Positronium formation in the laser assisted collision of positron with hydrogen atom in the first excited state

A straightforward method for the study of positronium formation in the ground state in the laser assisted positron-hydrogen atom collisions, the target hydrogen atom being in the first excited state (n = 2), is presented in the framework of the first Born approximation (FBA). The laser field is treated classically as a homogeneous, single mode and linearly polarised electric field while the collision dynamics is treated quantum mechanically. The projectile-field interaction and the dressing effects on the hydrogen and positronium atoms have been considered to first order. The dressed wave functions have been constructed adopting the A.p gauge. The FBA rearrangement scattering amplitudes considering the full interaction have been obtained in closed analytic forms for field direction (ε0) parallel to the incident positron momentum (ki) i.e. ε0 parallel to ki. The differential cross sections for Ps formation have been presented for no photon and one photon exchange (l = 0,±1) at 50, 100 and 200 eV incident energies for laser field parameters ε0 = 0.00002 a.u. and ω 0.0043 a.u. along with the corresponding field free results. The variations of the differential cross sections with laser field strength, frequency and incident positron energy have also been shown. (author). 10 refs., 6 figs., 1 ill