Application of the particle-number projected proton-neutron QRPA to the muon capture on 136Ba

The proton-neutron quasiparticle random-phase approximation (QRPA) has been widely used to describe various nuclear processes, in particular the ordinary muon capture (OMC). In the present work, we apply for the first time the particle-number projected QRPA (PQRPA) to calculate the OMC on the 0 + ground state of 136 Ba and include a comparison with the results obtained using the standard QRPA, both in the proton-neutron channel. The nucleus 136 Ba is the daughter nucleus in the neutrinoless double beta ( 0 ν β β ) decay Xe 136 ( 0 + ) → Ba 136 ( 0 + ) , an important transition for searches of Majorana neutrinos in the present and future large-scale 0 ν β β -decay experiments. Both the 0 ν β β decay and OMC populate the ground and excited states of the 0 ν β β -decay intermediate nucleus 136 Cs in the same momentum-exchange region of q ∼ 100 MeV, thus making the OMC a perfect probe of the 0 ν β β decay. We compute OMC rates to nuclear states below 1 MeV of excitation energy in 136 Cs, a region accessible to present-day OMC experiments, like MONUMENT. We use a Bonn G-matrix based effective interaction and a large no-core single-particle basis, also adding the chiral two-body meson-exchange currents (2BC) and using exact Dirac wave function for the captured s -orbital muon. It turns out that the OMC rates computed in the PQRPA framework are notably larger than those computed using QRPA for few very low-lying 3 + states offering a strong incentive for future experimental studies of the OMC on 136 Ba.