Linear to quadratic crossover of Cooper-pair dispersion relation

Cooper pairing is studied in three dimensions to determine its binding ener gy for all coupling using a general separable interfermion interaction. Als o considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (C MM). A coupling-independent linear term in the CMM dominates the pair excit ation energy in weak coupling and/or high fermion density, while the more f amiliar quadratic term prevails only in the extreme low-density (i.e., vacu um) limit for any nonzero coupling. The linear-to-quadratic crossover of th e CP dispersion relation is analyzed numerically, and is expected to play a central role in a model of superconductivity (and superfluidity) simultane ously accommodating a Bardeen-Cooper-Schrieffer condensate as well as a Bos e-Einstein condensate of CP bosons. (C) 2001 Elsevier Science B,V. All righ ts reserved.