# Description of shape coexistence in $^{96}$Zr based on the collective quadrupole Bohr Hamiltonian

## TL;DR

This paper models the shape coexistence in $^{96}$Zr using the collective quadrupole Bohr Hamiltonian, achieving good agreement with experimental data by adjusting the inertia coefficients and considering shell effects.

## Contribution

It introduces a detailed geometrical model with a double-minimum potential to describe shape coexistence in $^{96}$Zr, highlighting the importance of inertia parameters and shell effects.

## Key findings

- Good agreement with experimental energies and transition probabilities.
- Shape coexistence is well reproduced with a tailored potential.
- Shell effects and pairing vibrations influence specific transition rates.

## Abstract

Experimental data on $^{96}$Zr indicate coexisting spherical and deformed structures with small mixing amplitudes. We investigate the properties of the low-lying collective states of $^{96}$Zr based on the collective quadrupole Bohr Hamiltonian. The $\beta$-dependent collective potential having two minima -- spherical and deformed, is fixed so to describe experimental data in the best way.Good agreement with the experimental data on the excitation energies, $B(E2)$ and $B(M1)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of $^{96}$Zr can be reproduced in a satisfactory way in the geometrical model with a potential function supporting shape coexistence. However, the excitation energy of the $2^+_2$ state can be reproduced only if the rotation inertia coefficient is taken five times smaller then the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of the $B(M1;2^+_2 \rightarrow 2^+_1)$ value. An indication on the influence of the pairing vibrational mode on the $\rho^2 (0^+_2 \rightarrow 0^+_1)$ value is obtained.