BCS THEORY TESTED IN AN EXACTLY SOLVABLE FERMION FLUID

Remarkably the one-dimensional (1D) many-fermion fluid with pairwise-a ttractive delta-function interactions is exactly solvable in that one can determine the exact many-body ground-state energy and chemical pot ential for all values of the coupling strength and/or density. Bardeen -Cooper-Schrieffer (BCS) theory is tested in this model by numerically determining the BCS total ground-state energy and chemical potential as a function of the coupling strength and/or density, and comparing w ith the exact results. As is the case for 2D and 3D theories, two regi mes are apparent: (a) a BCS-proper regime of weakly coupled, overlappi ng Cooper pairs and (b) a Bose-gas regime of strongly interacting ferm ions which pair to form an ideal Bose gas at low density. In the two e xtremes the BCS energy and chemical potential are identical to the exa ct values and are moderately close for intermediate coupling and/or de nsity.