High-energy $\mu^+\mu^-$ electroproduction

The cross sections of high-energy $\mu^+\mu^-$ pair production and paradimuonium production by a relativistic electron in the atomic field are discussed. The calculation is performed exactly in the parameters of the atomic field. Though the Coulomb corrections to the cross sections, related to the multiple Coulomb exchange of $\mu^+,\,\mu^-$ and an atom, are negligible, the Coulomb corrections to the differential cross sections, related to the electron interaction with an atom, are large. However, the latter Coulomb corrections to the cross sections integrated over the final electron momentum are small. Apparently, this effect can easily be observed experimentally. Furthermore, it is shown that the asymmetry of the cross section with respect to the permutation of the momenta of $\mu^-$ and $\mu^+$ is large.