A Time Dependent Local Isospin Density Approximation (TDILDA) for the response function in asymmetric nuclear matter

In this talk I will discuss a derivation of the zero temperature density response function in the longitudinal and transverse isospin channel for nuclear matter with arbitrary isospin polarisation, which is based on the standard Time Dependent Density Functional Theory (TDDFT). The employed functional is based on the equation of state of symmetric nuclear matter and pure neutron matter computed by Stefano Gandolfi et al. using an AV6' interaction with the addition of a density dependent term. Following the work of Cowell and Pandhariphande, I will also discuss some results we have obtained for the contribution of the transverse isospin channel (describing essentially direct URCA processes) to the suppression of the mean free path of neutrinos as a function of the proton fraction in nuclear matter.