Perturbative neutrino pair creation by an external source

We consider the rate of fermion-antifermion pair creation by an external field. We derive a rate formula that is valid for a coupling with arbitrary vector and axial vector components to first order in perturbation theory. This is then applied to study the creation of neutrinos by nuclear matter, a problem with astrophysical relevance. We present an estimate for the creation rate per unit volume, compare this to previous results and comment on the role of the neutrino mass.