Double-electron capture in collision of fast alpha particles with helium atoms

A four-body boundary-corrected first-order Jackson-Schiff approximation (JS1-4B) is developed to calculate the differential and integral cross-sections (DCSs) for double-electron exchange in collision of fast alpha ions with helium atoms in their ground states. The influence of the static electron correlations on cross-sections is taken into account through choosing the different wave functions to describe the initial and final bound states of the electrons. The quantum-mechanical post and prior transition amplitudes for double charge exchange are derived in terms of two-dimensional real integrals which can be calculated numerically. The validity and utility of the applied approach is critically assessed in comparison with the available experimental data for differential and integral cross-sections. The present calculations are also compared with the results obtained from the other theories.