  The spectral flow of three-body (trimer) states consisting of two heavy
(impurity) particles sitting in a condensate of light bosons is considered.
Assuming that the condensate is weakly interaction and that an impurity and a
boson have a zero-range two-body interaction, we use the Born-Oppenheimer
approximation to determine the effective three-body potential. We solve the
resulting Schr\"odinger equation numerically and determine the trimer binding
energies as a function of the coherence length of the light bosonic condensate
particles. The binding energy is found to be suppressed by the presence of the
condensate when the energy scale corresponding to the coherence length becomes
of order the trimer binding energy in the absence of the condensate. We find
that the Efimov scaling property is reflected in the critical values of the
condensate coherence length at which the trimers are pushed into the continuum.
