Transition matrix elements for the exotic double-charge exchange μ−→e+ conversion in 27Al

The lepton and lepton flavor violating process of the muon-to-positron conversion in 27Al is studied with emphasis on mechanisms mediated by heavy neutrinos. We investigate two such cases: (i) the mode which involves only nucleons in the nucleus (nuclear mode) and (ii) the mode mediated by pions (1-pion and 2-pions in flight between the interacting nucleons). The nuclear wave functions for the initial state of 27Al and all accessible final states of 27Na are obtained in the framework of 1s–0d shell model employing the well-known Wildenthal realistic interaction. The total strength is calculated by summing over all excited states up to the energy Ex=25 MeV. We found that the contributions from the 1-pion and nuclear mode are about eight times smaller than the 2-pion mode.