Calculation of differential and total cross section for electron capture from atomic hydrogen by proton impact with first-order interaction approximation

In this work the differential and total cross section in charge transfer channel for poroton-Hydrogen In the present work the differential and total cross section in charge transfer channel has been calculated analytically for proton-hydrogen collision within first-order interaction approximation. The calculation has been done in the frame of three-body formalism to formation of atomic hydrogen from and transition at intermediate and high energy range. The scattering amplitudes have been calculated by using Fourier technique with Feynman and Nordsieck integrals at three different approximations. The results of calculation as differential and total cross section are compared with available theoretical and experimental data. It is shown that Knock-on scattering at high impact energies and large scattering angles for transition is a remarkable problem.