Measurements of ordinary muon capture rates on ${}^{100}\mathrm{Mo}$ and natural Mo for astro-antineutrinos and double-$\beta$ decays

Ordinary muon capture (OMC) rates are valuable for studying the neutrino nuclear responses of astrophysical antineutrinos and double-$\beta$ decays (DBDs). Currently, there is interest in experimental studies of the OMC rates and their mass number ($A$) dependence for ${}^{100}\mathrm{Mo}$ and natural Mo. To obtain these rates, a negative muon beam from the MuSIC facility at the Research Center for Nuclear Physics (RCNP), Osaka University was utilized. The half-lives of trapped muons were measured by using a muon stopping signal from a scintillation counter and the time distribution of the OMC nuclear gamma rays and the muon-decay electrons by Ge detectors. The present measurements yielded OMC rates for enriched and natural molybdenum of $\mathrm{\Lambda }\left({}^{100}\mathrm{Mo}\right)=(7.07\pm 0.32)\times {10}^6{\mathrm{s}}^{-1}$ and $\mathrm{\Lambda }\left({}^{\mathrm{nat}}\mathrm{Mo}\right)=(9.66\pm 0.44)\times {10}^6{\mathrm{s}}^{-1}$, respectively. The observed OMC rate for ${}^{100}\mathrm{Mo}$ is approximately 27% smaller than that for natural Mo due to the blocking effect of the excess neutrons on the proton-to-neutron transformation in OMC. The present experimental observation is consistent with the Goulard-Primakoff (GP) and Primakoff (P) empirical equations. The impacts of the present results on the astro-antineutrinos and double-$\beta$ decays are discussed.

Figure 1

Experimental setup and electronic configuration of muon irradiation on ${}^{\mathrm{nat}}\mathrm{Mo}$ and ${}^{100}\mathrm{Mo}$ at RCNP, Osaka University's MuSIC facility.

Figure 2

Electron time distributions for (a) ${}^{100}\mathrm{Mo}$ and (b) ${}^{\mathrm{nat}}\mathrm{Mo}$.

Figure 3

Calculated and experimental OMC rates as a function of $A$ for all Mo isotopes. The weighted average of the mass number for ${}^{\mathrm{nat}}\mathrm{Mo}$ is 96.14 $\pm$ 0.20. The weighted average for ${}^{100}\mathrm{Mo}$ is 99.8 and the deviation from 100 is less than 0.15. A small difference is observed in the low $A$ region between GP and P values.