Abstract
We present a shell-model analysis of π=51 isotones,
93
Mo
,
95
Ru
,
97
Pd
, and
99
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
Mo
, a prominent candidate for nuclear excitation by electron capture (NEEC), which misses an πΈβ’2 decay branch due to a higher-lying 17/2+ state and instead proceeds via a long-lived πΈβ’4 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 π=51 isotones. Our results show a distinct dominance of the neutron-proton interaction in
93
Mo
, in contrast to its neighbors (
95
Ru
,
97
Pd
, and
99
Cd
) where no analogous isomeric behavior emerges due to structural evolution. These findings reveal that the favorable structure for NEEC in
93
Mo
stems from subtle interaction systematics that do not persist across the chain. We find that the πΈβ’2 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.