Repulsive Bardeen-Cooper-Schrieffer Pair-Interaction

With the mere use of the sum rules, the effect of interaction on the energy and one-particle momentum distribution of a system of Fermi particles, interacting with the repulsive BCS-type pair interaction, is investigated with the assumption that the coupling constant is of order one, together with the case when the coupling constant is of the order $\frac{1}{\Omega }$ ($\Omega$ being the volume of the quantization box) which was treated earlier by Van Hove in connection with the question of sharpness of Fermi surface. It is observed that in some region of density, this type of interaction has no effect on the energy and sharpness of the Fermi sphere, and above critical density the system will go over a phase change, but still the Fermi sphere remains rigid.