Cascade process in muon capture and gamma-neutrino angular correlations

A nuclear cascade process resulting from muon capture and subsequent deexcitation by gamma emission is considered. Possible observable quantities such as the final nuclear polarization and the gamma-neutrino angular correlation coefficients are investigated. It is shown that the nuclear transition with the spin sequence 0 → J_I → 0 is very favorable for study since the angular correlation coefficients in this case are not affected by the uncertainties in the gamma decay matrix elements. For a more restricted transition with J_I = 1, there exist some simple relations connecting the asymmetry coefficient of the recoil nucleus emitting the gamma ray and the gamma-neutrino angular correlation coefficients. These relations are shown to be independent of both the nuclear structure and the muon capture coupling constants. Numerical results are presented for the nuclear transition

${}^{16}\text{O}\text{(0}{}^{\mathrm{+}}\text{, g.s.)}\textcolor{red}{}{}^{16}\text{N}\text{(1}{}^{\mathrm{?}}\text{, 392}\text{KeV}\text{)}\textcolor{red}{}{}^{16}\text{N}\text{(0}{}^{\mathrm{?}}\text{, 120}\text{KeV}\text{).}$