Shell-model effective operators for muon capture in²⁰Ne

Abstract

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

Value of the Axial-Vector Coupling Strength in β and ββ Decays: A Review

“…Most of the theoretical attempts to describe the muon capture to individual nuclear states have concentrated on very light nuclei, A ≤ 20 [211,217,222,223,224,225,226] or to the mass region A = 23 − 40 [213,214,218,219,227,228,229,230,231,232,233]. Also studies in the 1s − 0d and 1p − 0f shells have been performed [234,235].…”

Comparative analysis of muon-capture and 0νββ -decay matrix elements

“…Through the years a number of calculations for the OMC transitions in different nuclear-structure formalisms and for various nuclei have been performed in order to probe the right-leg virtual transitions of 0νββ decays as well as the value of the particle-particle interaction parameter g pp of the proton-neutron quasiparticle random-phase approximation (pnQRPA) [4][5][6], or the in-medium renormalization of the axial-vector coupling constant g A [7][8][9][10][11][12]. Thanks to the large momentum exchange in the OMC, the process activates also the induced weak currents, including the weak magnetism and pseudoscalar contributions, quite like in the case of the 0νββ decay [13].…”

Muon-capture strength functions in intermediate nuclei of 0νββ decays

“…Over years nuclear-structure calculations for the OMC transitions have been performed in a wide range of nuclear masses in order to probe the right-leg (the β + side) virtual transitions of 0νββ decays and the value of the particle-particle parameter g pp of the proton-neutron quasiparticle random-phase approximation (pnQRPA), as discussed in Refs. [6][7][8], or the in-medium renormalization of the axialvector coupling constant g A [9][10][11][12][13][14]. The large momentum exchange involved in the OMC activates the induced weak currents, including the weak magnetism and pseudoscalar contributions, quite like in the case of the 0νββ decay [15].…”