Isotope dependence of muon decay in orbit

The decay $\mu^-\to e^- \bar{\nu}_e\nu_\mu$ of a muon that is bound to a nucleus poses an unavoidable background for experiments such as Mu2e, COMET, and DeeMe searching for lepton-flavor-violating $\mu^-\to e^-$ conversion and thus requires a precise understanding. We calculate the electron-energy spectra of muon decays in orbit near the electron energy endpoint for all stable isotopes and estimate uncertainties due to the nuclear charge distribution. Our results enable background studies of mixed or enriched target materials that are necessary for the next generation of $\mu^-\to e^-$ conversion experiments.