Study of the muon number violating (μ, e conversion in a nucleus by using quasi-particle RPA

The exotic (μ⁻, e⁻) conversion reaction for the ⁴⁸Ti nucleus is studied in the framework of the quasi-particle random phase approximation (QRPA). For the non-coherent processes the relevant total rate is calculated by summing over partial rates for all the possible intermediate states constructed in the above approximation. For the coherent process the contribution is obtained by using an uncorrelated BCS vacuum. In order to check the validity of closure approximation, which is almost unavoidable in shell-model calculations, we also evaluate the total (μ⁻, e⁻) conversion rates by QRPA sum-rules by first explicitly calculating a suitable mean excitation energy of the nucleus. The influence of the ground state correlations to the (μ⁻, e⁻) conversion matrix elements is estimated by using a correlated RPA vacuum. The fraction of the transition rate of the coherent process for each of these methods is calculated and the results are compared to those found previously by using shell-model closure approximation.