The independent-pair model for one-dimensional fermions interacting through a repulsive delta-potential

The single-particle energies and the ground-state energy for a one-dimensional system of interacting fermions via a repulsive delta-function potential are self-consistently calculated using the Brueckner and Gammel method. The breakdown of the usual quasi-particle description is signaled in this approach by the occurrence of a negative gap at +/-k(F) in the excitation spectrum. A new ground-state configuration of the system emerges: a reduced Fermi sea and an assembly of bosons at +/-k(F). The ground-state energy computed within this scheme is in remarkable agreement with the Bethe-ansatz results at all coupling constants.