Quasi Sturmian Basis in Two-Electron Continuum Problems

TL;DR

This paper introduces Convoluted Quasi Sturmian functions as a new basis for modeling two-electron continuum states in atomic ionization processes, demonstrating improved convergence in numerical solutions.

Contribution

The paper proposes a novel basis called Convoluted Quasi Sturmian functions for two-electron continuum problems, enhancing convergence by incorporating electron-electron interaction effects.

Findings

Convergence rate improves with phase factor inclusion.

Modified boundary conditions significantly affect solution magnitude.

Basis functions asymptotically resemble six-dimensional spherical waves.

Abstract

A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms of the recently introduced Quasi Sturmian functions, Convoluted Quasi Sturmian functions (CQS). By construction, the CQS functions look asymptotically like a six-dimensional spherical wave. The driven equation describing an $(e, 3e)$ process on helium in the framework of the Temkin-Poet model has been solved numerically using expansions on the basis CQS functions. The convergence behavior of the solution has been examined as the size of the basis has been increased. The calculations show that the convergence rate is significantly improved by introducing a phase factor corresponding the electron-electron interaction into the basis functions. Such a modification of the boundary conditions leads to appreciable change in the magnitude of the solution.