Quantum Phase Transition in the Shape of Zr isotopes

TL;DR

This paper investigates the quantum phase transition in Zr isotopes near neutron number 60, revealing shape changes driven by shell evolution and proton excitations, supported by shell-model calculations matching experimental data.

Contribution

It demonstrates that the shape transition in Zr isotopes is a quantum phase transition caused by shell evolution and proton excitations, using comprehensive shell-model calculations.

Findings

Identification of shape coexistence in Zr isotopes.

Good agreement between calculations and experimental energy levels.

Evidence of a quantum phase transition driven by shell evolution.

Abstract

The rapid shape change in Zr isotopes near neutron number $N$=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its $0g_{9/2}$ orbit, and is shown to be a quantum phase transition. Monte Carlo shell-model calculations are carried out for Zr isotopes of $N$=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in a good agreement with experiments, depicting various shapes in going from $N$=50 to 70. Novel coexistence of prolate and triaxial shapes is suggested.