QRPA and PQRPA treatments of Ordinary Muon Capture: the case of 136Ba

The proton-neutron quasiparticle random-phase approximation (QRPA) and its particle-number projected version (PQRPA) are used to calculate the ordinary muon capture (OMC) on the ground state of $^{136}$Ba. Both the neutrinoless double beta decay ($0\nu\beta\beta$) and OMC populate the ground and excited states of $^{136}$Cs. This offers, for the case of the OMC, a valuable source of information about the still unobserved lepton number violating $0\nu\beta\beta$ process. We have computed OMC rates to nuclear states in $^{136}$Cs, in a region accessible to present-day OMC experiments. It turns out that the OMC rates computed in the PQRPA framework are larger than those computed using the QRPA.