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The neutrino emissivity from the proton branch of the modified Urca process is calculated. Angular integrations in momentum space are performed numerically without recourse to widely used, but unjustified in this specific case, approximations. To deal with nuclear correlation effects, the independent-pair approximation for nucleon quasiparticles is assumed. The realistic nuclear correlation effects are extracted from a modified extended version of the lowest-order constrained variational method in asymmetric nuclear matter in β equilibrium with electrons and muons that allows for three-body nucleon interactions and fits all semiempirical saturation parameters of nuclear matter quite well. Two-body nucleon interaction is modeled by a realistic Argonne AV18 potential and the three-body potential used is a phenomenological Urbana UIX, generalizing parametrization of its component strengths in a manner suitable for application in asymmetric nuclear matter. Limiting to the two-body forces only, we find that, at fixed temperature, neutrino emissivity is a (weakly) decreasing function of density. This is also the case for the neutron branch of the modified Urca process analyzed by us in a recent paper. Inclusion of the modified three-body force effects changes this behavior. Quantitatively the value of the emissivity at each density increases and qualitatively the overall effect of the modified three-body force addition is such that dependence on density becomes weak in a density range from n 0 to 3.5n 0. An updated version of neutron branch results obtained using our modified three-body force model is also presented. This is done using exact treatment of the angular integrations of nuclear transition rate in momentum space.

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The modified Urca processes are the most effective weak interactions that produce neutrinos in neutron star medium. Emissivity and mean-free path of electron neutrinos arising from the neutron branch of the modified Urca process are calculated supposing the neutron star matter is a beta stable one. The effect of strong nuclear interactions on the rate of this weak interaction is taken into account through the pair nuclear densitydependent correlation functions adapted from the lowest-order constrained variational (LOCV) method using the AV18 two-body potential.