State-by-state calculations for all channels of the exotic (μ-,e-) conversion process

Abstract

The coherent and incoherent channels of the neutrinoless muon to electron conversion in nuclei, ${\ensuremath{\mu}}^{\ensuremath{-}}(A,Z)\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{(A,Z)}^{*}$, 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 quasiparticle random phase approximation. The obtained results are discussed in view of the existing at PSI and TRIUMF experimental data for ${}^{48}\mathrm{Ti}$ and ${}^{208}\mathrm{Pb}$ 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.