Structural evolution in Pt isotopes with the interacting boson model Hamiltonian derived from the Gogny energy density functional

Abstract

Spectroscopic calculations are carried out for the description of the shape/phase transition in Pt nuclei in terms of the interacting boson model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density-dependent Gogny-D1S energy density functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. By using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and sideband levels are well reproduced. From the systematics of the calculated spectra and the reduced $E2$ transition probabilities $B$($E2$), the prolate-to-oblate shape/phase transition is shown to take place quite smoothly as a function of neutron number $N$ in the considered Pt isotopic chain, for which the $\ensuremath{\gamma}$ softness plays an essential role. All of these spectroscopic observables behave consistently with the relevant PES and the derived parameters of the IBM Hamiltonian as functions of $N$. Spectroscopic predictions are also made for those nuclei that do not have enough experimental $E2$ data.