Temperature dependence of nuclear symmetry energy and equation of state of charge neutral n + p+ e+ μ matter in beta equilibrium

The temperature and density dependence of nuclear symmetry energy, ES ( ,T) , is a subject of current interest for its implications not only in various aspects of nuclear physics but also in astrophysics. In particular, in presupernovae explosions electron capture rate on nuclei and/or free protons is especially sensitive to the symmetry energy at finite temperature. The predictions of various microscopic models as well as effective theories on n and p effective mass splittings in ANM diverge which can be attributed to the deficiencies in our present day understanding on the subject. There have been attempts to constrain the n and p effective mass splitting in neutron rich asymmetric matter from the study of observables sensitive to the isovector features of the nuclear EOS, but the task has not been accomplished as yet and the magnitude of effective mass splitting is still an open problem