Single ionization of helium by high energy proton impact using the parabolic Sturmians representation

Ionization of helium by a proton constitutes a very challenging quantum mechanical four-body problem. For fast incident protons, one may reduce the difficulty by employing a frozen-core model for the target, and thus deal with a more tractable Coulomb three-body problem (e-, He+, p); the ionization problem is recast as an inhomogeneous Schroedinger equation. In this way, the ionization amplitude can be formally extracted from the asymptotic behavior of the function generated by the action of the three-body Green's function operator on the driven term of the inhomogeneous equation. In our approach we assume that for a high enough incident energy, we can approximate the Green operator by that corresponding to the Hamiltonian without the proton-electron interaction which is treated as a perturbation. Besides, we make use of a L2 parabolic Sturmians representation which allows us to calculate the amplitude analytically in terms of the expansion coefficients. We have made Fully Differential Cross Sections calculations at 1 MeV incident energy, and for several geometrical and kinematical configurations. Our results reasonably agree with the experiment [1] and recent WP-CCC cross sections [2].

[1] Chuluunbaatar O et al 2017 Phys. Rev. A 96 042716

[2] Abdurakhmanov I B et al 2017 Phys. Rev. A 96 022702; 2019 Phys. Rev. A 100 062708