Ordinary muon capture rates on $^{100}$Mo and $^{\rm nat}$Mo for astro-antineutrinos and double beta decays

\item[Background] The nuclear responses for antineutrinos associated with double beta decays (DBDs) and astro-antineutrino interactions are studied by measuring ordinary muon capture (OMC) rates. \item[Purpose]The experimental studies of absolute OMC rates and their mass number dependence for $^{100}$Mo and the natural Mo are currently of interest in astro-antineutrinos and DBDs. \item[Method]The OMC rates were obtained experimentally by measuring the time spectrum of the trapped muon's decay into electrons to obtain the half-lives of the trapped muons. \item[Results]The OMC rate for the enriched isotope of $^{100}$Mo is $\Lambda$($^{100}$Mo)=(7.07$\pm$0.32)$\times10^{6}$ s$^{-1}$, while that for the natural Mo is $\Lambda$($^{\rm nat}$Mo)=(9.66$\pm$0.44)$\times10^{6}$ s$^{-1}$, i.e., $\Lambda$($^{100}$Mo) is about 27$\%$ of $\Lambda$($^{\rm nat}$Mo), reflecting the blocking effect of the excess neutrons for the proton-to-neutron transformation in OMC. The present experimental observation is consistent with the predictions using Goulard-Primakoff's (GPs) and Primakoff's (Ps) empirical equations. \item[Conclusions] The absolute OMC rates for $^{100}$Mo and $^{\rm nat}$Mo were measured. The large neutron excess in $^{100}$Mo gives a much lower OMC rate than $^{\rm nat}$Mo. On both $^{100}$Mo and $^{\rm nat}$Mo, consistent OMC rates with the GP and P values are observed.