Transformation of high energy electrons to muons in the Coulomb field of a nucleus

The Fermi V-A theory of weak interactions (with possible extension to include neutral currents), satisfactorily describes all relevant experimental measurements to date. On the other hand, the Fermi interaction, treated as usual in lowest order, predicts a scattering amplitude which continually increases with energy, a result which is in conflict with the condition of unitarity of the S-matrix (conservation of probability) for a contact interaction. An examination is given of the predictions of the Fermi theory for inverse muon decay in the Coulomb field of a nucleus, computed in the lowest order of weak and electromagnetic interactions. It is hoped that a knowledge of the detailed cross sections for this process will encourage experimentalists to measure the corresponding reaction, and thereby test the validity of the Fermi theory for a purely leptonic process at energies higher than have been studied previously