Refined shell-model matrix elements for muon-capture processes

Recently many shell-model calculations have been performed in order to extract the value of the ratio C _P/C _A in light nuclei. Most of these calculations fail to reproduce the value given by the partially conserved axial vector hypothesis, roughly 7. We show, that by using the effective transition operators, calculated by the perturbative techniques, this discrepancy can be, at least partly, solved. New angular correlation data for ²⁸Si is used for the extraction of C _P/C _A. In the case of ²⁰Ne, the capture rate data is used for extraction.