Formation of anti-hydrogen in presence of laser field in antiproton-positronium collisions

A detailed calculation in the framework of first Born approximation has been presented for the study of anti-hydrogen formation in antiproton-positronium collisions in presence of a laser field considered classically in the dipole approximation. The projectile-laser field interaction and the dressing of the bound states are considered to first order. The anti-hydrogen formation amplitudes are obtained in closed forms in the A - p gauge, the field direction being parallel to the incident momentum. The differential as well as total cross-sections are presented for no photon (l = 0) and one photon (l = +/-1) exchange with held strengths so = 10(6)V/cm (0.0002 a.u) and so = 10(7)V/cm (0.002 a.u) and compared with the corresponding field free results.