Coulomb tunneling for fusion reactions in dense matter: Path integral Monte Carlo versus mean field

TL;DR

This paper compares Path Integral Monte Carlo and mean-field calculations of Coulomb tunneling in dense matter, providing a simple parameterization of reaction rates and analyzing uncertainties in nuclear reactions relevant to stellar environments.

Contribution

It introduces a validated mean-field model for Coulomb tunneling rates that aligns with Monte Carlo results at high temperatures, offering a practical tool for astrophysical reaction rate calculations.

Findings

Good agreement between Monte Carlo and mean-field methods above 1/5 of plasma temperature.

Provided a simple parameterization for mean-field potentials and reaction rates.

Discussed uncertainties in nuclear reaction rates in dense stellar matter.

Abstract

We compare Path Integral Monte Carlo calculations by Militzer and Pollock (Phys. Rev. B 71, 134303, 2005) of Coulomb tunneling in nuclear reactions in dense matter to semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean-field potential. We find a very good agreement of two approaches at temperatures higher than ~1/5 of the ion plasma temperature. We obtain a simple parameterization of the mean field potential and of the respective reaction rates. We analyze Gamow-peak energies of reacting ions in various reaction regimes and discuss theoretical uncertainties of nuclear reaction rates taking carbon burning in dense stellar matter as an example.