We consider a gas of bosonic atoms (at zero temperature) with the scattering length a enhanced by means of the Feshbach resonance. We calculate the mean-field interaction energy in the case of breakdown of the dilute gas limit. We show that if a exceeds the mean interatomic distance n^-1/3, n being the atomic number density, the chemical potential of the gas is proportional to n^2/3. We call it effective fermionization of a Bose-system.

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