Isospin dependence of nuclear matter symmetry energy coefficients

Generalized symmetry energy coefficients of asymmetric nuclear matter are obtained as screening functions. The dependence of the isospin symmetry energy coefficient on the neutron proton (n-p) asymmetry may be determined unless by a constant (exponent) $Z$ which depend on microscopic properties. The dependence of the generalized symmetry energy coefficients with Skyrme forces on the n-p asymmetry and on the density, only from .5 up to 1.5 $\rho_0$, are investigated in the isospin and scalar channels. The use of Skyrme-type effective forces allows us to obtain analytical expressions for these parameters as well as their dependences on the neutron-proton (n-p) asymmetry, density and even temperature. Whereas the density dependence of these coefficients obtained with Skyrme forces is not necessarily realistic the dependence on the n-p asymmetry exhibit a more consistent behaviour. The isospin symmetry energy coefficient (s.e.c.) increases as the n-p asymmetry acquires higher values whereas the isoscalar s.e.c. decreases. Some consequences for the Supernovae mechanism are discussed.