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

We consider the production of ultrarelativistic positronium (Ps) in gamma A -->Ps+A and eA-->Ps+eA processes, where A is an atom or a nucleus with char ge Ze. For the photoproduction of para-and ortho-Ps and the electroproducti on of para-Ps we obtain the most complete description compared to previous works. It includes high-order Z alpha corrections and polarization effects. The accuracy of the obtained cross sections is determined by omitted terms of the order of the inverse Ps Lorentz factor. The high-order multi-photon electroproduction of ortho-Ps studied dominates for the collision of elect rons with heavy atoms over the bremsstrahlung production from the electron via a virtual photon proposed by Holvik and Olsen [Phys. Rev. D 35, 2124 (1 987)]. Our results complete and correct the studies of those authors. [S105 0-2947(98)03112-6].