Ground-State Energy of a Many-Fermion System

Abstract

This paper contains a critique of the Brueckner-Goldstone perturbation series for the ground-state energy of an interacting gas of fermions. We have calculated this energy by first constructing the grand partition function at finite temperature, and then carefully taking the limit as $T\ensuremath{\rightarrow}0$. In general this leads to a series which differs from that of Brueckner and Goldstone. An exception is the case where both the unperturbed single-particle energy as well as the interaction potential have spherical symmetry. Reasons for the breakdown of the Brueckner-Goldstone formalism are briefly discussed.