Production of bound triplet $\mu^{+} \mu^{-}$ system in collisions of electrons with atoms

This paper deals with the production of orthodimuonium (OM) ($\mu^{+} \mu^{-}$ atom in triplet state) in collisions of high-energy electrons with nuclei or atoms. This reaction was previously studied by Holvik and Olsen [Phys. Rev. D 35, 2124 (1987)] on the basis of a bremsstrahlung mechanism where OM is produced by only one virtual photon. In the present paper we consider a competing three-photon mechanism where the production of OM results from the collision of a photon generated by the electron with two photons emitted by the nucleus. We derive the corresponding spectrum and production rate of OM and show that the three-photon mechanism is the dominant one for heavy atom target.