  Relativistic 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 $\hbar^{2}$. In general, our theory leads to an ${\cal O}(10)$ 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.
