Valence-mirror symmetry in the first g9/2 subshell for semi-magic nuclei

Abstract

The ${}_{28}^{70}$Ni₄₂/${}_{42}^{92}$Mo₅₀, ${}_{28}^{72}$Ni₄₄/${}_{44}^{94}$Ru₅₀, ${}_{28}^{74}$Ni₄₆/${}_{46}^{96}$Pd₅₀ and ${}_{28}^{76}$Ni₄₈/${}_{48}^{98}$Cd₅₀ valence-mirror pairs have been studied using valence-mirror energy differences for the first time. Valence-mirror symmetry is discussed based on a systematic analysis of the valence-mirror energy differences and supported by shell-model calculations. Mass scaling of the energy spacings in ⁷⁴Ni/⁹⁶Pd/¹²⁸Pd and ⁷⁶Ni/⁹⁸Cd/¹³⁰Cd has been investigated, focusing on the $8^{+}-0^{+}$ and $8^{+}-2^{+}$ spacings. In particular, simple schematic shell-model calculations using a $\delta$ interaction have been performed for ⁷⁶Ni and ¹³⁰Cd to study the structural evolution with increasing spin.