Calculation of the positronium formation differential cross section for collision of electron with anti-hydrogen atoms

The positronium formation differential cross sections in collision of the high-energy but non-relativistic electrons with anti-hydrogen atoms are calculated by using the three-body Faddeev-Watson-Lovelace formalism. In a second-order approximation, the inter-nuclear and nuclear-electronic partial amplitudes therein the Faddeev-Watson series are calculated, analytically, in the range of 0-180 degrees of the scattering angles. The presence of the Thomas peakat 45degreeis investigated. The results are discussed for 1 and 10 keV impact energies and for electron transition from anti-hydrogen ground state into the different states therein the K-, L- and M- shells of the positronium atoms.