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

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 very good agreement of the two approaches at temperatures higher than $\sim \frac{1}{5}$ of the ion plasma temperature. We obtain a simple parametrization 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.