Eur. Phys. J. D (2017) 71: 177
https://doi.org/10.1140/epjd/e2017-70661-5

Regular Article

Introducing a phase factor for the two-electron continuum representation^*

¹ Pacific National University, Khabarovsk 680035, Russia
² Equipe TMS, SRSMC, UMR CNRS 7565, Université de Lorraine, 57078 Metz, France

^a e-mail: ugo.ancarani@univ-lorraine.fr

Received: 24 October 2016
Received in final form: 24 March 2017
Published online: 4 July 2017

Abstract

In the asymptotic region Ω₀ (large hyperradius), the two-electron continuum wave function presents formally a logarithmic phase term corresponding to the electron-electron interaction. The idea of this contribution is to somehow include this phase into a Convoluted Quasi Sturmian (CQS) basis whose elements already behave asymptotically as an outgoing (incoming) six-dimensional spherical wave. With an appropriately introduced phase factor, the new CQS possess an asymptotic form very close to the formal one, and hopefully constitute a suitable set of basis functions for the three-body Coulomb continuum wave function representation in the entire space. To illustrate this numerically, we have considered a first order (e,3e) non-homogeneous Schrödinger equation for the electron impact double ionization of helium: a considerable improvement of the partial transition amplitudes’ convergence rate is observed with a simple two-parameters form of the introduced phase factor.