The charged lepton flavor violating (CLFV) processes of µ − e − → e − e − decay by four Fermi contact interactions in a muonic atom for various atoms are investigated. The wave functions of bound and scattering state leptons are properly treated by solving Dirac equations with Coulomb interaction of the finite nuclear charge distributions. This new effect contributes significantly in particular for heavier atoms, where the obtained decay rate is about one order of magnitude larger than the previous estimation for 208 Pb. We find that, as the atomic number Z increases, the µ − e − → e − e − decay rates increase more rapidly than the result of the previous work of Z 3 , suggesting this decay as one of the promising processes to search for CLFV interaction.

Studies of the charged lepton flavor violating process of µ − e − → e − e − in muonic atoms by the four Fermi interaction [Y. Uesaka et al., Phys. Rev. D 93, 076006 (2016)] are extended to include the photonic interaction. The wave functions of a muon and electrons are obtained by solving the Dirac equation with the Coulomb interaction of a finite nuclear charge distribution. We find suppression of the µ − e − → e − e − rate over the initial estimation for the photonic interaction, in contrast to enhancement for the four Fermi interaction. It is due to the Coulomb interaction of scattering states and relativistic lepton wave functions. This finding suggests that the atomic number dependence of the µ − e − → e − e − rate could be used to distinguish between the photonic and the four Fermi interactions.

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