Dia 1

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Even-A Pb level systematics
Prolate 4p-4h
Oblate 2p-2h
Spherical 0p-0h
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Classification of the levels
Classification based on systematics
Thus follow the E2-decay starting from
high-spin levels using as a criterion for the
band that interband transitionslt intraband
transitions
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188Pb construction of bands
Start from high spin members and follow E2-decay
using as criterium for band intra-band
gtinterband
(for this case) Smooth variation
of B(E2)-values at high spin

• G. D. Dracoulis et al.,
• PRC 69 (2004), 054318
• V. Hellemans et al.,
• PRC 71 (2005), 034308
• T. Grahn et al., PRL97
• (2006) 062501

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188 Pb
V. Hellemans, unpublished (Ph. D thesis)
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Comparison with collective rotational model
IBM quadrupole moment (lab)
Intrinsic quadrupole moment (body-fixed) in
collective model
Deformation parameter Unperturbed 2p-2h -0.11
à 0.12 Unperturbed 4p-4h 0.19 à0.22
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E0-transitions in 188Pb and isotopic shifts
H. De Witte et al, PRL 98 (2007) 112502
Dimensionless monopole transition strength that
contains all the information about the nuclear
structure
A least square fit to the r2-values for 188Pb
does not impose enough constraints
Isotopic shifts can be related to E0-transitions
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H. De Witte, Ph. D. thesis, Leuven (2004),
unpubl. H. De Witte et al, PRL 98 (2007) 112502
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Connection with geometry
calculate the expectation value in a
coherent state basis
Energy surface (ES) in ? and ?
IBM
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4 Collective interpretation
... and similarly for configuration mixed systems
...
Configuration mixed IBM
Associated energy surface
the lowest eigenvalue of
energies are the eigenvalues of
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Potential energy surfaces constructed by applying
the coherent state formalism

to the mixing within the IBM.
3-configuration mixing can give rise to a
potential energy surface with one, two or three
minima depending on the IBM parameters
Aim a general study of the dependence of the
PES with configuration mixing on the IBM
parameters !
j Connection with HFBCSGCM beyond mean-field
studies
A. Frank et al., PRC 034323
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• Scaling with number of proton
• particles and holes

P. Van Duppen et al., Phys. Rev. C35 (1987)
1861, K. Heyde et al., Nucl. Phys. 484 (1988) 275
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OUTLOOK
One of the primary goals of nuclear physics is to
understand nuclear phenomena both in terms of the
microscopic models but also using collective
models, using either geometrical aspects or
algebraic methods.

• A complete understanding of all facets available
  from both perspectives
• is clearly unattainable
• Shell-model becomes limited by its complexity,
• Collective models are often restricted to too
  few degrees of freedom
• Path to succes would appear to lie in a judicious
  combination of the two.

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