# Shape-phase transitions in odd-mass $\gamma$-soft nuclei with mass $A\approx 130$

## TL;DR

This paper investigates quantum shape-phase transitions in odd-mass nuclei around mass 130 using a microscopic energy density functional approach combined with a particle-boson coupling model, successfully reproducing experimental spectra.

## Contribution

It introduces a microscopic framework that models shape-phase transitions in odd-mass nuclei, incorporating self-consistent mean-field calculations and particle-core coupling with minimal parameter adjustment.

## Key findings

- Reproduces experimental low-energy spectra and electromagnetic properties.
- Confirms phase transition between spherical and $ ext{gamma}$-soft shapes in odd-A nuclei.
- Applies successfully to Ba, Xe, La, and Cs isotopes around mass 130.

## Abstract

Quantum phase transitions between competing equilibrium shapes of nuclei with an odd number of nucleons are explored using a microscopic framework of nuclear energy density functionals and a particle-boson core coupling model. The boson Hamiltonian for the even-even core nucleus, as well as the spherical single-particle energies and occupation probabilities of unpaired nucleons, are completely determined by a constrained self-consistent mean-field calculation for a specific choice of the energy density functional and pairing interaction. Only the strength parameters of the particle-core coupling have to be adjusted to reproduce a few empirical low-energy spectroscopic properties of the corresponding odd-mass system. The model is applied to the odd-A Ba, Xe, La and Cs isotopes with mass $A\approx 130$, for which the corresponding even-even Ba and Xe nuclei present a typical case of $\gamma$-soft nuclear potential. The theoretical results reproduce the experimental low-energy excitation spectra and electromagnetic properties, and confirm that a phase transition between nearly spherical and $\gamma$-soft nuclear shapes occurs also in the odd-A systems.