Cooper pairs as resonances

Using the Bethe-Salpeter (BS) equation, Cooper pairing can be generalized t o include contributions from holes as well as particles from the ground sta te of either an ideal Fermi gas (IFG) or of a BCS many-fermion state. The B CS model interfermion interaction is employed throughout. In contrast to th e better-known original Cooper pair (CP) problem for either two particles o r two holes, the generalized Cooper equation in the IFG case has no real-en ergy solutions. Rather, it possesses two complex-conjugate solutions with p urely imaginary energies. This implies that the IFG ground state is unstabl e when an attractive interaction is switched on. However, solving the BS eq uation for the BCS ground state reveals two types of real solutions: one de scribing moving (i.e., having nonzero total, or center-of-mass., momenta) C Ps as resonances (or bound composite particles with a finite lifetime). and another exhibiting superconducting collective excitations analogous to And erson-Bogoliubov-Higgs RPA modes. A Bose-Einstein-condensation-based pictur e of superconductivity is addressed, (C) 2001 Elsevier Science B.V. All rig hts reserved.