Theoretical study of differential cross sections for the ionization of helium by fast proton impact

Abstract We present the angular distribution of the ejected electron for single ionization of He by fast proton impact. A four-body formalism of the three-Coulomb wave is applied to calculate the triple differential cross sections at several impact energies in the scattering, perpendicular and azimuthal planes. Moreover, the three-body formalism of three-Coulomb, two-Coulomb and first Born approximation models has also been used to study the many-body effect on electron emission and the validity of the models. In the three-Coulomb wave model, the final state wave function incorporates distortion due to the three-body mutual Coulombic interaction. In this formalism, we use an uncorrelated and correlated Born initial state, which consists of a plane wave for the incoming projectile times a two-electron bound state wavefunction of the helium atom representing the 1s 2 ( 1 S) state. But, in the case of the three-body formalism, the initial state wavefunction consists of a long-range Coulomb distortion for the incoming projectile and one active electron of the He atom described by the Roothaan–Hartree–Fock wavefunction. The structure with a single or two peaks with unequal intensity is observed in the angular distributions of the triple differential cross sections for the different kinematic conditions. In addition, the influence of static electron correlations is investigated using different bound state wavefunctions for the ground state of the He target. In the four-body formalism, the present computations are very fast by reducing a nine-dimensional integral to a two-dimensional real integral. Despite the simplicity and speed 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 theories.