Final-stateΦ2wave function in ion-helium collisions

Abstract

In this work we study the double-differential cross sections ͑DDCSs͒ 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 ⌽ 2 , a confluent hypergeometric function of two variables. We introduce a series representation of the ⌽ 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 ⌽ 2 and eikonal initial-state ⌽ 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 ionhelium collisions in the intermediate-to high-energy regime with the Born ⌽ 2 approximation and show that it qualitatively agrees with the available experimental data. ͓S1050-2947͑98͒06610-4͔

Electron capture to the continuum by proton and positron impact

“…In order to be consistent with our full treatment of the kinematics, it is necessary to describe the final state − f by means of a wavefunction that considers all the interactions on the same footing. Complex correlated wavefunctions have recently been derived for systems where one of the masses is much larger or smaller than the other two (Gasaneo et al 1997, Colavecchia et al 1998. However, in this work we are much more interested in stressing the importance of avoiding any kinematic restriction than in discussing the benefits of using a sophisticated approximation of the final three-body state.…”

Electron-ion correlation effects in ion-atom single ionization

“…We observe that the CCWEIS1 model has a good agreement with the experiment for all emission energies. We note that this model introduces an improvement over the previous Born-2 theory [23,29] that includes an undistorted initial channel. The CCWEIS1 theory gives a slightly lower contribution than the non-correlated CDWEIS model.…”

“…From a computational point of view, the most important feature of the state (5) is that the transition matrices for single ionization within a distorted wave framework can be obtained analytically. They can also be represented by a series expansion that has an excellent numerical convergence [22,23]. The final expressions for the transition matrices involve the calculation of a two-variable non-confluent hypergeometric F 1 of Appell and Kampé de Feriet [24].…”

Derivatives of Horn hypergeometric functions with respect to their parameters

“…One of them is the simple, uncorrelated, product of two Coulomb distortion factors. 52 Martínez and co-workers 49 used the Φ 2 model introduced in the context of ion-atom collisions 47,48 to include correlation. In the process we are considering here, the distortion factor is built using the Φ 2 model; it can be understood as a sum of products of Coulomb functions, corresponding to the Sommerfeld parameters η = Z 1 /v and η = Z 2 /v where v and v are the relative electron-ion velocities with respect to each nuclei.…”

“…After an ion-molecule double electron capture, say He ++ + H 2 → He * * + H ++ 2 , the doubly excited He * * autoionizes, i.e., He * * → He + + e . We propose to use the Φ 2 model 47,48 to describe the interaction between the autoionized electron and the two nuclei of the doubly ionized molecule. Such a model leads to interference fringes on the electron spectra.…”