Formation of antihydrogen in antiproton - positron collision

A quantum mechanical approach is proposed for the formation of antihydrogen in the ground and excited states (2s, 2p) via the mechanism of three body recombination (TBR) inside a trapped plasma of anti proton and positron or in the collision between the two beams of them. Variations of the differential (DCS) as well as the total (TCS) formation cross sections are studied as a function of the incident energies of both the active and the spectator positrons. Significantly large cross sections are found at very low incident energies in the TBR process as compared to other processes leading to antihydrogen. The present formation cross section decreases with increasing positron energy (temperature) but no simple power law could be predicted for it covering the entire energy range, corroborating the experimental findings qualitatively. The formation cross sections are found to be much higher for unequal energies of the two positrons than for equal energies, as expected physically.