It has been proposed that the discrepancy between the partially-conserved axialcurrent 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 shellmodel analysis employing effective transition operators in the shell-model formalism for the transition 20 Ne(0 + g.s. ) + µ − → 20 F(1 + ; 1.057 MeV) + ν µ . 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.
Key words: Shell model; Muon capture; Effective operatorsThe large energy release in the ordinary (non-radiative) capture of stopped negative muons by atomic nuclei probes the hadronic current much deeper than ordinary beta decay or electron capture. In particular, the role of the induced pseudoscalar coupling C P becomes important in muon capture. Based on this, there have been many attempts in the past to extract the ratio of the induced pseudoscalar and axial-vector coupling constants, C P /C A , from measured capture rates (see e.g. [1-6]) as well as from angular correlations of the gamma emission following the capture reaction A Z X N +µ − → A Z−1 X ′ * N +1 +ν µ of polarized muons (see e.g. [7][8][9]).The angular correlation data, available for muon capture in 28 Si, has been in a key role in pointing out discrepancies in the shell-model calculations of C P /C A . In various shell-model calculations (see e.g. [7,9] and references therein) anomalously small values of this ratio (C P /C A ∼ 0) have been obtained. In [9] we have proposed a method which, at least partly, lifts this discrepancy. This method is based on the use of effective transition operators