Shell-Model Effective Operators for Muon Capture in ^{20}Ne

Abstract

It has been proposed that the discrepancy between the partially-conserved axial-current prediction and the nuclear shell-model calculations of the ratio $C_P/C_A$ in the muon-capture reactions can be solved in the case of ^{28}Si by introducing effective transition operators. Recently there has been experimental interest in measuring the needed angular correlations also in ^{20}Ne. Inspired by this, we have performed a shell-model analysis employing effective transition operators in the shell-model formalism for the transition $^{20}Ne(0^+_{g.s.})+\mu^- \to ^{20}F(1^+; 1.057 MeV) + \nu_\mu$. Comparison of the calculated capture rates with existing data supports the use of effective transition operators. Based on our calculations, as soon as the experimental anisotropy data becomes available, the limits for the ratio $C_P/ C_A$ can be extracted.