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Recoil effects in bound muon decay Brookfield, Gary John


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.

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