An unbound muon at rest decays into two neutrinos and an electron. Momentum conservation forbids the electron to have energy greater than one half the muon mass. However, if the muon is bound to a nucleus, its orbital motion -and nuclear recoil make it possible for the decay electron energy to approach the muon mass. These high energy electrons are an important background effect in the search for muon to electron conversion. This thesis investigates recoil corrections to the electron spectrum and asymmetry from bound muon decay using an effective potential approach. This approach simplifies the equations describing a finitely massive nucleus and electron (or muon) interacting electromagnetically, to a one particle Dirac equation for a potential well. For large Z, calculation of the electron spectrum requires including the effects of finite nuclear size and electron wave function distortion. Such a calculation would involve numerically generated wave functions and numerical integrations, and is not done here, though the applicable methods and general formulas are presented. For small Z the calculation can proceed analytically and an expression has been derived for the spectrum and asymmetry including recoil. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis contains a study of the effects of massive Dirac and Majorana neutrinos and their mixings in the e’ spectrum for the muon decay μ⁺→e⁺ v[sub=e]v[sub=μ] (v[sub=μ; sup=c]. The spectra for both polarized and unpolarized muons are given for the three-neutrino world with a single neutrino of mass in the MeV/c² range. Electron-neutrino correlations are calculated and proposed as a possible signature of Majorana neutrinos. The first-order radiative corrections to the muon decay and the radiative decay μ⁺→e⁺ v[sub=e][v=sub u] are included in this analysis for the case of a single Dirac neutrino of mass in the MeV/c² range mixing into the three-neutrino world. The method of dimensional regularization is used for the calculation of the radiative corrections. / Science, Faculty of / Physics and Astronomy, Department of / Graduate