curve that includes all the neutrino and antineutrino flavors consists of two parts. In the first part ( t < 5 s ) the non-thermal neutrino emission is dominated by the electron neutrinos ν$_{e}$ produced by the non-thermal neutronization. For t ≈ 0 . 5 s , the core is transparent to ν$_{e}$ emitted due to electrons captures by nuclei and free protons. By this time, the mean individual ν$_{e}$ energy becomes 10 − 20 MeV . Thus, the non-thermal neutrinos carry away approximately a small fraction of the total available energy E$_{νtot}$ = (3 − 5) × 10 53 erg. Nearly 90% of this energy is emitted in the regime of thermal emission once the innermost region of the core becomes opaque to all the neutrino flavors, which get decoupled from the stellar mass at a surface so-called neutrinosphere. Therefore, one of the crucial parameters which strongly affect the stellar evolution is the cooling rate. During their lifetime, stars can emit energy in the form of electromagnetic or gravitational waves, and a flux of neutrinos. However, in late stages a star mainly looses energy through neutrinos, and this is quite independent of the star mass. In fact, white dwarfs and supernovae, which are the evolution end points of stars formed from very different masses, have cooling rates largely dominated by neutrino production. An accurate determination of neutrino emission rates is therefore mandatory in order to perform a careful study of the final branches of star evolutionary tracks. In particular, a change in the cooling rates at the very last stage of massive star evolution could perceptibly affect the evolutionary time scale and the iron core configuration at the onset of the supernova explosion whose triggering mechanism still waits a full theoretical understanding [20]. The energy loss rate due to neutrino emission receives contributions from both weak nu- clear reactions and purely leptonic processes. However, for the large values of density and temperature which characterize the final stage of stellar evolution, the latter are largely dom- inant, and are mainly produced by four possible interaction mechanisms: e $^{+}$e − → ν ¯ ν (pair annihilation), γe ± → e $^{±}$ν ¯ ν ( ν -photoproduction), γ ∗ → ν ¯ ν (plasmon decay), e $^{±}$Z → e $^{±}$Zν ¯ ν (bremsstrahlung on nuclei). These mechanisms play an important role in astrophysics and cosmology and have been considered by many authors in various theories of weak interac- tions. Actually these processes are the dominant cause of the energy loss rate in different re- gions in a density-temperature plane. For very large core temperature, T > ∼ 10 9 $^{o}$K , and not excessively high values of density, pair annihilations are most efficient, while ν photopro- duction gives the leading contribution for 10 8 $^{o}$K < ∼ T < ∼ 10 9 $^{o}$K and relatively low density, 3