Application of sampling theory in modeling of continuum processes: photoionization cross-sections of atoms

TL;DR

This paper introduces a sampling theory-based method for calculating atomic photoionization cross-sections, demonstrating high accuracy and convergence through examples involving hydrogen and sodium atoms.

Contribution

It applies the Whittaker-Shannon-Kotel'nikov sampling theorem to quantum calculations, offering a novel approach to model continuum processes in atomic physics.

Findings

Accurately reproduces known photoionization data

Converges to exact solutions with larger basis sets

Effective for different atomic systems

Abstract

We describe a method for the calculation of photoionization cross-sections using square-integrable amplitudes obtained from the diagonalization of finite-basis set representations of the electronic Hamiltonian. Three examples are considered: a model example in which the final state is a free particle, the hydrogen atom and neutral atomic sodium. The method exploits the Whittaker-Shannon-Kotel'nikov sampling theorem, which is widely used in digital signal sampling and reconstruction. The approach reproduces known data with very good accuracy and converges to the exact solution with increase of the basis set size.