  Electron degeneracy effects are dominant in ultra-dense plasmas (UDP), such
as those found in white dwarfs. These effects can be treated systematically by
obtaining an expansion of the screening length in inverse powers of
$\hbar^{2}$. The theory exhibits Thomas-Fermi-like screening in an appropriate
regime. In general, our theory leads to an ${\cal O}(1)$ effect on the
enhancement of fusion rates in white dwarfs. Further, it is shown analytically
for these stellar conditions that Bose statistics of nuclei have a negligible
effect on the screening length, in consonance with Monte Carlo simulations
found in literature.
