Quenching of spin matrix elements in nuclei

Abstract

Matrix elements of spin operators evaluated in a nuclear medium are systematically quenched compared to their values in free space. There are a number of contributing reasons for this. Foremost is the traditional nuclear structure difficulty of the inadequacy of the lowest-order shell-model wavefunctions. We use the Rayleigh-Schrödinger perturbation theory to correct for this, arguing that calculations must be carried through at least t o second order. This is a question of the appropriate effective interaction. We review the Landau-Migdal approach in which only RPA graphs are retained and discuss the strength of this interaction in the spin-isospin channel expressed in terms of the parameter g'. We also consider one-boson-exchange models and compare the two. The advantage of the OBEP models is that the two-nucleon meson-exchange current operators can be constructed to be consistent with the potential as required by the continuity equation for vector currents and the partial conservation (PCAC) equation for axial currents. We give a complete derivation of the MEC operators of heavy-meson range starting with the chiral Lagrangians used by Ivanov and Truhlik. Nonlocal terms are retained in the computations. We single out one class of MEC processes involving isobar excitation and demonstrate that in lowest order there is an equivalence between treating the isobar as an MEC correction and treating it as a nuclear constituent through the transition spin formalism. Differences occur in higher orders. There are a number of uncertainties in the isobar calculation involving the neglect of the isobar's natural width, the relativistic propagator being off the mass shell and the coupling constants not being known with any precision. We present a comprehensive calculation of core-polarisation, meson-exchange current and isobar-current corrections to low-energy M1 and Gamow-Teller transitions in closed-shell-plus-one nuclei (at LS and jj closed shells) expressing the results in terms of equivalent effective one-body operators. We compare with the empirically-determined operators in the sd-shell of Brown and Wildenthal. While overall agreement is good, a closer inspection reveals two discrepancies which suggest two benchmark tests for newer and alternative models.