On the nuclear dependence of the mu-e conversion branching ratio

The variation of the coherent branching ratio $R_{\mu e}$ (ratio of the ${\mu }^{-}\to e^{-}$ reaction rate divided by the total muon-capture rate) through the periodic table is studied by using exact muon wave functions. It was found that, by using very heavy nuclei (e.g. \nuc{197}Au, the SINDRUM II target) as ${\mu }^{-}\to e^{-}$ conversion stopping-targets, the above ratio is favored by a factor of about four to five than by using light ones (e.g. \nuc{48}Ti, chosen as PRIME target).