A four-body distorted-wave approximation is applied for theoretical analysis of the fully differential cross sections (FDCS) for proton-impact single ionization of helium atoms in their ground states. The nine-dimensional integrals for the partial amplitudes are analytically reduced to closed-form expressions or some one-dimensional integrals which can be easily calculated numerically. Calculations are performed in the scattering and perpendicular planes. The influence of the target static electron correlations on the process is investigated using a number of different bound-state wave functions for the ground state of the helium targets. An illustrative computation is performed for 75-keV proton-helium collisions and the obtained results are compared with experimental data and other theoretical predictions. Although for small momentum transfers, the comparison shows a reasonable agreement with experiments in the scattering and perpendicular planes, some significant discrepancies are still present at large momentum transfers in these planes. However, our results are compatible and for some cases, better than those of the other sophisticated calculations.

A four-body distorted wave approximation is presented for theoretical investigations of the single ionization of ground-state helium atoms by fully stripped carbon ions at impact energies of 2 MeV/amu and 100 MeV/amu. The nine-dimensional integrals for the partial quantum-mechanical transition amplitudes of the specified reaction are reduced to some analytical expressions or one-dimensional integrals over real variables. Fully differential cross sections (FDCSs) are calculated and compared with their experimental values as well as the results obtained from other theories. Despite the simplicity and quickness of the proposed quadrature, the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other complicated theories.

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