Study of atomic effects on electron spectrum in bound-muon decay process

For the bound-muon decay process, the study of atomic effects on the electron spectrum near its endpoint is performed within the framework of the Fermi effective theory. The analysis takes into account for corrections due to finite-nuclear-size, nuclear-deformation, electron-screening, and vacuum-polarization effects, all of which are incorporated self-consistently into the Dirac equation. Furthermore, the nuclear-recoil correction to the muon binding energy is included. Calculations are carried out for the isotopes of C, Al, and Si, which are of a particular importance for forthcoming experiments aimed at search for the charged-lepton flavor-violating process of muon-to-electron conversion in a nuclear field.