  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.
