The effect of electron gas polarization on thermonuclear reaction rates in dense stars

In dense stars the nuclear reaction rates are influenced by screening effects arising from both ions and electrons. In this paper we calculate the enhancement factors due to electron polarization in the high-density, degenerate and relativistic regime, for non-resonant nuclear reaction rates. In an earlier analysis, Sahrling had proposed the possibility that the polarized electrons would lower the reaction rate instead of enhancing it. This analysis was based on Monte Carlo simulations with only one choice of density, temperature and charge. Here we extend the analysis to a wider range of densities, temperatures and charges and calculate analytical expressions for the enhancement factors. We concentrate on carbon and oxygen ions and show that at very high-densities, high-order quantum effects will be important and act to reduce the zeroth order, classical value for the enhancement factor. We show that in any case, the total electron contribution remains weak, namely an enhancement in the reaction of about a factor 2, contrarily to what had been claimed by some authors in previous calculations. We examine the astrophysical implications of these results on the final stages of massive white dwarfs, near the carbon-ignition curve.