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

We present a shell-model analysis of ${}^{93}$Mo to investigate the unusual behavior of its ${21\mathrm{/}2}^{+}$ 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.