Improved Kelbg Potentials for $Z>1$ and Application to Carbon Plasmas

TL;DR

This paper develops an improved Kelbg potential for atomic numbers up to 54 and applies it to simulate hot, dense carbon plasmas, comparing results with advanced quantum models to assess accuracy and limitations.

Contribution

It introduces a generalized form of the Kelbg potential for higher atomic numbers and evaluates its effectiveness in modeling warm dense carbon plasmas.

Findings

The improved Kelbg potential accurately reproduces internal energies and pressures for carbon plasmas.

Validity regions for carbon are consistent with hydrogen when pressure ionization is included.

The potential's applicability is discussed for high energy density plasma simulations.

Abstract

In this work, we present a general form for the electron-ion diffractive potential derived from the quantum pair density matrix and fit to the improved Kelbg potential for atomic numbers up to $Z = 54$. We apply classical molecular dynamics using the improved Kelbg potential for carbon with various forms of the Pauli potential to compute internal energies and pressures for hot, dense plasma conditions. Our results are compared to an equation of state model based on path integral Monte Carlo and density functional theory simulations to examine the extent to which the improved Kelbg potential reproduces the internal energy and pressure of carbon plasmas. The regions of validity for carbon agree generally with those derived previously for hydrogen once pressure ionization effects are incorporated. Based on our carbon results and previously published hydrogen studies, we discuss the general applicability and limitations of these potentials for equation of state studies in warm dense matter and high energy density plasmas.