Transverse isospin response function of asymmetric nuclear matter from a local isospin density functional

The time dependent local isospin density approximation (TDLIDA) has been extended to the study of the transverse isospin response function in nuclear matter with an arbitrary neutron-proton asymmetry parameter xi. The energy density functional has been chosen in order to fit existing accurate quantum Monte Carlo calculations with a density dependent potential. The evolution of the response with xi in the Delta T-z = +/- 1 channels is quite different. While the strength of the Delta T-z = + 1 channel disappears rather quickly by increasing the asymmetry, the Delta T-z = -1 channel develops a stronger and stronger collective mode that in the regime typical of neutron star matter at beta equilibrium almost completely exhausts the excitation spectrum of the system. The neutrino mean free paths obtained from the TDLIDA responses are strongly dependent on xi and on the presence of collective modes, leading to a sizable difference with respect to the prediction of the Fermi gas model.