Origin of the electric hexadecapole isomer in $^{93}$Mo

TL;DR

This paper uses shell-model calculations to analyze the unique electric hexadecapole isomer in $^{93}$Mo, revealing the microscopic origin of its slow E4 decay and contrasting it with $^{99}$Cd.

Contribution

It provides a detailed shell-model explanation for the E4 isomer in $^{93}$Mo, highlighting the structural factors behind its unusual decay behavior.

Findings

The E4 transition in $^{93}$Mo is dominated by specific wave function components.

The E2 decay path is energetically forbidden in this isomer.

Contrasts with $^{99}$Cd show the absence of similar E4 transitions.

Abstract

We present a shell-model analysis of $^{93}$Mo to investigate the unusual behavior of its ${21/2}^+$ isomer -- a prominent candidate for nuclear excitation by electronic capture. This state is unique as its decay is dominated by a slow electric hexadecapole $E4$ transition, while the typically much faster electric quadrupole $E2$ decay path is energetically forbidden. We investigate the microscopic origin of this phenomenon by examining in detail the structure of the wave functions of the initial and final states, and the $E4$ transition matrix elements. This analysis of $^{93}$Mo is contrasted with that of its particle-hole conjugate, $^{99}$Cd, where such an $E4$ transition is absent.