COOPER INSTABILITY FOR A GIVEN FIELD IN A QUIESCENT FERMI GAS

The Cooper instability in a Fermi gas is examined using the perturbati ve diagram approach. A graphical functional derivative technique based on Ward's identity is developed to obtain two-particle interactions a nd then to calculate the vertex part. The pairing instability for a gi ven interaction, such as a phonon (plasmon, etc.) field, occurs in a q uiescent Fermi sea, i.e. without exciting or involving background part icles (holes), only if the interaction is attractive, as first propose d by Cooper and adopted in the BCS (Bardeen-Cooper-Schrieffer) theory. The consequence from this technique provides a way to evaluate the ef fect of the vertex corrections and responses of the Fermi gas in both charge and spin channels incorporating the backward scattering process . The significance of the methodology presented in the present work li es in the fact that it can both reproduce the known results, and, more importantly, be extended to investigate the intermediate or strong co upling case, such as nuclear interactions, where a neglect of vertex c orrections may not be a good approximation.