Quantum acoustic bremsstrahlung of impurity atoms in a Bose--Einstein condensate

We study the process of scattering of two impurity atoms accompanied by generation of an elementary excitation in a surrounding Bose--Einstein condensate. This process, unlike the phonon generation by a {\it single} impurity atom, has no velocity threshold and can be regarded as a quantum acoustic analog of a bremsstrahlung in quantum electrodynamics.