On lepton-pair production in neutrino-nucleus collisions

A calculation of the cross section for the reaction νγ → νμ ⁺ μ ^? which is induced by the neutrino magnetic moment, is described in detail. The expression obtained for this cross section is used to determine the asymptotic behavior of the cross section for the reaction νN → νNμ ⁺ μ ^? by the Weiszäcker-Williams method. It is shown that, upon going over from the nucleus involved to a structureless particle (for example, an electron), the resulting expression is doubled owing to integration with respect to the virtual-photon momentum over the region m _μ?Q?E _ν, where the Weiszäcker-Williams approximation is not applicable. The method developed here makes it possible to obtain straightforwardly the known asymptotic expressions for the cross sections describing the reactions eN → eNμ ⁺ μ ^? and e ⁺ e ^? → W ⁺ W ^? e ⁺ e ^?.