž h29r2 ,0q .
™ 1065 ™ <9r2 q n Ž g y
™,
™,
with transition strengths of ) 33.4 and 19.1Ž3. W.u. respectively. Taking account of the mixed nature of the 31r2y states in 209 Po, these two transitions can be used to predict strengths of ) 30 and 17.6Ž3. W.u. respectively for transition Ž1.. Transition Ž2. has been discussed by Bergstrom ¨ et al. w1x. It is weak because it involves the p Ži 13r2 h 9r2 . spin flip transition from the valence particle component of the <31r2y ce ) state. The strength of 3.8Ž1. W.u. for the 210 Po p Žh 9r2 i 13r2 11y h 29r2 8q . transition can be used to predict a strength of 0.57Ž2. W.u. for this transition. This is to be compared with the observed value of 0.47Ž3. W.u. Only a limit of ) 0.36 W.u. is available for the spin flip transition Ž3.. It is however in accord with that predicted using the strength of the 11y 8q transition in 210 Po. The prediction is 3.2 W.u. Finally, transition Ž4. for which only an approximate mean life is available is expected to have the same strength as the 210 Po p Žh 9r2 i 13r2 11y h29r2 8q . transition. Its approximate strength of ; 3.6 W.u. is in accord with this expectation.
™
™
™
™
5. Conclusions We have investigated the properties of high spin states of 209 Po to an excitation energy of nearly 8400 keV and spins up to J s Ž47r2.. Empirical Shell Model calculations have enabled us to understand the major features of the decay scheme and to confirm that core-excited states intrude onto the yrast line at an excitation energy of 4266 keV. Furthermore, they dominate the yrast sequence above this energy. The properties of the E3 transitions in 209 Po which have been discussed above support the proposed configurations but also indicate a need for much improved measurements of their mean lives and decay properties. In particular, further study of the E3 transitions involving the two 31r2y states would greatly illuminate the interaction between valence and core excited states, in a nucleus which is simple enough that reliable calculations are possible.
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
331
Acknowledgements The first author thanks the academic and technical staff of the ANU 14UD accelerator facility for willing assistance offered over the course of many visits and the staff at Laboratori Nazionali Legnaro for their patience with someone whose Italian should have been much better.
References w1x I. Bergstrom, ¨ J. Blomqvist, C.J. Herrlander, K. Wikstrom, ¨ Physica Scripta 10 Ž1974. 287. w2x K.-G. Rensfelt, C. Roulet, K. Westerberg, Physica Scripta 14 Ž1976. 95. w3x O. Hausser, T.K. Alexander, J.R. Beene, E.D. Earle, A.B. McDonald, F.C. Khanna, I.S. Towner, Nucl. ¨ Phys. A 273 Ž1976. 253. w4x E. Dafni, M.H. Rafailovich, T. Marshall, G. Schatz, G.D. Sprouse, Nucl. Phys. A 394 Ž1983. 245. w5x M.J. Martin, Nuclear Data Sheets 63 Ž1991. 723. w6x A.R. Poletti, G.D. Dracoulis, A.P. Byrne, A.E. Stuchbery, B. Fabricius, T. Kibedi, P.M. Davidson, Nucl. Phys. A 615 Ž1997. 95. w7x A.R. Poletti, G.D. Dracoulis, A.P. Byrne, A.E. Stuchbery, B. Fabricius, T. Kibedi, P.M. Davidson, Nucl. Phys. A 580 Ž1994. 43. w8x A.R. Poletti, G.D. Dracoulis, A.P. Byrne, A.E. Stuchbery, B. Fabricius, T. Kibedi, P.M. Davidson, Nucl. Phys. A 580 Ž1994. 64. w9x G.D. Dracoulis, A.P. Byrne, Nuclear Physics Annual Report, Australian National University, 1989, p. 115, unpublished. w10x J. Blomqvist, in: Proc. Argonne Symp. on High-spin Phenomena, 1979, p. 155. w11x T.R. McGoram, G.D. Dracoulis, A.P. Byrne, A.R. Poletti, S. Bayer, Nucl. Phys. A 637 Ž1998. 469.
Core-excitations in 209 Po A.R. Poletti a,1, G.D. Dracoulis b, A.P. Byrne b,2 , A.E. Stuchbery b, B. Fabricius b, T. Kibedi ´ b, P.M. Davidson b b
a Department of Physics, UniÕersity of Auckland, PriÕate Bag 92019, Auckland, New Zealand Department of Nuclear Physics, Research School of Physical Sciences and Engineering, Australian National UniÕersity, Canberra, ACT 0200, Australia
Received 27 April 1999; received in revised form 12 July 1999; accepted 11 October 1999
Abstract The properties of high spin states in 209 Po have been investigated using the 204 Hg Ž9 Be,4n. Po reaction at a bombarding energy of 62 MeV. Decay properties for states in 209 Po up to an excitation energy of 8392 keV and spins up to J s Ž47r2. have been deduced. The mean life of the level at 4266 keV was determined as 172Ž5. ns and a limit of - 15 ns was determined for that at 5504 keV. The level scheme is compared with predictions of multi-particle shell model calculations. The lowest core excited state is confirmed to be the 31r2y state at 4266 keV. Another core excited state lies at 5356 keV, while above 5.5 MeV the yrast line is exclusively composed of such excitations. q 2000 Elsevier Science B.V. All rights reserved.
209
Keywords: NUCLEAR REACTIONS 204 HgŽ9 Be,4n.209 Po, E s 55–65 MeV; Measured gg Ž t ., Eg , Ig Ž u ., Ig Ž E,t .; Linear polarisation; 209 Po deduced high spin levels J, p , T1r2 ; Enriched target; Pulsed beam; Compton suppressed detectors; Ge hyper pure detectors in linear polarimeter; NUCLEAR STRUCTURE 209 Po; Calculated levels; Semi-empirical shell model
1. Introduction Over twenty years ago the Stockholm group established the high spin level scheme of Po up to an energy of 4354 keV, provided a shell model interpretation of the scheme and showed that the 31r2y isomer at 4266 keV was a core excited state ŽBergstrom ¨ et al., Rensfelt et al. w1,2x.. Since that time, there has been no further attempt to investigate 209
1 2
Visiting Scientist, Laboratori Nazionali Legnaro, 1998. Joint appointment, Department of Physics, Faculties, Australian National University.
0375-9474r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 Ž 9 9 . 0 0 4 2 1 - 2
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
319
the scheme to higher excitation energies and establish the positions of other core excited states. This is surprising because 209 Po, with two protons and one neutron hole outside the doubly closed shell 208 Pb126 core is a particularly simple system and the results of multiparticle shell model calculations are readily compared to the experimental data. The magnetic moment of the 17r2y and 31r2y isomers were determined by Hausser et al. ¨ w3x, and Rensfelt et al. w2x respectively, while the quadrupole moment of the 17r2y state was measured by Dafni et al. w4x. Martin w5x summarises all nuclear structure information on 209 Po as known up to 1991. No reports relevant to the subject of the present work have been published since. In this paper we report the extension of the high spin level scheme of 209 Po to an excitation energy of 8391 keV and a spin of Ž47r2y. . The results have been interpreted in terms of the multi particle shell model and the role played by core excited states along the yrast line has been determined. The data relevant to 209 Po has been obtained by analyses of experimental results from an investigation of the high spin states of 208 Po. That work has already been published w6x as have the results for the nuclei 205,206 Pb and 204,205 Hg Žsee Refs. w7,8x. which were obtained from the same data set.
2. Experimental procedure Details concerning the different experiments are summarized in the first paper in this series w7x. The prime aim of the experiments had been to investigate the high spin structure of 208 Po using the 204 HgŽ9 Be, 5n.208 Po reaction. Following an excitation function measurement, a bombarding energy of 62 MeV, which optimized the population of 208 Po, was chosen for all subsequent experiments. Pulsed beam– g-timing and g – g-time measurements using the CAESAR array w9x were carried out as well as angular distribution measurements using a single moveable detector and a linear polarization measurement using a three crystal polarimeter. Although 209 Po was weakly populated compared to 208 Po with only 9% of its intensity, the high bombarding energy increased the relative population of the high spin levels in 209 Po. Despite its relative weakness at the energies used, the Ž9 Be, 4n. reaction is nevertheless the best fusionevaporation reaction for the population of these high spin levels.
3. Results and level schemes The level scheme deduced from our work is given in Fig. 1 in which level energies are given to the nearest keV. For completeness, Table 1 lists all electromagnetic transitions Žinvolving high spin states. assigned to 209 Po from the present and previous work w1,2x, together with their assigned position and precise energies. Relative intensities observed in the present work together with the a 2 coefficient in the Legendre polynomial expansion describing the angular distribution of each gamma ray transition are presented. In cases where they could not be extracted reliably from the angular distribution data, intensities have been inferred from coincidence spectra. The deduced
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
320
Fig. 1. The high spin structure of 209 Po as observed in this and previous work.
energy levels are listed in Table 2, together with branchings deduced from this and previous works. All of the levels above 4500 keV are new. The results of the linear polarization measurements are given in Table 3. The bases of spin-parity assignments are discussed in Section 3.6 below. 3.1. The
209
Po leÕel scheme
Ten nuclei were populated to a significant extent in this study w7x, hence cross contamination of coincidence spectra has been an especially severe problem. In Fig. 2, however we present three spectra which between them clearly show all of the transitions which we ascribe to 209 Po and which lie above the 17r2y isomer at 1472.9 keV. The upper panel shows the spectrum of transitions which are early with respect to the 782 keV gate: all transitions assigned as feeding the 17r2y isomer are clearly seen. In the middle panel is the spectrum of transitions which are early with respect to the 1289 keV gate. The prominent peaks in this spectrum arise from transitions which ultimately feed
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331 Table 1 Electromagnetic transitions observed in
209
Po in the
Energy ŽkeV.1
g-ray intensity
Initial level
Final level
54.9 Ž88.6. 90.9 Ž92.1. 96.9 137.1 148.0 161.5 176.8 185.6 206.5 265.6 275.2 299.9 420.1 440.3 444.7 465.1 467.1 519.9 545.1 548.0 557.2 574.6 603.0 643.9 654.0 694.3 729.4 752.8 782.0 824.6 953.8 1028.7 1108.6 1231.3 1238.0 1289.0 1297.3 1304.1 1377.6 1771.2
– – – – 70 350 47 35 109 300 470 27 120 30 52 26 40 25 30 40 1000 215 450 40 670 260 60 190 80 50 980 145 45 50 80 25 110 230 90 27 30 95
1472.9 4354.2 1418.0 2030.1 4265.6 2167.2 5503.6 6464.1 4531.1 4354.2 2976.7 4531.1 6739.3
1418.0 4265.6 1327.1 1938.0 4168.6 2030.1 5355.7 6302.6 4354.2 4168.6 2770.2 4265.2 6464.1
7159.4 7247.8
6739.3 6807.5
1938.0
1472.9
1938.0 545.1 4168.6 2030.1 6807.5 2770.2 3620.6
1418.0 0.0 3620.6 1472.9 6233.0 2167.2 2976.7
2167.2 6233.0
204
321
Hgq9 Be reaction at 62 MeV 100= a2
100= a4
Multipolarity 2 E2 M1 E2 M1 M1 M1 E1 E2 M1 E1 M1 ŽM1. M1
y03Ž22.
05Ž01. y24Ž11. y12Ž04. y02Ž12. y26Ž07.
ŽM1rE2. ŽM1rE2. 01Ž05.
ŽM1.
28Ž03. y26Ž04.
E2 E2 M1rE2 M1rE2 ŽM1. E1 M1rE2
1472.9 5503.6
y46Ž12.
E2 M1
1327.1 5355.7 7693.1
545.1 4531.1 6739.3
00Ž01. y12Ž07. 10Ž36.
E2 M1 ŽE2.
6464.1 8390.7 5503.6 4265.6 2770.2 6807.5 4354.2 6302.6
5355.7 7159.4 4265.6 2976.7 1472.9 5503.6 2976.7 4531.1
y03Ž02. y29Ž05. y32Ž03.
y16Ž22. 10Ž07. 09Ž18.
00Ž17.
y18Ž10. y30Ž26.
ŽE3. ŽE1. E3 E3 E3 ŽE2. E3 ŽE3.
1 Uncertainties on transition energies are "0.1 keV Ž"0.2 keV. for lines less than Žgreater than. 1 MeV and an intensity of greater than 50. For weak lines the corresponding uncertainties are "0.2 keV and "0.4 keV respectively. 2 See text for discussion of the bases for these assignments.
the 31r2y isomer at 4265.6 keV. Although the spectrum in coincidence with the prompt gate at 644 keV in the lower panel is dominated by transitions lower in the scheme, the
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
322 Table 2 Energy levels in this work.
209
Po excited in the
204
Level
Jp
0.0 545.1 1327.1 1418.0 1472.9 1938.0
1r2y 5r2y 9r2y 13r2y 17r2y 17r2y
2030.1
19r2y
2167.2
21r2y
2770.2
23r2q
2976.7 3620.6 4168.6 4265.6
25r2q 27r2q 29r2q 31r2y
4354.2
31r2y
-10 ns
4531.1
33r2y
-10 ns
5355.7 5503.6
35r2y 37r2q
- 5 ns -15 ns
6233.0 6302.6 6464.1
39r2q Ž39r2q . Ž41r2q .
6739.3 6807.5
Ž43r2q . Ž41r2q .
7159.4 7247.8 7693.1 8390.7
Ž45r2q . Ž43r2q . Ž47r2q . Ž47r2y .
Hgq9 Be reaction at 62 MeV. An asterisk signifies a new level from
Mean-life
a
36Ž1.ns 134Ž7.ns
; 3.6 ns
-10 ns 172Ž6. ns
-10 ns
Transitionsb 545.1 782.0 90.9 54.9 465.1 38Ž8.% 92.1c 16Ž2.% 137.1 65Ž4.% 603.0 88Ž2.% 206.6 643.9 548.0 96.9 c 30Ž5.% 88.6 c 37Ž3.% 176.8 80Ž4.% 824.6 148.0 30Ž4.% 729.1 1771.2 161.5 27Ž5.% 275.2 574.6 60Ž5.% 420.1 440.3 953.8 1231.2
519.9 62Ž8.% 557.2 c 84Ž2.% 694.3 35Ž4.% 1297.3 12Ž2.%
1289.0 c 70Ž5.% 185.6 c 58Ž3.% 265.6 20Ž4.% 1238.0 70Ž4.%
1108.6 73Ž5.% 1304.1 40Ž5.%
1377.6 c 5Ž2.% ) ) ) ) ) ) ) ) ) ) ) )
a Limits on mean lives are from the present work. Mean lives are from Ref. w5x, except for that of the 4265.6 keV level which is an average of the present result and that given in Ref. w1x. b Percentages refer to gamma ray branchings except where specified. c The branchings refer to the total transition intensity for each branch.
presence of many lines placed above 4300 keV demonstrates that a substantial fraction of the decay intensity bypasses the 31r2y isomer. ŽGamma ray energies shown in Figs. 2 and 3 are given to the nearest keV.. 3.2. LeÕels up to the 4354 keV state We confirm the level scheme as reported in Refs. w1,2x. Coincidences observed between the 137.1 keV and 519.9 keV lines demonstrate that the 17r2y level at 1938.0
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331 Table 3 Linear polarization measurements in
209
323
Po
Energy
100= a 2
100= Pex
100= Ptha
265.6 275.2 545.1 548.0 557.2 643.9 729.4 782.0 824.6 953.8 1289.0 1297.3
y02Ž12. y26Ž07. y03Ž02. y29Ž05. y32Ž03. y26Ž04. y46Ž12. 00Ž01. y12Ž07. 10Ž36. 10Ž07. c 09Ž18. e
y71Ž60. y83Ž26. y08Ž08. y19Ž23. 15Ž08. y46Ž17. y86Ž27. 05Ž05. y14Ž24. y37Ž116. 48Ž34. 41Ž83.
y03Ž18. y35Ž08. y04Ž03. y38Ž06. y41Ž03. y35Ž05. y56Ž12. 00Ž02. y17Ž09. 15Ž60. 62Ž32. d 100Ž89. d
Assignment M1 E2 b M1rE2 M1rE2 M1rE2 M1 E2 b M1
Mixing ratio
q0.53Ž05. b or 1.67Ž16. b
E3 E3
a
If a4 is neglected, Pth s 3 az 2 rŽ2y a 2 . for pure M1 or E2 transitions while Pth sy3a 2 rŽ2y a 2 . for pure E1 or M2 transitions. If a6 is neglected, Pth s Ž2 a 2 y5a4 .rŽ2y a 2 q0.75a 4 . for pure E3 transitions. The values given in this column are for pure M1 or E2 transitions except for the 1289.0 and 1297.3 keV transitions which are for pure E3. b Bergstro¨ m et al. c 100= a 4 sy18Ž10.. d E3 transition. e 100= a4 sy30Ž26..
keV is fed from the 2030.1 keV level via a 92.1 keV transition which is obscured by the 92.4 keV polonium X-ray line. There is no evidence of direct feeding of the 1938.0 keV level from either the 2167.2 or 2770.2 keV levels. 3.3. The leÕels associated with the 1238.0 keV transition Transitions coincident with a prompt gate at 1238 keV are shown in the middle panel of Fig. 3 and show the major feeding transitions. The 1238.0 keV transition which directly populates the 31r2y isomer defines a level at 5503.6 keV which is in turn populated by transitions of 729.4 and 1304.1 keV, defining levels at 6233.0 and 6807.5 keV respectively. The latter level populates that at 6233.0 keV via a transition of 574.6 keV and is in its turn populated by a transition of 440.3 keV. 3.4. The 4531.1 keV leÕel and associated transitions and leÕels The major branch from the level at 4531.1 keV is the 176.8 keV transition to the level at 4354.2 keV. The strongest transition, of 185.6 keV, from this latter level bypasses the 31r2y isomer at 4265.6 keV. In addition to the 1238.0 keV transition, the 31r2y isomer is however populated by weak transitions from the 4354.2 and 4531.1 keV levels with energies of 88.6 and 265.6 keV respectively. ŽThe existence of an 88.6 keV transition is inferred from coincidence relationships.. A strong 824.6 keV transition Žsee the lower panel of Fig. 3. defines a level at 5355.7 keV which is fed in parallel by transitions of 148.0 keV and 1108.6 keV. The former transition provides a connecting path to transitions which feed the 5503.6 keV level, while the latter defines a level at 6464.1 keV. This level is also de-excited by a transition of 161.5 keV which populates a
324
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
Fig. 2. Representative coincidence spectra illustrating the decay of the high spin states in 209 Po. The top panel shows the transitions which lie above the isomeric levels at 1418 and 1473 keV. Middle panel: all of the transitions placed above the 31r2y isomer at 4266 keV are labelled, as are six others. Although we were unable to place the following transitions: those of 654, 752 and 1029 keV predominantly feed the isomer, while those of 300, 444 and 467 keV largely bypass it. Bottom panel: for the transitions lying high in the scheme, this shows those which populate the levels at 4531 and 4354 keV, thereby largely bypassing the 31r2y isomer at 4266 keV.
level at 6302.6 keV which in turn is de-excited by a transition of 1771.2 keV to the level at 4531.1 keV. The upper panel of Fig. 3 displays the spectrum of gamma rays in prompt coincidence with a gate set on the 1771.2 keV transition. A cascade of three transitions which feed the 6464.1 keV level defines higher states at 6739.3, 7159.4 and 8390.7 keV which are respectively de-excited by transitions of 275.2, 420.1 and 1231.3 keV. A transition of 953.8 keV in coincidence with that of 275.2 keV defines a level at 7693.1 keV. All four transitions are seen in the prompt gate set on the 824.6 transition Žlower panel, Fig. 3.. 3.5. Mean life of the 4265.6 keV leÕel, lifetime limits We confirmed the measured mean life of the 4265.8 keV level. This was determined as t s 172Ž5. ns from a weighted average of fits to the time spectra of the 1289, 603 and 207 keV transitions, in excellent agreement with the mean life of 170Ž4. ns determined
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
325
Fig. 3. Spectra further illustrating the decay of the high spin states of 209 Po. Middle panel: the 1238 keV transition directly populates the 31r2y isomer at 4266 keV. Its major feeding transitions are labelled. The 109 keV line arises from the 109–1236 keV cascade in 19 F. Top and bottom panels: the 1771 and 825 keV transitions carry a major part of the decay flux from the high lying levels.
by Bergstrom ¨ et al. w1x. The time spectrum of the 1289 keV transition is illustrated in Fig. 4. A limit on the mean life of the level at 5503.6 keV was determined as t - 15 ns from the time spectrum of the 825 keV gate. The gates set on the 1238.0 and 148.0 transitions immediately depopulating the isomer were heavily contaminated. Limits on mean lives of other transitions and present and previous measurements of mean lives are given in Table 2. 3.6. Spin and parity assignments Spin-parity assignments are based on the results of several different measurements. 1. Angular distributions of gamma rays ŽTables 1 and 2.. 2. Linear polarizations of gamma rays with energies greater than approximately 250 keV ŽTable 3..
326
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
Fig. 4. Time spectrum of the 1289 keV transition.
3. Mean lives and lifetime limits ŽTable 2.. 4. Intensities and intensity balances of gamma rays ŽTable 1 and intensities obtained from relevant coincidence spectra.. In addition to confirming several previous multipolarity assignments, multipolarities were obtained for the newly placed transitions of 148.0, 161.5 and 176.8 keV from total conversion coefficient measurements. The total conversion coefficient, a T s 1.7Ž6., of the 176.8 keV transition is consistent only with M1. ŽFor 176.8 keV, a T ŽM1. s 2.34 and a T ŽE2. s 0.75.. This and the lack of any transitions to states of spin less than 31r2 implied a spin-parity assignment of 33r2y for the level at 4531.1 keV. Linear polarization and angular distribution measurements showed the 824.6 keV transition to be stretched and M1, fixing the level at 5355.7 keV as 35r2y. For the 148.0 keV transition, a T - 0.37 and hence it is E1. ŽFor 148.0 keV, a T ŽE1. s 0.17, a T ŽM1. s 3.85 and a T ŽE2. s 1.46.. This E1 assignment and the upper limit on the mean life for the 5503.6 keV level of t - 15 ns are consistent with a spin-parity assignment of 37r2q to this level and an E3 character for the 1238.0 keV transition. The measured linear polarization and angular distribution of the 729.4 keV transition, consistent with stretched M1, further imply the spin-parity of the 6233.0 keV level is 39r2q. For the higher lying levels, assignments are less certain. The total conversion coefficient, a T s 1.4Ž5., for the 161.5 keV transition is consistent with M1rE2. ŽFor 161.5 keV, a T ŽM1. s 3.01 and a T ŽE2. s 1.05.. This is consistent with spin-parity assignments of Ž41r2q. and Ž39r2q. to the levels at 6464.1 and 6302.6 keV respectively and E3 assignments to both of the 1771.2 and 1108.6 keV transitions. The linear polarization data suggests that the 275.2 keV transition is stretched and M1. The 6739.3 keV level is thus likely to Ž43r2q. . For the remaining five high lying levels the suggested spins and parities are consistent with the decay scheme which has been established, but definitive information on spins and parities is lacking. 4. Discussion 4.1. Empirical Shell Model (ESM) calculations The Empirical Shell Model Žsee for instance, Refs. w6,7,10x. has been used to interpret the observed nuclear structure of 209 Po. Calculations were carried out for two
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
327
Fig. 5. The single-particle orbits used in the ESM calculations.
classes of states: those arising from the valence particles alone and those which occur as a result of core excitation. Fig. 5 illustrates the orbitals which were considered, while Table 4 lists the theoretical levels identified with those experimentally observed. Fig. 6 gives an overview of the calculated level energies together with their spins and parities and compares these properties to those of the experimentally determined levels. 4.1.1. Valence particle states All configurations in which the two protons were in any of the three lowest proton particle orbitals outside the 208 Pb closed core were considered. These were the 1h 9r2 , 2f 7r2 and 1i 13r2 orbitals. The neutron hole was allocated to any of the four neutron-hole orbitals, that is to the 3p1r2 , 2f 5r2 , 3p 3r2 and 1i 13r2 orbitals. ŽThe calculations did not include mixing between configurations containing different orbitals.. 4.1.2. Core excited states Table 4 shows that there are a relatively small number of configurations involved in the lowest core excited states. These entailed the excitation of a neutron across the energy gap to the 2g 9r2 or 1j15r2 orbitals and involved just one proton configuration which was p Žh 9r2 i 13r2 .. For the levels above that at 6233.0 keV, the spins and parities are those of the corresponding theoretical levels. Their association with the experimental levels can only be tentative. 4.1.3. Comparison of the ESM calculations with the leÕel scheme The levels arising from the valence configurations are all well reproduced by the ESM calculations which are in good agreement with those of Refs. w1,2x where the two calculations overlap. The ESM calculation also give a good account of the ground state and first excited state energies and also agrees well with the energy of the 33r2y state found to lie at 4531.1 keV. Bergstrom ¨ et al. w1,2x had already shown that the lowest lying core excited state Ž J p s 31r2y . which entered the yrast line at an energy of 4266 keV arose from the . Ž . Ž y2 . Ž . n Žpy2 1r2 g 9r2 p h 9r2 i 13r2 configuration. The n p 1r2 j15r2 p h 9r2 i 13r2 configuration
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
328
Table 4 Experimental and theoretical level energies in Energy ŽkeV. experiment
J
p
209
Po Configurationa
Energy ŽkeV. theory present y
0.0 545.1 1327.1 1418.0 1472.9 1938.0 2030.1 2167.2 2770.2 2976.7 3620.6
1r2 5r2y 9r2y 13r2y 17r2y 17r2y 19r2y 21r2y 23r2q 25r2q 27r2q
4168.6 4265.6 4354.2 4531.1 5355.7
29r2q 31r2y 31r2y 33r2y 35r2y
5503.6 6233.0 6302.6 6464.1 6739.7 6807.5 7159.4 7247.8 7693.1 8390.7
37r2q 39r2q Ž39r2q . Ž41r2q . Ž43r2q . Ž41r2q . Ž45r2q . Ž43r2q . Ž47r2q . Ž47r2y .
y51 558 1351 1384 1455 1912 2048 2131 2758 2977 3713 3860 4164 4281 4356 4572 5263 5526 5441 6317 6349 6551 6660 6363 7228 7201 7750 8319
b
previous
1338 1372 1443 1901 2036 2119 2787 2965 3684 4153 4700 4371
c
n Žpy1 .p Žh2 . n Žfy1 .p Žh2 . n Žpy1 .p Žh2 . n Žpy1 .p Žh2 . n Žpy1 .p Žh2 . n Žfy1 .p Žh2 . n Žfy1 .p Žh2 . n Žfy1 .p Žh2 . n Žpy1 .p Žhi. n Žiy1 .p Žh2 . n Žfy1 .p Žhi. n Žiy1 .p Žh2 . n Žiy1 .p Žh2 . n Žpy2 g.p Žhi. n Žiy1 .p Žhi. n Žiy1 .p Žhi. n Žpy1 fy1 g.p Žhi. n Žiy1 .p Žhi. n Žpy2 j.p Žhi. n Žpy1 fy1 j.p Žhi. n Žpy1 iy1 g.p Žhi. n Žpy1 fy1 j.p Žhi. n Žpy1 iy1 g.p Žhi. n Žpy1 iy1 g.p Žhi. n Žfy1 iy1 g.p Žhi. n Žpy1 fy1 j.p Žhi. n Žfy1 iy1 g.p Žhi. n Žiy2 g.p Žhi.
a For neutrons Ž n ., i s i 13 r 2 , ps p1 r 2 , f s f 5 r 2 , g s g 9 r 2 js j15 r 2 . For protons Žp ., h s h 9 r 2 , i s i 13 r 2 . b Present work. c Bergstrom ¨ et al. w1x, Rensfelt et al. w2x.
™
gives rise to the 37r2q state at 5503.6 keV. Its major decay is via an E3 transition y1 . Ž . n Ž j15r2 g 9r2 . to the 31r2y state at 4266 keV. The n Žpy1 1r2 f 5r2 g 9r2 p h 9r2 i 13r2 y configuration gives rise to the 5355.7 keV level, although a 35r2 valence particle state is predicted to lie 170 keV above it at 5526 keV. The levels at 6233.0, 6464.1 and y1 . Ž . 7247.8 keV arise from the n Žpy1 1r2 f 5r2 j15r2 p h 9r2 i 13r2 configuration, while the level y1 . Ž at 6302.6 keV is assigned to the n Žpy1 i g p h 9r2 i 13r2 . configuration. This 1r2 13r2 9r2 latter configuration also gives rise to the levels at 6739.3 and 6807.5 keV. Three further levels demand the complete filling of the n Žp 1r2. shell. Those at 7159.4 and 7693.1 keV y1 . Ž . arise from the n Žfy1 5r2 i 13r2 g 9r2 p h 9r2 i 13r2 configuration, while the highest lying . Ž . level at 8390.7 keV is identified with the n Žiy2 13r2 g 9r2 p h 9r2 i 13r2 configuration. 4.1.4. E3 transitions in 2 0 9Po Table 5 summarises the experimental information on the transition strengths of four E3 transitions. The strength of these may be understood in terms of the configuration
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
329
Fig. 6. Comparison of the experimental level scheme with the ESM calculations. The valence particle states are indicated by triangular symbols in both panels. In the left hand panel, core excited states are indicated by square symbols. All transitions are also shown. In the right hand panel, the configurations of the core excited states are indicated: I n Žp y 2 g .p Žhi. ( n Žp y 1 fy 1 g .p Žhi. I n Žp y 2 j.p Žhi. en Žp y 1 fy 1 j.p Žhi. , n Žpy1 iy1 g.p Žhi. v n Žfy1 iy1 g.p Žhi. en Žiy2 g.p Žhi.. In the above, we have used the following abbreviations for neutron states: ps p1 r 2 , f s f 5 r 2 , i s i 13 r 2 , g s g 9 r 2 , js j15 r 2 . For the proton states, the abbreviations are: h s h 9 r 2 , i s i 13 r 2 . Transitions which require configuration mixing are shown dashed Žsee text..
assignments given in Table 4 and the mixing between the two 31r2y states which was previously proposed by Bergstrom ¨ et al. w1x. The transitions and configurations involved may be written in terms of the core excitation Žce. or valence Žv. configurations:
™ 1238 ™ <31r2 ce ™ Ž 1. <31r2 ce ™ 1289 ™ <25r2 n Ž i Ž 2. . p Žh . ™ <31r2 v ™ 1378 ™ <25r2 n Ž i Ž 3. . p Žh . ™ <23r2 n Ž p . p Ž h i Ž 4. . ™ 1297 ™ <17r2 n Ž p . p Ž h . ™ Here as proposed in Ref. w1x, we take the mainly core excited 31r2 state as <31r2 ce ™s0.922 <31r2 n Ž p g . p Ž h i . q 0.387 <31r2 n Ž i . p Žh i . ™ , while the 31r2 state which arises mostly from the valence particle configuration is <31r2 v ™sy0.387 <31r2 n Ž p g . p Ž h i . q 0.922 <31r2 n Ž i . p Žh i . ™ . <37r2q n Ž py2 1r2 j15r2 . p Ž h 9r2 i 13r2 . y
q
y q
2 9r2
y1 13r2
q
y1 1r2
y
2 9r2
y1 13r2
y
9r2 13r2
y1 1r2
2 9r2
y
y
y
y2 1r2
y
9r2
y1 13r2
9r2 13r2
9r2 13r2
y
y
y
y
y2 1r2
y1 13r2
9r2
9r2 13r2
9r2 13r2
A.R. Poletti et al.r Nuclear Physics A 665 (2000) 318–331
330 Table 5 E3 strengths in Transition q
209
Po
3
™ ™ ™ ™
y
37r2 31r2 ce 31r2y ce 25r2q 31r2yn 25r2q q 23r2 17r2y 3 4
Eg ŽkeV.
1238 1289 1378 1297
)7 0.47Ž3. ) 0.36 ; 3.6
The 31r2y states are mainly core excited Žce. and valence particle Žv. states respectively, see text. Strength in Weisskopf single particle units ŽW.u...
™
The limit of ) 7 W.u. on the strength of transition Ž1. is consistent with that expected for the non-spin flip transition Žj15 r 2 g 9r2 . and can be compared to the directly related transition ŽMcGoram et al. w11x. in 211 Po: <37r2q n Ž j15r2 . p Ž h 9r2 i 13r2 .
™ 1308 ™ <31r2 n Ž g y
9r2
. p Ž h 9r2 i 13r2 .
9r2
. p Ž h29r2 ,0q .
and in the same nucleus, the transition w11x <15r2y n Ž j15r2 . p Ž h29r2 ,0q .
™ 1065 ™ <9r2 q n Ž g y
™,
™,
with transition strengths of ) 33.4 and 19.1Ž3. W.u. respectively. Taking account of the mixed nature of the 31r2y states in 209 Po, these two transitions can be used to predict strengths of ) 30 and 17.6Ž3. W.u. respectively for transition Ž1.. Transition Ž2. has been discussed by Bergstrom ¨ et al. w1x. It is weak because it involves the p Ži 13r2 h 9r2 . spin flip transition from the valence particle component of the <31r2y ce ) state. The strength of 3.8Ž1. W.u. for the 210 Po p Žh 9r2 i 13r2 11y h 29r2 8q . transition can be used to predict a strength of 0.57Ž2. W.u. for this transition. This is to be compared with the observed value of 0.47Ž3. W.u. Only a limit of ) 0.36 W.u. is available for the spin flip transition Ž3.. It is however in accord with that predicted using the strength of the 11y 8q transition in 210 Po. The prediction is 3.2 W.u. Finally, transition Ž4. for which only an approximate mean life is available is expected to have the same strength as the 210 Po p Žh 9r2 i 13r2 11y h29r2 8q . transition. Its approximate strength of ; 3.6 W.u. is in accord with this expectation.
™
™
™
™
5. Conclusions We have investigated the properties of high spin states of 209 Po to an excitation energy of nearly 8400 keV and spins up to J s Ž47r2.. Empirical Shell Model calculations have enabled us to understand the major features of the decay scheme and to confirm that core-excited states intrude onto the yrast line at an excitation energy of 4266 keV. Furthermore, they dominate the yrast sequence above this energy. The properties of the E3 transitions in 209 Po which have been discussed above support the proposed configurations but also indicate a need for much improved measurements of their mean lives and decay properties. In particular, further study of the E3 transitions involving the two 31r2y states would greatly illuminate the interaction between valence and core excited states, in a nucleus which is simple enough that reliable calculations are possible.
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Acknowledgements The first author thanks the academic and technical staff of the ANU 14UD accelerator facility for willing assistance offered over the course of many visits and the staff at Laboratori Nazionali Legnaro for their patience with someone whose Italian should have been much better.
References w1x I. Bergstrom, ¨ J. Blomqvist, C.J. Herrlander, K. Wikstrom, ¨ Physica Scripta 10 Ž1974. 287. w2x K.-G. Rensfelt, C. Roulet, K. Westerberg, Physica Scripta 14 Ž1976. 95. w3x O. Hausser, T.K. Alexander, J.R. Beene, E.D. Earle, A.B. McDonald, F.C. Khanna, I.S. Towner, Nucl. ¨ Phys. A 273 Ž1976. 253. w4x E. Dafni, M.H. Rafailovich, T. Marshall, G. Schatz, G.D. Sprouse, Nucl. Phys. A 394 Ž1983. 245. w5x M.J. Martin, Nuclear Data Sheets 63 Ž1991. 723. w6x A.R. Poletti, G.D. Dracoulis, A.P. Byrne, A.E. Stuchbery, B. Fabricius, T. Kibedi, P.M. Davidson, Nucl. Phys. A 615 Ž1997. 95. w7x A.R. Poletti, G.D. Dracoulis, A.P. Byrne, A.E. Stuchbery, B. Fabricius, T. Kibedi, P.M. Davidson, Nucl. Phys. A 580 Ž1994. 43. w8x A.R. Poletti, G.D. Dracoulis, A.P. Byrne, A.E. Stuchbery, B. Fabricius, T. Kibedi, P.M. Davidson, Nucl. Phys. A 580 Ž1994. 64. w9x G.D. Dracoulis, A.P. Byrne, Nuclear Physics Annual Report, Australian National University, 1989, p. 115, unpublished. w10x J. Blomqvist, in: Proc. Argonne Symp. on High-spin Phenomena, 1979, p. 155. w11x T.R. McGoram, G.D. Dracoulis, A.P. Byrne, A.R. Poletti, S. Bayer, Nucl. Phys. A 637 Ž1998. 469.