Towards a Nuclear Parameter Calculation for Astrophysical Applications

We evaluate the electronic neutrino-nucleus cross section within the context of a nuclear gross theory. We adopt an improved version of the gross theory of $\beta$-decay with a new trend for the theoretical parameter representing the energy spread of Gamow-Teller resonance by the spin-dependence part of the nuclear force within this model is obtained. A first application of this calculation is made in the region of nuclei involved in pre-supernova collapse where a comparison with available experimental results can be done ($A<70$). The obtained results agree with previous evaluations within other microscopic models. Present formalism can be extended to the region $A>70$ and offers an useful tool to perform nuclear calculations of neutrino capture cross section and $\beta$-decay rates for $r$-process nucleosynthesis within supernova neutrino wind environment.