Towards the solution of theCP/CAanomaly in shell-model calculations of muon capture

Abstract

Recently many authors have performed shell-model calculations of nuclear matrix elements determining the rates of the ordinary muon capture in light nuclei. These calculations have employed well-tested effective interactions in large scale shell-model studies. For one of the nuclei of interest, namely, ${}^{28}\mathrm{Si},$ there exists recent experimental data which can be used to deduce the value of the ratio ${C}_{P}{/C}_{A}$ by using the calculated matrix elements. Surprisingly enough, all the shell-model results suggest a very small value $(\ensuremath{\simeq}0)$ for ${C}_{P}{/C}_{A},$ quite far from the PCAC prediction and recent data on muon capture in hydrogen. We show that this rather disturbing anomaly is solved by employing effective transition operators. This finding is also very important for realistic muon-capture calculations where one explores the strength of the scalar coupling in the weak charged current of leptons and hadrons.