Muon-capture strength functions in intermediate nuclei of 0νββ decays

Capture rates of ordinary muon capture (OMC) to the intermediate nuclei of neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of current experimental interest are computed. The corresponding OMC (capture-rate) strength functions have been analyzed in terms of multipole decompositions. The computed low-energy OMC-rate distribution to $^{76}\mathrm{As}$ is compared with the available data of Zinatulina et al. [Phys. Rev. C 99, 024327 (2019)]. The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The participant nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of proton-neutron quasiparticle random-phase approximation (pnQRPA) with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. The Hamiltonian parameters are taken from our earlier work [Jokiniemi et al., Phys. Rev. C 98, 024608 (2018)], except for $A=82$ nuclei for which the parameters were determined in this work. Both the OMC and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decays involve momentum exchanges of the order of 100 MeV and thus future measurements of the OMC strength functions for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ daughter nuclei help trace the in-medium renormalization of the weak axial couplings with the aim to improve the accuracy of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements.