Nuclear fusion reaction rates for strongly coupled ionic mixtures

Abstract

We analyze the effect of plasma screening on nuclear reaction rates in dense matter composed of atomic nuclei of one or two types. We perform semiclassical calculations of the Coulomb barrier penetrability taking into account a radial mean-field potential of plasma ions. The mean-field potential is extracted from the results of extensive Monte Carlo calculations of radial pair distribution functions of ions in binary ionic mixtures. We calculate the reaction rates in a wide range of plasma parameters and approximate these rates by an analytical expression that is expected to be applicable to multicomponent ion mixtures. Also, we analyze Gamow-peak energies of reacting ions in various nuclear burning regimes. For illustration, we study nuclear burning in $^{12}\mathrm{C}$-$^{16}\mathrm{O}$ mixtures.