We report here the results of the numerical calculations of the gamma-neutrino angular correlation coefficients in the capture of polarized muons by the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ nucleus. Closed expressions for these coefficients are derived taking into account the relativistic terms in the muon capture Hamiltonian, in the impulse approximation. Relations among these coefficients, the average and the longitudinal polarization of the recoil nucleus in muon capture, are derived and are shown to be independent of nuclear models and muon-capture coupling constants. By comparing with experimental data, we obtain a value for the induced pseudoscalar coupling constant $g_P$, as $\mathrm{}(13.5+3.5,-5.5)\mathrm{}{g}_A$, indicating a possible absence of quenching of $g_P$ in the ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ nucleus. The effect of meson exchange currents on these correlation coefficients are discussed.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({\mu }^{-},\gamma {\nu }_{\mu }{}_{}{}^{28}{}_{}{}^{}\mathrm{Al})$, $\gamma$-neutrino angular correlation, polarized muon capture, particle-hole model, induced pseudoscalar, second class current, induced tensor coupling constants, meson exchange corrections.

• Received 26 June 1979

DOI:https://doi.org/10.1103/PhysRevC.23.861