Final-stateΦ2wave function in ion-helium collisions

Abstract

In this work we study the double-differential cross sections (DDCSs) of ejected electrons in single-ionization collisions of protons with helium atoms. The final state of the emitted electron is modeled by the correlated wave function ${\Phi }_2,$ a confluent hypergeometric function of two variables. We introduce a series representation of the ${\Phi }_2$ wave function in terms of two-body Coulomb-like states, corresponding to the electron-projectile and electron-target relative motions. We consider undistorted and eikonal initial states that give rise to the Born ${\Phi }_2$ and eikonal initial-state ${\Phi }_2$ approximations, respectively. In both cases we obtain analytic series representations of the transition matrices, which exhibit a strong numerical convergence. We obtain DDCSs in ion-helium collisions in the intermediate- to high-energy regime with the Born ${\Phi }_2$ approximation and show that it qualitatively agrees with the available experimental data.