Simple electron-impact excitation cross-sections including plasma density effects

TL;DR

This paper introduces an analytical method to calculate electron-impact excitation cross-sections in plasmas, incorporating plasma density effects and correction factors, enabling fast and accurate modeling for high-energy-density physics applications.

Contribution

It develops an analytical approach based on the Plane Wave Born approximation with corrections, accounting for plasma density effects, to efficiently compute excitation cross-sections.

Findings

Analytical expressions for EIE cross-sections are derived.

Plasma density effects like Coulomb screening and degeneracy are incorporated.

The method achieves accurate rates without numerical integration.

Abstract

The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for many aspects of high-energy-density physics. It often requires collisional-radiative models coupled with radiative-hydrodynamics simulations. Therefore, there is a strong need for fast and as accurate as possible calculations of the cross-sections and rates of the different collisional and radiative processes. We present an analytical approach for the computation of the electron-impact excitation (EIE) cross-sections in the Plane Wave Born (PWB) approximation. The formalism relies on the screened hydrogenic model. The EIE cross-section is expressed in terms of integrals, involving spherical Bessel functions, which can be calculated analytically. In order to remedy the fact that the PWB approximation is not correct at low energy (near threshold), we consider different correcting factors (Elwert-Sommerfeld, Cowan-Robb, Kilcrease-Brookes). We also investigate the role of plasma density effects such as Coulomb screening and quantum degeneracy on the EIE rate. This requires to integrate the collision strength multiplied by the Fermi-Dirac distribution and the Pauli blocking factor. We show that, using an analytical fit often used in collisional-radiative models, the EIE rate can be calculated accurately without any numerical integration, and compare our expression with a correction factor presented in a recent work.