Wigner-Kirkwood quantum corrections for the pair distribution function in a plasma

Abstract

We study the quantum corrections for the pair distribution function ${g}_{2}{(r}_{12})$ in a one-component plasma. Our analysis is based on the ${\ensuremath{\Elzxh}}^{2}$ expansion of the Wigner-Kirkwood $N$-particle distribution function in phase space. A resulting expression for ${g}_{2}{(r}_{12})$ is derived exactly, at order ${\ensuremath{\Elzxh}}^{4},$ valid at any interparticle distance. This quantum pair distribution function is expressed in terms of the classical two-, three-, four-, and five-particle distribution functions. Analytical properties of this expression are studied, both for small and large ${r}_{12}.$ Accurate approximate expressions, depending only on the classical pair distribution function, are proposed.