Neutrino Photoproduction on the Electron of a Hydrogen-Like Atom

Abstract

The process of interaction of a photon with the bound electron of a hydrogen-like atom with creation of a neutrino pair \( \upgamma +{(Ze)}^{\ast \ast}\to \overline{\upnu \upnu}+{(Ze)}^{\ast } \) is considered here for the first time. This process can take place with and without a change in the energy of the pair relative to the energy of the “initial” photon due to atomic transitions. It is shown that in the case when the system of atoms is located in an equilibrium radiation field with temperature T << m_e this process can be neglected in comparison with spontaneous emission of the hydrogen-like atom \( {(Ze)}^{\ast}\to (Ze)+\upnu \overline{\upnu} \), despite the smaller power of the expansion parameter (Zα) <  < 1, α = e²/ℏc ≈ 1/137 in the expressions for the cross sections and probabilities. Calculations have been performed for the first time using the density matrix, introduced in the previous paper, of the electron in the field of the nucleus in the leading approximation in (Zα).