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1001One-loop corrections to vpe~vpe, 17pe~17peand Vpe~f1Ve scatterings are calculatedanalytically in the Weinberg-Salam theory. The on-mass-shell renormalization procedure is employed. We find the corrections are considerably large. It is shown that our results are completely consistent with those of similar calculations by other groups in a different renormalization scheme in spite of seeming disagreement. t Fellow of the Japan Society for the Promotion of Science. *) Preliminary results have been reported in Ref. 3). One-loop corrections to vpe~ IJpe and 17pe ~ v pe scatterings were first calculated by Salomonson and Ueda 4 ) in a different renormalization scheme, where the quark contribution was not taken into account.

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The neutrino production of a lepton pair in the electromagnetic field of the nucleus is treated. Using the local Fermi interaction together with the electromagnetic form factor of the nucleus, we derive rigorously the differential cross section d 2 a/ dr 1 dr 2 • In the case where the incident neutrino momentum and the two produced charged lepton momenta ri are coplanar, our expression is completely analytical.

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