  We studied the properties of a single impurity atom immersed in a dilute Bose
condensate at low temperatures. In particular, we perturbatively obtained the
momentum dependence of the impurity spectrum and damping. By means of the
Brillouin-Wigner perturbation theory we also calculated the self-energy both
for attractive and repulsive polaron in the long-wavelength limit. The
stability problem of the impurity atom in a weakly-interacting Bose gas is also
examined.
