The photo-neutrino process in astrophysical systems

Explicit expressions for the differential and total rates and emissivities of neutrino pairs from the photo-neutrino process $e^\pm + \gamma \to e^\pm + \nu + \bar\nu$ in hot and dense matter are derived. Full information about the emitted neutrinos is retained by evaluating the squared matrix elements for this process which was hitherto bypassed through the use of Lenard's identity in obtaining the total neutrino emissivities. Accurate numerical results are presented for widely varying conditions of temperature and density. Analytical results helpful in understanding the qualitative behaviors of the rates and emissivities in limiting situations are derived. The corresponding production and absorption kernels in the source term of the Boltzmann equation for neutrino transport are developed. The appropriate Legendre coefficients of these kernels, in forms suitable for multigroup flux-limited diffusion schemes are also provided.