Phase change near $N=70$ in the wave function of the $I^{\pi}=11/2^-$ isomers along the cadmium-isotope chain

TL;DR

This paper investigates a sudden phase change in the wave functions of $11/2^-$ isomers in cadmium isotopes around neutron number 70, using shell-model calculations and analyzing electromagnetic properties.

Contribution

It identifies and confirms a phase transition at $N=70$ in the wave functions of these isomers, providing a new explanation based on particle-hole transformation properties.

Findings

Phase change at $N=70$ confirmed by wave-function analysis.

Different linear relations for $Q$ and $\mu$ values across $N=70$.

Shell-model reproduces experimental electromagnetic data.

Abstract

The electromagnetic features of the $11/2^-$ isomers in the $^{111-127}$Cd isotopes are reproduced by numerically optimized shell-model wave-functions. A sudden phase change of the wave functions at $N = 70$ is identified and further confirmed by the evolution of B(E2, $7/2^-_1\rightarrow 11/2^-_1$) values. This phase change gives rise to different linear relations for the $Q$ and $\mu$ values with $N<70$ and $N>70$, as needed to reproduce the experimental data. The particle-hole transformation properties for $h_{11/2}$ neutrons in a well-isolated subshell involving degenerate $s_{1/2}$, $d_{3/2}$, $d_{5/2}$ and $h_{11/2}$ orbits is suggested as a possible explanation for this phase change.