State-by-state calculations for all channels of the exotic $(\hat{I}{¼}^{-},e^{-})$ conversion process

Abstract

The coherent and incoherent channels of the neutrinoless muon to electron conversion in nuclei, $\hat{I}{¼}^{-}(A,Z)\to e^{-}(A,Z{)}^{\ast }$, 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.

16 pages (LATEX-file) including 6 tables, 2 PostScript Figures included (Fig1(a)-(d), Fig2(a)-(b)), Refs. 35. Phys. Rev. C, accepted