Study of the flavour violating (μ,e) conversion in nuclei

The muon number violating (μ⁻, e⁻) conversion in the presence of nuclei is investigated. The effective operators resulting from various mechanisms, both photonic and non-photonic, are expressed in terms of nuclear coordinates: (i) for intermediate neutrino models, and (ii) for supersymmetric theories. Using these operators the (A, Z) dependence of the corresponding widths is discussed throughout the periodic table. For the coherent process the dependence of the conversion rate on the nuclear parameters is given in terms of the elastic nuclear form factors, which are obtained in the context of shell model, taking into account finite nucleon-size effects. For the inclusive μ−e conversion process the total rates are calculated for closed-shell nuclei. The method of calculation utilizes microscopic non-energy-weighted sum rules (closure). The isospindependent part of the total (μ⁻, e⁻) rate is also related to that of the total (μ⁻, _vμ capture rate, the latter being calculated with Primakoff's phenomenological method. The agreement between the two provides a good test of the reliability of the shell-model closure calculations. For non-closed-shell nuclei the relevant rates can be obtained by interpolation techniques from the functions obtained in the present work for closed-shell nuclei. Finally the experimentally interesting ratio of the coherent to the total μ−e conversion rate is discussed.