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 γ 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.

Quadrupole collective dynamics from energy density functionals: Collective Hamiltonian and the interacting boson model

“…This feature appears to be independent of the choice of the EDF. A recent microscopic calculation using the Gogny-D1S EDF [13] also yielded shallow triaxial shapes, rather flat in the oblate region [37], but quantitatively consistent with the present analysis. A similar trend was reported in other EDF-based studies of ground-state shapes of Pt isotopes [39,48,49].…”

“…The corresponding IBM energy surfaces follow this evolution, but do not reproduce the triaxial minima because of the reasons explained above. The recent Gogny-EDF calculation [37] predicts 192 Pt to be the softest Pt isotope in this mass region.…”

Shape coexistence in lead isotopes in the interacting boson model with a Gogny energy density functional

“…A possible application would be to analyze neighboring isotopic chains, mercury, polonium, and platinum isotopes. In particular, the study in the platinum isotopes will help to disentangle if the single configuration is the appropriate picture to describe those isotopes (see, e.g., [19,43] and references therein). Other mass regions, including neutron-deficient krypton, selenium, and germanium isotopes and neutron-rich krypton, strontium, and zirconium isotopes, which are also known as regions of shape coexistence [4], would be a potential target.…”

“…By mapping the potential-energy surface (PES), obtained within the constrained self-consistent mean-field method with a given EDF, onto the expectation value of the corresponding IBM Hamiltonian, the energy spectra and electromagnetic transition rates have been computed. This method has been successfully applied to various shape phenomena, including vibrational and γ -unstable [41] as well as rotational deformed [42] nuclei, to prolate-oblate shape transitions [43], and to the study of the fingerprints of triaxiality [44].…”

Nuclear shape coexistence in Po isotopes: An interacting boson model study

“…In contrast to the standard shell-model to boson-model mapping method [67,68], it has been shown that an IBM Hamiltonian can be determined, mapping a self-consistent mean-field total energy surface E(β,γ ) (over the full β-γ plane) onto the corresponding IBM mean-field energy. Very recently, this method was extended to include intruder mp-nh configurations, with a detailed coverage of the Pt, Pb, and Hg isotopes [69][70][71][72].…”