Semi-empirical cross-section formulas for electron-impact ionization and rate coefficient calculations

TL;DR

This paper introduces a semi-empirical formula for electron-impact ionization cross sections, adaptable for different ions and plasma conditions, enabling accurate rate coefficient calculations with practical interpolation and extrapolation capabilities.

Contribution

The authors develop a semi-empirical cross-section formula that incorporates adjustable parameters, validated against experimental and numerical data, suitable for diverse plasma environments and ion species.

Findings

The formula accurately fits measured and calculated cross sections.

It allows analytical and numerical computation of rate coefficients.

Results agree well with experimental data and previous calculations.

Abstract

We propose a semi-empirical formula for the cross section of ionization by electron impact. The formula involves adjustable parameters which are determined by comparison with measured or numerically calculated cross sections. In the latter case, the ions are perturbed by their environment which is a high-density plasma. As a consequence, the cross section is significantly modified. We investigate Be-like carbon, nitrogen and oxygen as well as aluminum ions. We also show that the formula is well-suited for interpolation and extrapolation. Knowing the cross section, we calculate the rate coefficient within the Boltzmann and Fermi-Dirac statistics. In the first case, the rate can be calculated analytically. In the second one, it can be expressed in terms of special functions, but the numerical evaluation is more convenient while providing accurate results. Our results are compared to experiment and to other calculations.