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

Abstract The process in which a muon bound to the nuclear potential decays into an unbound electron, a muon neutrino, and an electron antineutrino is considered. The study examines atomic effects on the differential transition rate relative to the energy of the emitted electron, specifically the electron spectrum, near its high-energy boundary, within the framework of Fermi effective theory. The analysis takes into account 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 particularly important for forthcoming experiments aimed at search for the charged-lepton flavor-violating process of muon-to-electron conversion in a nuclear field.