The Cooper pair dispersion relation

The binding energy of a Cooper pair formed with the BCS model interaction potential is obtained numerically for all coupling in two and three dimensions for all non-zero center-of-mass momentum (CMM) of the pair. The pair breaks up for very small CMM, at most about four orders of magnitude smaller than the maximum CMM allowed by the BCS model interaction, and its binding energy is remarkably linear over the entire range of the CMM up to breakup.