Theory of neutrino emission from nucleon-hyperon matter in neutron stars: Angular integrals

Investigations of thermal evolution of neutron stars with hyperon cores require neutrino emissivities for many neutrino reactions involving strongly degenerate particles (nucleons, hyperons, electrons, muons). We calculate the angular integrals $I_n$ (over orientations of momenta of $n$ degenerate particles) for major neutrino reactions with $n$ =3, 4, 5 at all possible combinations of particle Fermi momenta. The integrals $I_n$ are necessary ingredients for constructing a uniform database of neutrino emissivities in dense nucleon-hyperon matter. The results can also be used in many problems of physical kinetics of strongly degenerate systems.