High-density expansion of the electron-gas correlation function

A high-density expansion of the electron-gas correlation function $g(r)$ is carried out in powers of the coupling constant αrₛ. It is found that at zero interparticle separation, $g(0)=1/2{-}{α}{r}ₛ{({{π}}²+6ln2{-}3)}{5{π}}{-}{({3{α}{r}ₛ}{2{π}})}²ln({r}ₛ)(3{-}{{{π}}²}{4})+O({r}ₛ²)$. For large interelectronic separation, the zero-order correction to $g(r)$ is obtained and the correction linear in ${r}ₛ$ is estimated.