Electromagnetic Interactions of Neutrinos

The cross sections for the process (a) $\nu +\mathrm{nucleus}\to \nu +\gamma \left(\mathrm{virtual}\mathrm{Coulomb}\right)+\mathrm{nucleus}\to \nu +\gamma +\mathrm{nucleus}$ and the related process (b) $\gamma +\mathrm{nucleus}\to \gamma +\gamma \left(\mathrm{virtual}\mathrm{Coulomb}\right)+\mathrm{nucleus}\to \nu +\overline{\nu }+\mathrm{nucleus}$ are calculated to lowest order in the weak and electromagnetic interactions, assuming the existence of a direct electron-neutrino weak interaction. While the relevant Feynman amplitude is given by a formally divergent expression, a finite amplitude is obtained by imposing the condition of gauge invariance. The contribution of process (b) to the neutrino luminosity of stars is worked out and found to be somewhat smaller than that of the processes: $e^{-}+e^{+}\to \nu +\overline{\nu }$, $\gamma +e^{\pm }\to e^{\pm }+\nu +\overline{\nu }$. The present calculation is motivated by recent suggestions that stellar evolution may be significantly affected by energy lost by the star due to the emission of neutrinos. A very crude estimate is given for the contribution of the process (c) $\gamma +\gamma \to \nu +\overline{\nu }+\gamma$ to the neutrino luminosity. It is pointed out that a calculation of process (b) which exists in the literature is non-gauge-invariant.