  We consider elementary excitations of an interacting Bose-Einstein condensate
in the mean-field framework. As a building block for understanding the dynamics
of systems comprising interaction and disorder, we study the scattering of
Bogoliubov excitations by a single external impurity potential. A numerical
integration of the Gross-Pitaevskii equation shows that the single-scattering
amplitude has a marked angular anisotropy. By a saddle-point expansion of the
hydrodynamic mean-field energy functional, we derive the relevant scattering
amplitude including the crossover from sound-like to particle-like excitations.
The very different scattering properties of these limiting cases are smoothly
connected by an angular envelope function with a well-defined node of vanishing
scattering amplitude. We find that the overall scattering is most efficient at
the crossover from phonon-like to particle-like Bogoliubov excitations.
