Relativistic Corrections in the Theory of Muon Capture

Abstract

Computations are presented in closure approximation on the effect of relativistic corrections (∼[velocity of capturing proton]/[velocity of light]) on calculated muon total capture rates. A numerical estimate is made for the cases ${\mu }^{-}+{}_2{}^{}{}_{}{}^{}\mathrm{He}_{}^3{}_{}{}^{}\to {}_1{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}+{\nu }_{\mu }$ and ${\mu }^{-}+{}_2{}^{}{}_{}{}^{}\mathrm{He}_{}^4{}_{}{}^{}\to {}_1{}^{}{}_{}{}^{}\mathrm{H}_{}^4{}_{}{}^{}+{\nu }_{\mu }$ and a comparison with experiment is given.