The Quenching of the Axial Coupling in Nuclear and Neutron-Star Matter

Using a chirally invariant effective Lagrangian, we calculate the density and isospin dependences of the in-medium axial coupling, $g_A^*$, in spatially uniform matter present in core collapse supernovae and neutron stars. The quenching of $g_A^*$ with density in matter with different proton fractions is found to be similar. However, our results suggest that the quenching of the nucleon's $g_A^*$ in matter with hyperons is likely to be significantly greater than in matter with nucleons only.