Title: Behavior of the impurity atom in a weakly-interacting Bose gas
Author(s):

	G. Panochko (College of Natural Sciences, Ivan Franko National University of Lviv, 107 Tarnavsky St., 79010 Lviv, Ukraine) ,
	V. Pastukhov (Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Dragomanov St., 79005 Lviv, Ukraine) ,
	I. Vakarchuk (Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Dragomanov St., 79005 Lviv, Ukraine)

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.

Key words: Bose polaron, the damping spectrum, the self-energy
PACS: 67.60.Bc, 03.75.Hh

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