  Neutrino Bremsstrahlung of flavor-degenerate pairs in the field of a nucleus
is of potential importance for neutrino astrophysics and is representative of a
class of processes connecting leptonic electroweak sectors to real or virtual
photons. We focus on first generation flavor production by both electron and
muon neutrinos and present Standard Model cross sections and distributions for
lead and iron nuclei. The results (of order 10-41 cm2 for electron neutrino -
lead collisions at 100 MeV) have been fitted to empirical formulae that can be
used to estimate backgrounds to neutrino detection experiments and flux
normalizations. A compact form of the matrix element obtained by analytic
reduction is used to explain the distributions. The V-A limits of the cross
sections are shown to agree with published work from the pre-neutral current
era. Event signatures and the possible roles of these processes in stellar and
laboratory neutrino physics are discussed. Cross sections are compared with
those for neutrino-electron scattering for neutrino spectra corresponding to
typical supernovae temperatures.
