We present a shell-model analysis of $N=51$ isotones, ${}^{93}\mathrm{Mo}, {}^{95}\mathrm{Ru}, {}^{97}\mathrm{Pd}$, and ${}^{99}\mathrm{Cd}$ to quantify the role of neutron-proton interactions in shaping the location and half-life of isomeric states. The study is motivated by the anomalous behavior of the ${21/2}^{+}$ isomeric state in ${}^{93}\mathrm{Mo}$, a prominent candidate for nuclear excitation by electron capture (NEEC), which misses an $E2$ decay branch due to a higher-lying ${17/2}^{+}$ state and instead proceeds via a long-lived $E4$ isomeric transition. Employing a consistent configuration space and empirically derived effective interaction, we extract and compare the proton-proton and neutron-proton matrix elements for the four $N=51$ isotones. Our results show a distinct dominance of the neutron-proton interaction in ${}^{93}\mathrm{Mo}$, in contrast to its neighbors (${}^{95}\mathrm{Ru}, {}^{97}\mathrm{Pd}$, and ${}^{99}\mathrm{Cd}$) where no analogous isomeric behavior emerges due to structural evolution. These findings reveal that the favorable structure for NEEC in ${}^{93}\mathrm{Mo}$ stems from subtle interaction systematics that do not persist across the chain. We find that the $E2$ strength of the key NEEC transition is reduced by 40% compared to the previously estimated value. The analysis provides microscopic insights into the origin of long-lived isomerism in medium-mass nuclei and outlines a framework for identifying future candidates in other mass regions for exploiting the potential energy storage capacities of isomeric states.

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• Electromagnetic transitions
• Isomer decays
• Nuclear structure & decays
• Shell model
• 90 ≤ A ≤ 149