Summability of the Many-Fermion Perturbation Series with Attractive Forces

Abstract

The summability of the many‐fermion perturbation series in the presence of attractive forces is considered. We find that, although it is an asymptotic series, the potential‐strength perturbation series is summable. We find that some rearrangements to handle the hard‐core potentials also lead to the correct sum; however, the ``hole‐line'' summation procedure using Brandow's choice for intermediate state energies is either wrong or deceptive in its convergence.