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Single electron ionization of helium targets produced by the impact of fast proton beams is investigated. The postversion of the continuum distorted wave-eikonal initial state into a three-body approximation is reformulated, including the dynamic screening produced by the nonionized electron. This dynamic screening is shown to play a main role in the determination of double differential cross-sections. A good agreement is found with predictions obtained employing the prior version of the model, so that post-prior discrepancies are almost eliminated.

Electron ionization in ion-atom collisions has been a subject of main interest in the last decades [

The CDW-EIS model was applied with success to describe experiments for numerous collisional systems, where multiple and single differential as well as total ionization cross-sections were measured [

Furthermore, numerical initial bound and final continuum wavefunctions, corresponding to the same Hartree-Fock potential in both the entry and exit channels, respectively, were also considered to describe the active electron-residual target interaction in the CDW-EIS model [

In the present work we revisit the formulation of the post-version of the CDW-EIS approximation showing that a residual potential that was neglected in previous works must be included to obtain agreement with prior version calculations. This potential is associated with a correct description of the dynamic screening produced by the passive electrons on the evolution of the active one and its inclusion allows evaluation of the influence of this interaction on single ionization cross sections.

In Section

Let us consider the single electron ionization of an atomic target of nuclear charge

The straight line version of the impact parameter approximation is considered, where the internuclear vector is given by the expression

Following Fainstein et al

In (

The potential

The potential

The impact of protons on He targets is investigated. The initial orbital is described by a simple single-zeta function

For the He case,

In Figures

Doubly differential cross section for electron emission in collisions of 1 MeV

The same as Figure

Doubly differential cross section for electron emission in collisions of 1.5 MeV

The same as Figure

As an example for angular distributions, in Figures

Doubly differential cross section for electron emission in collisions of 1 MeV

The same as Figure

A complete three-body CDW-EIS model to describe single electron ionization is proposed, and a potential that has been excluded in previous calculations is now considered. This potential, which gives the contribution of dynamic electron screening, is shown to play a principal role in the determination of double differential cross sections. A close agreement between DDCS obtained within the prior-version and the complete post-version of the CDW-EIS model is found in the energy as well as in the angular distributions of ejected electrons. An appropriate representation of experimental data is observed. Moreover, the small post-prior discrepancies that still remain must be attributed to the different treatment employed to obtain the initial and final wavefunctions. We have recently checked that the use of more complete initial target wavefunctions does not change our main conclusions. Work along this direction is in progress. The present analysis may be extended to study ionization by multicharged ions and to investigate the case of a target with more than two electrons, assuming that the nonionized electrons remain in their initial orbitals. In order to describe fully differential cross sections, internuclear potentials and projectile-passive electron ones must be incorporated in the model. This is matter of our future research.

This work has been done as a part of investigations planned into the project PICT