Four-body treatment of the single-electron capture in energetic proton-helium collisions

Both the post and prior versions of the four-body Coulomb-Born distorted wave (CBDW-4B) approximation are applied to calculate the single-electron capture differential and integral cross sections in collision of the fast protons with helium atoms. The outlined model satisfies the correct boundary conditions, and the incident energy is considered in a range of 20 to 1000 keV for which the applied approach is valid. For proton-helium collisions, the CBDW-4B method exactly coincides with the four-body first-order Jackson-Schiff approximation (JS1-4B). The influence of the static and dynamic electronic correlations on the cross sections is investigated. The ground state of the helium atom is described using two different wave functions to show the influence of the static correlation on the captured cross sections. In order to illustrate the validity of the present method, the obtained results are compared with the other theoretical investigations as well as the available experimental measurements. Although the overall agreement of the present numerical differential cross sections (DCS) with the reported experimental findings is acceptable, contrary to our general expectation, the three-body version of the formalism gives a better description of the angular distribution of the captured cross sections. However, for integral cross sections, the agreement of the four-body results with the reported measurements is better than those of three-body formalism.