The binding energy of a Cooper pair formed with the BCS model interact
ion potential is obtained numerically for all coupling in two and thre
e dimensions for all non-zero center-of-mass momentum (CMM) of the pai
r. 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 inter
action, and its binding energy is remarkably linear over the entire ra
nge of the CMM up to breakup. (C) 1998 Elsevier Science B.V.