State-by-state calculations for all channels of the exotic $(\mu^-,e^-)$ conversion process

Abstract

The coherent and incoherent channels of the neutrinoless muon to electron conversion in nuclei, $\mu^- (A,Z) \to e^- (A,Z)^*$, are studied throughout the periodic table. The relevant nuclear matrix elements are computed by explicitly constructing all possible final nuclear states in the context of the quasi-particle RPA. The obtained results are discussed in view of the existing at PSI and TRIUMF experimental data for $^{48}Ti$ and $^{208}Pb$ and compared with results obtained by: (i) shell model sum-rule techniques (ii) nuclear matter mapped into nuclei via a local density approximation and (iii) earlier similar calculations.