E(5) and X(5) shape phase transitions within a Skyrme-Hartree-Fock + BCS approach

Abstract

Self-consistent Skyrme-Hartree-Fock plus BCS calculations are performed to generate potential energy curves (PECs) in various chains of Pd, Xe, Ba, Nd, Sm, Gd, and Dy isotopes. The evolution of shapes with the number of nucleons is studied in a search for signatures of E(5) and X(5) critical point symmetries. It is shown that the energy barriers in the PECs are determined to a large extent by the treatment of the pairing correlations.

Evolution of nuclear shapes in medium mass isotopes from a microscopic perspective

“…A comparison with similar results obtained in Ref. [19] with the parametrization SLy4 of the Skyrme force [21] plus a zero range pairing [22] will also be considered.…”

“…Different combinations of mean-field and pairing treatments were also considered in Ref. [19]. As a result of this study, it was found that the energy of the spherical barriers strongly depend on the details of the calculations, especially on the pairing force.…”

“…All the microscopic studies carried out so far, both relativistic [15][16][17] and nonrelativistic [19], have been based on very powerful and state-of-the-art mean-field approximations. Nevertheless, in all of them, the mean-field and pairing channels have been calculated using different forces.…”

“…[17,19], as part of an ongoing effort to explore the shape of the PES over an extended range of nuclei to search for those intermediate situations in which either good candidates to be described by simple dynamical symmetry models can be found or admit more elaborated treatments beyond the mean field. Therefore, in the present study we will use the HFB approximation with the Gogny interaction to study systematically the PEC and PES of several isotopic chains to check for the occurrence of the above-mentioned intermediate situations not corresponding either to well-deformed or spherical systems.…”

“…Only recently has the first step been undertaken using the selfconsistent Skyrme Hartree-Fock + BCS mean-field approximation [2,18]. The calculations [19] were based on the code EV8 [20] using the parametrization SLy4 [21] of the Skyrme interaction in the particle-hole (ph) channel together with a zero-range and density-dependent interaction in the pairing channel [22] (with strength g = 1000 MeV fm 3 ). Different combinations of mean-field and pairing treatments were also considered in Ref.…”