Quenching of axial-vector coupling constant in β-decay and pion-nucleus optical potential

A very simple description of the quenching in nuclear matter of the axial-vector coupling constant in β-decay is given in terms of the model of Barshay, Brown and Rho constructed to provide a microscopic picture to the pion-nucleus optical potential for π-mesic atoms. The connection between the two quantities suggests a plausible test of the Lorentz-Lorenz non-linear effect in π-nucleus scattering. By comparing with the sum rule estimate made by M. Ericson, we find that the quenching of g_A is consistent with an essentially unsuppressed Lorentz-Lorenz term in the optical potential.