Weak Response of Nuclear Matter at low Momentum transfer

A quantitative understanding of the weak nuclear response is a prerequisite for the computer simulations of astrophysical phenomena like supernov$\ae$ explosions and neutron star cooling. In order to reduce the systematic uncertainties associated with the simulations, a consistent framework, able to take into account dynamical correlation effects, is needed to compute neutrino-nucleon and neutrino-nucleus reaction rates. In this paper we describe the many-body theory of the weak nuclear response at low energy regime. We show how to include both short and long correlations effects in a consistent fashion.