Self-consistent approach to neutral-current processes in supernova cores

The problem of neutral-current processes (neutrino scattering, pair emission, pair absorption, axion emission, etc.) in a nuclear medium can be separated into an expression representing the phase space of the weakly interacting probe, and a set of dynamic structure functions of the medium. For a nonrelativistic medium we reduce the description to two structure functions ${\mathit{S}}_{\mathit{A}}$(ω) and ${\mathit{S}}_{\mathit{V}}$(ω) of the energy transfer, representing the axial-vector and vector interactions. ${\mathit{S}}_{\mathit{V}}$ is well determined by the single-nucleon approximation while ${\mathit{S}}_{\mathit{A}}$ may be dominated by multiply interacting nucleons. Unless the shape of ${\mathit{S}}_{\mathit{A}}$(ω) changes dramatically at high densities, scattering processes always dominate over pair processes for neutrino transport or the emission of right-handed states. Because the emission of right-handed neutrinos and axions is controlled by the same medium response functions, a consistent constraint on their properties from consideration of supernova cooling should use the same structure functions for both neutrino transport and exotic cooling mechanisms.