Towards the solution of the C-P/C-A anomaly in shell-model calculations ofmuon capture

Recently many authors have performed shell-model calculations of nuclear ma trix elements determining the rates of the ordinary muon capture in light n uclei. These calculations have employed well-tested effective interactions in large scale shell-model studies. For one of the nuclei of interest, name ly, Si-28, there exists recent experimental data which can be used to deduc e the value of the ratio C-P/C-A by using the calculated matrix elements. S urprisingly enough, all the shell-model results suggest a very small value (similar or equal to 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 disturbi ng anomaly is solved by employing effective transition operators. This find ing is also very important for realistic muon-capture calculations where on e explores the strength of the scalar coupling in the weak charged current of leptons and hadrons. [S0556-2813(99)50104-0].