Abstract <p> We calculate the amplitude of the process of generating a pair of a massive neutrino and antineutrino, to which a third-rank tensor caused by the contribution of an electron “three-pole” with two vector vertices and one “weak” vertex corresponds. We analyze procedures for reducing logarithmic divergences when integrating over the loop momentum and gauge-noninvariant contributions, obtaining a final gauge-invariant and finite result. We find the cross section for this inelastic process. </p>