Single ionization of helium by 75 keV protons outside the velocity-matching regime in the parabolic quasi-Sturmian approach

Abstract

The parabolic quasi-Sturmian approach is applied here to 75 keV \(p + \text{ He }\) ionization process. We calculate fully differential cross sections (FDCS) for electrons ejected into the scattering plane with energies far from the velocity-matching case. Our results provide the first comparison, on a variety of kinematical and geometrical configurations, with recent experimental absolute scale data. To obtain the ionization amplitude in such an energy regime, we use convolutions of two quasi-Sturmian functions (CQS) that satisfy the so-called 2C-like model, within which the proton-ion and electron-ion interactions are taken into account exactly. In turn, the proton-electron interaction is taken into account by means of an equation of the Lippmann-Schwinger type that is solved using an expansion of the potential in Sturmian functions. To improve the rate of convergence as more terms are included in the potential separable representations, it appears necessary to use smoothing factors in combination with an optimal choice of the basis scaling parameter. As far as the binary peak position is concerned, the calculated FDCSs are found to be in reasonable agreement with recent experimental data; the magnitude agreement goes from bad to good according to the considered configuration. In contrast to the experimental statement that non-postcollision interaction effects are dominant at small energy losses, we do not reach the same conclusion. Although the considered kinematics are far from the velocity-matching regime, the role played by electron capture may be responsible for some experimentally observed features that clearly do not appear in our theoretical description.