Study of shape transitions in $N\sim90$ isotopes with beyond mean field calculations

TL;DR

This study investigates shape transitions in certain isotopes using advanced beyond mean field calculations, comparing results with theoretical models and experimental data, and finds no evidence for a first order phase transition or critical point at N=90.

Contribution

It applies modern beyond mean field methods with Gogny D1S force to analyze shape transitions, challenging previous interpretations of N=90 as a critical point.

Findings

No support for first order phase transition in studied isotopes.

Results do not confirm N=90 as a critical point.

Calculations align with experimental data without indicating shape phase transition.

Abstract

We study the spherical to prolate-deformed shape transition in $^{144-158}$Sm and $^{146-160}$Gd isotopes with modern calculations beyond the mean field with the Gogny D1S force. We compare the results with the shape-phase transition predicted by the collective hamiltonian model and with the experimental data. Our calculations do not support the existence of a first order phase transition in these isotopic chains in the viewpoint of the Bohr hamiltonian neither the interpretation of the nuclei N=90 as critical points.