Shell-model matrix elements for muonic processes in light nuclei

The nuclear shell-model is used to calculate the nuclear matrix elements for the ordinary muon capture and the muon-electron conversion. In the ordinary muon capture, various residual interactions are applied, and the results are compared to experimental data on capture rates and angular correlations. The renormalized single-particle transition operators are introduced and applied in 28Si and 20Ne. These renormalized operators yield results, which are in better agreement with the predictions coming from the partially conserved axial vector hypothesis than the results obtained with bare operators. The renormalization effects are found to be interaction-independent. Otherwise, different interactions can give very contradictory results. The single-particle matrix elements with Woods-Saxon radial wave functions are compared to ones obtained with harmonic oscillator radial wave functions. The changes in the capture rates and angular correlation parameters are generally small, and they do not solve the discrepancies between the theory and experiment. The lepton-flavor violating muon-electron conversion in 27Al and 48Ti is used to restrict the lepton-flavor violating parameters that are included in the extensions of the standard model. Various possible reaction mechanisms are investigated, and channel-by-channel calculations are carried out. The results show that the ground-state to ground-state transition dominates in the two nuclei considered. This increases the possibility of the detection of the muon-electron conversion. In addition, we have separately calculated the vector and axial vector contributions as well as isoscalar and isovector contributions.