Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections

TL;DR

This paper introduces a nonlinear optimization method to fit continuum wavefunctions with complex Gaussians, enabling analytical calculations of ionization cross sections and demonstrating efficiency for one-center atomic targets.

Contribution

The paper develops a novel all-Gaussian approach using complex Gaussians for continuum states, improving computational efficiency and accuracy in ionization process calculations.

Findings

Validated the numerical feasibility of complex Gaussian fits for continuum states.

Demonstrated the superiority of complex over real Gaussian expansions.

Achieved efficient analytical computation of ionization cross sections.

Abstract

We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex over real Gaussian expansions. We then consider the photoionization of atomic hydrogen, and ionization by electron impact in the first Born approximation, for which the closed form cross sections serve as a solid benchmark. Using the proposed complex Gaussian representation of the continuum combined with a real Gaussian expansion for the initial bound state, all necessary matrix elements within a partial wave approach become analytical. The successful numerical comparison illustrates that the proposed all-Gaussian approach works efficiently for ionization processes of one-center targets.