${}^{93m}\mathrm{Mo}$ Isomer Depletion via Beam-Based Nuclear Excitation by Electron Capture

A recent nuclear physics experiment [C. J. Chiara et al., Nature (London) 554, 216 (2018)] reports the first direct observation of nuclear excitation by electron capture (NEEC) in the depletion of the ${}^{93m}\mathrm{Mo}$ isomer. The experiment used a beam-based setup in which Mo highly charged ions with nuclei in the isomeric state ${}^{93m}\mathrm{Mo}$ 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 $P_{\text{exc}}=0.01$ 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 9 orders of magnitude. This stands in conflict with the conclusion that NEEC was the excitation mechanism behind the observed depletion rate.

Figure 1

Sketch of the beam-based experimental setup with a graphical illustration of the NEEC process and the partial level scheme of ${}^{93m}\mathrm{Mo}$. In Ref. [28], the stopping target comprised a C and a Pb layer. The nuclear isomeric ($\mathrm{I}\mathrm{S}$), triggering ($T$), intermediate ($F$), and ground-state ($\mathrm{G}\mathrm{S}$) levels are labeled by their spin, parity, and energy in keV, taken from Ref. [29]. Energy intervals are not to scale.

Figure 2

Right axis: Mean charge state $\overline{q}$ (lines) and width $w$ (shaded area) for ${}^{93}\mathrm{Mo}$ ions as a function of the ion energy using the fit formulas (i) from Ref. [40] (blue dashed line and blue shading) and (ii) in Ref. [41] (orange solid line and orange shading). Left axis: Stopping power for ${}^{93}\mathrm{Mo}$ ions in the carbon solid target as a function of the total ion energy. Gray circles: casp simulation considering an averaged equilibrium charge state. Brown dash-dotted line: The Javanainen semiempirical formula [43]. A density of $2.0\mathrm{g}/{\mathrm{cm}}^3$ for the carbon target was considered.

Figure 3

NEEC probability $P_q^{\alpha }$ for all considered 648 recombination channels as a function of charge state $q$ and ion energy. For illustration, the $L$-shell values are presented in the inset.