μ−Capture Rate in (pμp)

Abstract

The probability of finding the ortho, $L=1\mathrm{}$, ($p\mu p$) system in an $s=\frac{1}{2}$ state at the time of ${\mu }^{-}$ capture, was calculated using the techniques developed by Weinberg. A wave function correct to first order in the muon-to-proton mass ratio was used in the calculation, giving a probability lying between 0.99933 and 0.99952. This result was due to the fact that the contact term in the spin-orbit Hamiltonian masked the effects of the other terms. The errors due to the use of the approximate wave function in this calculation were analyzed qualitatively and found to be small.