$^{93m}$Mo isomer depletion via beam-based nuclear excitation by electron capture

A recent nuclear physics experiment [C. J. Chiara {\it et al.}, Nature (London) {\bf 554}, 216 (2018)] reports the first direct observation of nuclear excitation by electron capture (NEEC) in the depletion of the $^{93m}$Mo isomer. The experiment used a beam-based setup in which Mo highly charged ions with nuclei in the isomeric state $^{93m}$Mo at 2.4 MeV excitation energy were slowed down in a solid-state target. In this process, nuclear excitation to a higher triggering level led to isomer depletion. The reported excitation probability $P_{\rm{exc}} = 0.01$ was solely attributed to the so-far unobserved process of NEEC in lack of a different known channel of comparable efficiency. In this work, we investigate theoretically the beam-based setup and calculate excitation rates via NEEC using state-of-the-art atomic structure and ion stopping power models. For all scenarios, our results disagree with the experimental data by approximately nine orders of magnitude. This stands in conflict with the conclusion that NEEC was the excitation mechanism behind the observed depletion rate.