Modification of single-hole-like states by configuration mixing in the $^{99-131}$In

Abstract

Large-scale shell-model calculations are performed for the $9/2^+_{\rm g.s.}$, $1/2^-_1$, $3/2^-_1$, and $5/2^-_1$ states in the odd-$A$ indium isotopes with $N=50-82$. The calculated energy levels, electromagnetic moments, and spectroscopic factors exhibit remarkable agreement with the experimental data due to significant configuration mixing for the neutron numbers away from the closed shells. The $1/2^-_1$ energy levels closely follow the trend of effective single-particle energies, which are determined using the fractional occupancies of neutron orbitals. However, configuration mixing with the proton $p_{3/2}$ and $f_{5/2}$ orbitals in the actual shell-model calculations plays a crucial role in accurately reproducing the positions of the $1/2^-_1$ levels, ensuring better agreement with the experimental data across the entire isotopic chain.