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

A detailed calculation in the framework of first Born approximation has bee n presented for the study of anti-hydrogen formation in antiproton-positron ium collisions in presence of a laser held considered classically in the di pole approximation. The projectile-laser field interaction and the dressing of the bound states are considered to first order. The anti-hydrogen forma tion 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 res ults.