Applicability of the ladder theory to the three-dimensional homogeneous electron gas

Abstract

Emphasizing a proper description of short-range interactions, the ladder theory (LT) is incapable of reliably reproducing any property of the three-dimensional electron gas except for the correlation function at the electron coalescence limit (the on-top density) $g(0)$ and the related large-$k$ tail of the momentum distribution $n(k)$. Because of the violation of the cusp condition, poor accuracy of the predicted $g(r)$ is expected for any nonvanishing $r$. Although the LT yields components of the correlation energy that satisfy the virial theorem for homogeneous interaction potentials, in the case of the Coulomb potential these components turn out to be infinite. A straightforward analysis shows that any effort at alleviating this problem by introducing a long-range screening is bound to violate the virial condition. A commonly employed approximate version of the LT, which avoids Coulomb singularities, yields incorrect energy components and an unphysical momentum distribution despite producing reasonable values of $g(0)$. Since lessening of the approximation worsens the accuracy of the high-density limit of $g(0)$, this result appears to be due to a fortuitous cancellation of errors.