Shape vibration and quasiparticle excitations in the lowest0+excited state in erbium isotopes

Abstract

The ground and first excited 0 + states of the 156−172 Er isotopes are analyzed in the framework of the generator coordinate method. The shape parameter β is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and E2 transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited 0 + states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between both degrees of freedom are necessary .

Variational approximations to exact solutions in shell-model valence spaces: Calcium isotopes in the pf shell

“…This effect can be understood as our minimization schemes probe primarily the ground-state energy. Such a deficiency can be corrected within the PGCM framework by enlarging the initial set of quasiparticle wave functions with: a) intrinsically rotating states through cranking calculations [52,53]; and/or, b) multi-quasi-particle excitations obtained through the blocking mechanism [25,26]. Both improvements will be explored in the future but are beyond the scope of the present work.…”

“…Moreover, Hartree-Fock (HF) total energy surfaces along quadrupole degrees of freedom have been used to interpret ISM [19,20] and Monte Carlo Shell Model (MCSM) [21,22] calculations. prominently Also, simpler Hamiltonians like Pairing-plus-quadrupole (PPQ) interactions have been also used in the past within the projected shell model (PSM) framework [23,24] and with GCM approximations including two quasi-particle excitations explicitly [25,26]. Our goal is to go beyond these simplistic Hamiltonians although, for the moment, some single-particle degrees of freedom included in the above methods will be omitted.…”

Prolate-to-oblate transition and backbending along the yrast line induced by quasiparticle alignment

“…As a generalization of the PSM, various deformations are taken into account in the framework proposed in Refs. [21,22], in which HFB vacua of different deformations, as well as two-quasiparticle configurations based on each of them, are involved in the configuration space. Such a framework can be expected to provide a proper description to the transitional nuclei, in which the shape coexistence or shape evolution might exhibit.…”

“…These modifications are done in order to obtain reasonable energy curves as noted in Ref. [21]. The strengths χ of the quadrupole-quadrupole interactions are 90% of those in the earlier PSM calculation for 78 Kr [19] and are kept constant for all of the isotopes studied.…”

“…In this paper the yrast lines of Kr isotopes with N = 42, 44, and 46 are studied within the framework proposed in Refs. [21,22], in order to show the effect of oblate pair breaking on the yrast behavior.…”