  We proposed the non-perturbative scheme for calculation of the impurity
spectrum in the Bose system at zero temperature. The method is based on the
path-integral formulation and describes an impurity as a zero-density ideal
Fermi gas interacting with Bose system for which the action is written in terms
of density fluctuations. On the example of the $^3$He atom immersed in the
liquid helium-4 a good consistency with experimental data and results of Monte
Carlo simulations is shown.
