Atomic ionization by multicharged ions interpreted in terms of poles in the velocity complex space

TL;DR

This paper models atomic ionization by multicharged ions using Padé approximants to interpret the cross section through poles in the velocity complex space, providing a new analytical perspective and fitting experimental data effectively.

Contribution

It introduces a Padé approximant approach to analyze ionization cross sections, revealing poles in the velocity complex plane that encode the physics of the process.

Findings

Padé approximants accurately describe ionization cross sections.

Poles in the complex plane relate to projectile charge dependence.

The approach fits experimental data across velocity ranges.

Abstract

We study the single ionization of hydrogen and helium by the impact of a highly-charged Coulomb projectile. To interpretate the cross section we introduce a diagonal Pad\'{e} approximant. We find that the use of Pad\'{e}% [4,4] describes very well the Continnum Distorted Wave Eikonal Initial State theory within its range of validity. The nodes of the denominator of the Pad% \'{e} approximant give rise to four poles in the velocity complex plane: two in the upper plane and their conjugate in the lower plane. The dependence of these poles with the projectile charge can be reasonably fitted to give a closed-form for the ionization cross section, resulting a scaling very near to the one of Janev and Presnyakov. The experiments available were described very well in its entire velocity range with the use of a Pad\'{e}[8,8], having four poles in the upper plane and their conjugate in the lower plane. We conclude that the poles of the Pad\'{e} approximant seem to have all the information of the total ionization cross section