# Structural evolution in germanium and selenium nuclei within the mapped interacting boson model based on the Gogny energy density functional

## TL;DR

This study combines microscopic mean-field calculations with the interacting boson model to analyze shape transitions and coexistence in germanium and selenium isotopes, providing insights into their structural evolution and predictions for neutron-rich nuclei.

## Contribution

It introduces a novel approach that maps Gogny energy density functional results onto the IBM framework to study nuclear shape coexistence and evolution.

## Key findings

- Many nuclei exhibit $b3$ softness.
- Coexistence of prolate, oblate, and spherical shapes observed.
- Reasonable agreement with experimental data and predictions for neutron-rich isotopes.

## Abstract

The shape transitions and shape coexistence in the Ge and Se isotopes are studied within the interacting boson model (IBM) with the microscopic input from the self-consistent mean-field calculation based on the Gogny-D1M energy density functional. The mean-field energy surface as a function of the quadrupole shape variables $\beta$ and $\gamma$, obtained from the constrained Hartree-Fock-Bogoliubov method, is mapped onto the expectation value of the IBM Hamiltonian with configuration mixing in the boson condensate state. The resultant Hamiltonian is used to compute excitation energies and electromagnetic properties of the selected nuclei $^{66-94}$Ge and $^{68-96}$Se. Our calculation suggests that many nuclei exhibit $\gamma$ softness. Coexistence between prolate and oblate, as well as between spherical and $\gamma$-soft, shapes is also observed. The method provides a reasonable description of the observed systematics of the excitation energy of the low-lying energy levels and transition strengths for nuclei below the neutron shell closure $N=50$, and provides predictions on the spectroscopy of neutron-rich Ge and Se isotopes with $52\leq N\leq 62$, where data are scarce or not available.