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Here we are interested in coherent scattering of neutrinos from heavy nuclei at subnuclear densities and thus a typical value of the momentum transfer q is qrN 1 and that of the energy transfer ω may be given by ∼ qvT∼ q(T/mA)1/2, where vT is the thermal velocity of heavy nuclei, T is the temperature, and m is the mass of nucleons. Therefore the energy transfer relative to the thermal energy is δ ω/T rN-1(1/mAT)1/2∼0.6A-1/2 for rN=10 fm and T=1 MeV. Provided δ is much smaller than unity, the assumption of elastic scattering is valid and effects of degeneracy of neutrinos can be also neglected [40]. However, at higher densities, where nucleons are strongly degenerate and the Fermi velocity of nucleons vF∼c, a typical energy transfer is ∼ qvF and δ is no longer small for the above values of q and T. Thus, in this case, the elastic assumption is not accurate [41,42] and one should also take account of effects of degeneracy of neutrinos.
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