  A relation between the number of bound collective excitations of an atomic
Bose-Einstein condensate and the phase shift of elastically scattered atoms is
derived. Within the Bogoliubov model of a weakly interacting Bose gas this
relation is exact and generalises Levinson's theorem. Specific features of the
Bogoliubov model such as complex-energy and continuum bound states are
discussed and a numerical example is given.
