Systematic quantum corrections to screening in thermonuclear fusion

Abstract

We develop a series expansion of the plasma screening length away from the classical limit in powers of ${\hslash }^2$. It is shown that the leading order quantum correction increases the screening length in solar conditions by approximately 2% while it decreases the fusion rate by approximately $0.34$. We also calculate the next higher order quantum correction which turns out to be approximately 0.05%.