  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 a
Hartree-Bogoliubov model 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 rated, which related more closely to what a given
experiment acturally measures, and better separate lepton physics from nuclear
physics effects.
