Ordinary Muon Capture on ¹³⁶Ba: Comparative Study Using the Shell Model and pnQRPA

In this work, we present a study of ordinary muon capture (OMC) on Ba-136, the daughter nucleus of Xe-136 double beta decay (DBD). The OMC rates at low-lying nuclear states (below 1 MeV of excitation energy) in Cs-136 are assessed by using both the interacting shell model (ISM) and proton-neutron quasiparticle random-phase approximation (pnQRPA). We also add chiral two-body (2BC) meson-exchange currents and use an exact Dirac wave function for the captured s-orbital muon. OMC can be viewed as a complementary probe of the wave functions in Cs-136, the intermediate nucleus of the Xe-136 DBD. At the same time, OMC can be considered a powerful probe of the effective values of weak axial-type couplings in a 100 MeV momentum exchange region, which is relevant for neutrinoless DBD. The present work represents the first attempt to compare the ISM and pnQRPA results for OMC on a heavy nucleus while also including the exact muon wave function and the 2BC. The sensitivity estimates of the current and future neutrinoless DBD experiments will clearly benefit from future OMC measurements taken using OMC calculations similar to the one presented here.