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We consider the production of ultrarelativistic positronium (Ps) in $\gamma A\to Ps + A$ and $e A \to Ps + e A$ processes where $A$ is an atom or a nucleuswith charge $Ze$. For the photoproduction of para- and ortho-Ps and theelectroproduction of para-Ps we obtain the most complete description comparedwith previous works. It includes high order $Z \alpha$ corrections andpolarization effects. The accuracy of the obtained cross sections is determinedby omitted terms of the order of the inverse Ps Lorentz factor squared. Thestudied high order multi-photon electroproduction of ortho-Ps dominates for thecollision of electrons with heavy atoms over the bremsstrahlung production fromthe electron via a virtual photon proposed by Holvik and Olsen. Our resultscomplete and correct the studies of those authors.Comment: 19 pages, 9 figures, RevTex; v2: minor corrections for the accuracy  of the results, a discussion of the literature added in a footnote, one  additional reference; v3: diagram of Fig.2 correcte

Production of relativistic positronium in collisions of photons and electrons with nuclei and atoms