Competing shape evolution, crossing configurations and single particle levels in nuclei

TL;DR

This paper investigates shape evolution, configuration crossing, and single particle energy changes in odd-mass zirconium isotopes using the interacting boson-fermion model, revealing insights into quantum phase transitions and shell evolution.

Contribution

It introduces a detailed analysis of odd-mass Zr isotopes' shape and configuration changes, highlighting quantum phase transitions and shell evolution with new interpretations for specific states.

Findings

Good agreement between calculated and experimental energy levels and moments.

Identification of quantum phase transitions near $^{99}$Zr.

New interpretation of the $^{99}$Zr isomeric state.

Abstract

The evolution of shape in the even-even zirconium (Zr) isotopes has been the subject of study for many years. However, the odd-mass isotopes have not been investigated as extensively due to limited experimental accessibility and computational challenges. This work, employing the interacting boson-fermion model with configuration mixing, examines the effect of rapid shape evolution and normal-intruder configuration crossing -- both identified as quantum phase transitions -- alongside evolution in single particle energies, on the positive-parity spectrum of odd-mass $^\text{93-103}$Zr isotopes. Calculated energy levels, magnetic moments, $B(E2)$ values, and quadrupole moments are compared to experimental data, showing good agreement. The special case of $^{99}$Zr, which lies near the critical point of both quantum phase transitions, is also addressed, offering a new interpretation to the $7/2^+_1$ isomeric state and the occurrence of the type II shell evolution, in light of recent debates.