Neutrino Scattering on Atomic Electrons in Searches for the Neutrino Magnetic Moment

The scattering of a neutrino on atomic electrons is considered in the situation where the energy transferred to the electrons is comparable to the characteristic atomic energies, as relevant to the current experimental search for the neutrino magnetic moment. The process is induced by the standard electroweak interaction as well as by the possible neutrino magnetic moment. Quantum-mechanical sum rules are derived for the inclusive cross section at a fixed energy deposited in the atomic system, and it is shown that the differential over the energy transfer cross section is given, modulo very small corrections, by the same expression as for free electrons, once all possible final states of the electronic system are taken into account. Thus, the atomic effects effectively cancel in the inclusive process.