1. Isomers and shape transitions in the n-rich A~190 region:
the influence of angular momentum
Phil Walker
University of Surrey
prolate K isomers vs.
oblate collective rotation

2. Segre chart with isomers
Z=72 (Hf)
K isomers
(A ~ )
This proposal is to study K isomers in deformed nuclei, extending the known A~180 region into the n-rich domain. We focus on hafnium isotopes, for which the Z=72 Fermi level is very favourably placed amongst high-K orbitals.
adapted from Walker and Dracoulis, Nature 399 (1999) 35

3. prolate-oblate shape transition
n-rich hafnium ground states
critical point
N = 116 60 γ 30
Here calculated ground-state shapes are shown (part of a much wider range of calculated shapes). The delicate balance in 188Hf between prolate and oblate shapes is evident. It is important also to consider the effects of angular momentum – see next slide.
Robledo et al., J. Phys. G: Nucl. Part. Phys. 36, (2009).

4. [PRL43 (1979) 1979]
Hilton and Mang
oblate
prolate
HFB calculations

5. 180Hf oblate band? three 20+ states pre-Gammasphere
high-K yrast isomers:
d'Alarcao et al.,
Phys. Rev. C59
(1999) 1227(R)
three 20+ states
Tandel et al.,
Phys. Rev. Lett. 101
(2008)
with Gammasphere
3600

6. cranked n-rich hafnium: 3 well-deformed minima
collective
prolate
ћω = 0.2
ћω = 0.3
ћω = 0.4
collective
oblate
non-collective
prolate
This cranking calculation shows an important role for angular momentum (approx 5, 15 and 25 units, going left to right). The well-deformed oblate shape is stabilised by reinforcing neutron and proton rotation alignments (low K), competing with prolate high-K isomers. We plan to study the high-K isomers in the ESR.
182Hf example: Xu, Walker and Wyss, Phys. Rev. C62 (2000)

7. 190Hf TRS 190Hf TRS oblate rotor prolate oblate I=32 ħω = 0 MeV
beyond the critical point
oblate
ħω = 0.3 MeV
ħω = 0.45 MeV
I=32
Xu et al., unpublished

8. Hf prolate vs oblate 182Hf 186Hf oblate prolate oblate prolate mqp
[Xu et al., Phys. Rev. C62 (2000) ]

9. Nilsson single-particle diagram N = 116 (188Hf, 190W, 192Os)
prolate
oblate

10. data for even-even A~190 nuclei
186Os ns
188Os ns
190Os m
192Os s
Z=76
Z=74
Z=72
184W μs μs
186W
16+ >3ms μs
188W
190W
10- ~1ms ?
182Hf μs m
184Hf s
186Hf
188Hf
new data
new data
critical point

11. W-190 gammas 190W ~1 ms a critical point nucleus
delayed gamma rays from 208Pb fragmentation at 1 GeV per nucleon
~1 ms
190W
a critical point nucleus

12. isomer energies, potential energy surfaces
190W: prolate
(keV)
2360±25
(exp)
ground state PES
~1ms
2015 6s
1920 m
10-
10-
(calc)
1700
1633
10- isomer PES 0+
190Os Os W116
[Walker and Xu, PLB636 (2006) 286]

13. 190W with Gammasphere
Lane et al.,
Phys. Rev. C82
(2010)

14. 190W with Gammasphere Lane et al., Phys. Rev. C82 (2010) 051304
10- isomer at 1839 keV

15. isomer energies, potential energy surfaces
190W: prolate
(keV)
2360±25
(exp)
ground state PES
~1ms
2015 6s µs
1920 m
10-
10-
(calc)
1700
1633
10- isomer PES 0+
190Os Os W116
[Walker and Xu, PLB636 (2006) 286]

16. 190W with Gammasphere That was the high-K isomer. What about the
Lane et al.,
Phys. Rev. C82
(2010)
That was the
high-K isomer.
What about the
oblate rotation?

17. 190W with Gammasphere That was the high-K isomer. What about the
(12+) yrast at 2653 keV
Lane et al.,
Phys. Rev. C82
(2010)
That was the
high-K isomer.
What about the
oblate rotation?

18. 190W TRS: prolate to oblate
rotation alignment of 2 i13/2 neutrons with oblate shape
ħω = MeV
ħω = MeV
γ=0o
I = 4
prolate
I = 14
oblate
γ=-60o
[Walker and Xu, PLB636 (2006) 286]

19. N=116 experimental energies, spins and half-lives 2653 (i 13/2)2 12+ ?
2451
2439
9 ns
190W
Lane
et al.
5 ns
194Pt and 196Hg: Levon et al., Nucl. Phys. A764 (2006) 24
192Os: Valiente-Dobon et al., Phys. Rev. C69 (2004)
412
329 2+
207
206 0+
74W Os Pt Hg

20. projected shell model (angular momentum basis)
Sun et al., PLB659 (2008) 165

21. summary oblate-prolate competition in N = 116 188Hf – 190W – 192Os
N = 116 seems to be the critical-point neutron number
focus on angular momentum effects
10- prolate K isomers
12+ isomers: bandheads of collective oblate bands??
giant backbending candidates: cf. Hilton and Mang 1979
oblate rotation becomes yrast over a wide spin range
more data needed!! (188Hf, 190W and/or 192Os)