Resonance conditions for ${}^{93m}\mathrm{Mo}$ isomer depletion via nuclear excitation by electron capture in a beam-based scenario

We present here a comprehensive analysis to understand the optimal atomic conditions for the first experimental observation of nuclear excitation by electron capture (NEEC) for the 6.85 h ${}^{93m}\mathrm{Mo}$ isomer with spin parity $21/2^{+}$. The NEEC process would provide an excitation from the long-lived isomer to a depletion level with spin parity $17/2^{+}$, which lies only 4.85 keV higher in energy, and is itself a shorter-lived isomer that subsequently decays, releasing a substantial amount of stored energy (2429.8 keV). The depletion level decays to a $13/2^{+}$ state through a 267.9-keV transition that offers the opportunity for identification of NEEC because it does not occur in the natural decay of the long-lived isomer. It has been shown that, for the proposed approach, high-precision atomic predictions are essential to understanding the proper physical conditions under which the experimental observation of the NEEC process will be possible using a beam-based scenario.

Figure 1

Partial level scheme (not to scale) for the ${}^{93}\mathrm{Mo}$ nucleus ($Z=42$). The gray arrow is the transition excited by NEEC, after production of the long-lived ${}^{93m}\mathrm{Mo}$ isomer, while the solid black arrows show the natural decay cascade from that isomer. The green transitions are unique signatures of NEEC that result in decay from the depletion level, once it is excited from the 6.85-h isomer. The right side of the figure gives the level energies (in keV) and half-lives, and the left side gives the angular momenta and parities, taken from Ref. [13].

Figure 2

General layout for experimental detection of the NEEC process as proposed in Ref. [12].

Figure 3

Cross section for the ${}^{91}\mathrm{Zr}+{}^4\mathrm{He}$ beam-target reaction, calculated with the pace4 code [15]. The total cross section leading to ${}^{93}\mathrm{Mo}$ (estimated to ${}^{93m}\mathrm{Mo}$) is plotted with squares and a solid (dashed) blue line. The $\left(3n\right)$, etc. in the legend refer to the evaporated nucleons from the nucleus due to the fusion-evaporation reaction modeled. The strongest competing reaction products are also indicated, with other background summing contributions from ${}^{93,94}\mathrm{Nb}$ and ${}^{90}\mathrm{Zr}$.

Figure 4

Two scenarios for NEEC resonance window width. Panel (a) describes production, after free electron capture, of a double (atomic and nuclear) excited intermediate state for the $1s^{2}2s^{2}2p^{4}3d^1$ excited atomic configuration of ${}^{93}\mathrm{Mo}$ ions (${\mathrm{\Gamma }}_{nl}^{\mathrm{Atomic}}>$ 0). Panel (b) describes production, after free electron capture, of an intermediate state which corresponds only to nuclear excitation. In this case, an electron has been captured into the $3s$ subshell of the ${}^{93}\mathrm{Mo}$ ion atomic ground state with $q=32+$ for the $1s^{2}2s^{2}2p^6$ closed-shell configuration and, therefore, ${\mathrm{\Gamma }}_{nl}^{\mathrm{Atomic}}=0$ (see Table 1).

Figure 5

The resonance conditions for ${}^{93m}\mathrm{Mo}$ ion energy release via the NEEC process with a schematic depiction of the discrete but varying steps ($\mathrm{\Delta }{E}^{\mathrm{kin}}$) for ions slowing down in a medium near the NEEC resonance. Two cases are shown: (a) ${\mathrm{\Gamma }}_{3d}^{\mathrm{Atomic}}\gg \mathrm{\Delta }{E}^{\mathrm{kin}}$ and (b) ${\mathrm{\Gamma }}_{3p}^{\mathrm{Atomic}}\ll \mathrm{\Delta }{E}^{\mathrm{kin}}$ (see Table 1). The $\mathrm{\Delta }{E}^{\mathrm{kin}}$ do not represent actual calculated steps.

Figure 6

Predicted $q_{\mathrm{mean}}$ of a ${}^{93m}\mathrm{Mo}$ ion as a function of its kinetic energy for He gas (top) and C solid (bottom) stopping media. The vertical bars present the potential positions of the ${}^{93m}\mathrm{Mo}$ ion NEEC resonance kinetic energies, which can occur for $q$ (vertical axis), from $q=32+$ to $q=36+$ as indicated when the tops of the bars are within the $q$ range. Each set of three bars represents, from left to right, electron capture into the $d, p$, and $s$ subshells.