The scattering of an antineutrino at an electron in an external field

The cross section of the process ν-barμ + e-→ν-barμ + e- in a constant crossed electromagnetic field is calculated in the case of a high-energy muon antineutrino when it is necessary to take into account non-local effects. The asymptotic behaviour of the cross section as a function of the kinematic and field parameters is investigated. The weak external field gives a small contribution to the cross section of the free process. In the region of the superhigh energy and the strong field the cross section of the process contains the multiplier connected with a Z0 boson propagator. This leads to a decrease of the cross section with increasing energy. In the high-energy, strong field region the dependence of the cross section on the mass of the electron disappears. (author)