Capture rate for the reaction³He+μ^-→³H+ν

The capture rate for the process³He+μ^-→³H+ν is calcultated following the usual approach involving an effective Hamiltonian. The trinucleon wave function that we have used is a solution to the three-body wave equation with separable two-body potentials including the tensor forces. It is a linear combination of the²S symmetric states, the mixed-symmetry²S state and the three mixed-symmetry⁴D states. The calculated capture rate agrees in general with existing work. The ratio of the induced pseudoscalar and axial vector coupling constants, m_μF_p/F_A, that is deduced from this calculation is somewhat smaller than that predicted by the Goldberger-Treiman relation. It is pointed out that since the contribution of the D-state apparently decreases the capture rate and consequently the pseudoscalar coupling constant, it is reasonable to expect that a wave function with a smaller D-state admixture will yield results consistent with both the radiative-muon-capture results and the Goldberger-Treiman prediction. A preliminary calculation and brief discussion of this possibility is also given.