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We consider the motion of an impurity in a Bose–Einstein condensate system at T = 0 K with the contact interactions for boson-boson and boson-impurity. Under the forward-scattering approximation, we obtain a Fröhlich-like Hamiltonian for this system, which means that a polaron can be formed. The effective mass, the phonon number and the energy to form a polaron are obtained. We also discuss the validity of the forward-scattering approximation for this system.
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Bei-Bing et al. (2009) studied this question.
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