  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.

Nuclear Theory