Self-consistent approach to deformation of intruder states in neutron-deficient Pb and Po

Abstract

We present systematic calculations of the properties of 11 − isomers in neutron-deficient [184][185][186][187][188][189][190][191][192][193][194][195][196][197][198] Po. These states are based on the π(h 9/2 i 13/2 ) K π =11 − configuration. They are calculated in the framework of the Hartree-Fock-Bogoliubov method with a Skyrme interaction and densitydependent pairing force. The energies and deformations of the 11 − states are compared to those of the intruder 0 + states in both Pb and Po isotopes. In the most neutron-deficient Po isotopes, the calculations predict, below a weakly oblate 11 − state, another oblate 11 − state which is even more deformed than the intruder oblate 11 − state in their Pb isotones. The energies and quadrupole moments of the 11 − isomers, corresponding to a weakly oblate nuclear shape, are in fair agreement with the available experimental data.The neutron-deficient nuclei around the Z = 82 shell closure constitute one of the most famous examples of shape coexistence [1,2]. In Pb isotopes, oblate, prolate and superdeformed configurations coexisting with a spherical ground state were predicted theoretically (see [3] and references therein) and identified experimentally [2, 4] more than ten years ago. By now, low-lying 0 + states, which are a characteristic feature of shape coexistence, are known from 202 Pb down to 184 Pb [5,6,7,8]. The interpretation of these low-lying 0 + states relies on proton excitations across the Z = 82 spherical shell gap. In a shell model picture [9,10], the energy of these multi-particle-multi-hole (mp-mh) configurations is lowered by the quadrupole-quadrupole and pairing interactions. In mean-field models [11,12], these structures are described by a state with an oblate (prolate) quadrupole deformation, whose low energy is due to the occupation of deformed intruder orbits, such as the down-sloping πh 9/2 -orbital for an oblate state.High-spin isomers constructed on these 0 + states are of particular interest since the measurement of their static electromagnetic moments provides direct information on both their single-particle structure and their deformation. Several isomeric states are known in Pb isotopes. In particular, 11 − levels have been observed from 188 Pb to 198 Pb (see, e.g. Ref.[13]). They are not known in heavier Pb, most probably because they are not yrast. These states are interpreted as a two-quasiparticle (2qp) excitation based on the π(h 9/2 i 13/2 ) K π =11 − single-particle configuration as confirmed in 196 Pb by the measurement of its g-factor [14]. Experimental information on deformation is extracted from the collective bands based on the excited 0 + [5, 7, 14, 15] and 11 − states [16,17]. Recent data on static quadrupole moments for 11 − states in 194,196 Pb [18,19] support the mean-field interpretation of these states as weakly deformed oblate configurations.The experimental excitation energies of the 11 − states and of the 0 + 2 states in Pb isotopes are shown in the left part of Fig. 1. Both exhibit a similar behavior. The steady decre...

Multi-quasiparticle excitation: Extending shape coexistence inA~190neutron-deficient nuclei

“…2. This is consistent with results given by the Skyrme-HFB calculations [34]. For the polonium isotopes, the PES's are more complicated.…”

“…For 190 Po, low-lying band structure with prolate shape has been observed [37], which is also consistent with our calculation. [10,34]. The experimental excitation energies of the 11 − isomers are about 2.5 MeV.…”

“…102 106 110 114 118 [10] and Skyrme-HFB [33,34] calculations which were limited to axially symmetric shapes. Compared with the situation in the lead isotopes, the shape-coexistence phenomenon is less established in the polonium isotopes.…”

Lifetimes of intruder states in 186Pb, 188Pb and 194Po

“…The dominance of oblate deformation in the ground state of 194 Po was predicted in Ref. [44], where a configuration mixing method similar to that of Ref. [7], but without projection on angular momentum was applied for neutron-deficient Po nuclei.…”

“…The theoretical predictions of Ref. [5,44] indicate that the spherical configuration does not correspond to an energy minimum in even-mass Po isotopes and will not play the same role as in the Pb isotopes. Therefore, the effect of weak mixing of oblate and near spherical structures may well fit within the error bars of the measured transition probabilities.…”