Comparative analysis of muon-capture and 0νββ -decay matrix elements

Abstract

Average matrix elements 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 and compared with the corresponding energy and multipole decompositions of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay nuclear matrix elements (NMEs). The present OMC computations are performed using the Morita-Fujii formalism by extending the original formalism beyond the leading order. The $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NMEs include the appropriate short-range correlations, nuclear form factors, and higher-order nucleonic weak currents. The nuclear wave functions are obtained in extended no-core single-particle model spaces using the spherical version of the proton-neutron quasiparticle random-phase approximation with two-nucleon interactions based on the Bonn one-boson-exchange $G$ matrix. Both the OMC and $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes involve 100-MeV-range momentum exchanges and hence similarities could be expected for both processes in the feeding of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ intermediate states. These similarities may help improve the accuracy of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ NME calculations by using the data from the currently planned OMC experiments.