Systematic quantum effects on screening of fusion rates in white dwarfs

Abstract

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.