A new determination of the (Z,A) dependence of coherent muon-to-electron conversion

Should muon-to-electron conversion in the field of a nucleus be found in the current generation of experiments, the measurement of the atomic number dependence of the process will become an important experimental goal. We present a new treatment of the (Z,A) dependence of coherent muon-to-electron conversion in 236 isotopes. Our approach differs from previous treatments in several ways. Firstly, we include the effect of permanent quadrupole deformation on the charged lepton flavor violating matrix elements, using the method of Barrett moments. This method also enables the addition of muonic X-ray nuclear size and shape determinations of the charge distribution to the electron scattering results used previously. Secondly, we employ the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) to calculate neutron-related matrix elements for even-even nuclei. This takes into account the quadrupole deformation of the neutron distributions and the fact that neutrons are, in general, in different shell model orbits than protons. The calculated conversion rates differ from previous calculations, particularly in the region of large permanent quadrupole deformation. Finally, we propose an alternative normalization of the muon-to-electron conversion rate, which is related more closely to what a given experiment actually measures, and better separates lepton physics from nuclear physics effects.