  The interaction of two spatially separated impurity atoms through phonon
exchange in a Bose-Einstein condensate is studied within a Bogoliubov approach.
The impurity atoms are held by deep and narrow trap potentials and experience
level shifts which consist of a mean-field part and vacuum contributions from
the Bogoliubov-phonons. In addition there is a conditional energy shift
resulting from the exchange of phonons between the impurity atoms.
