Cold Bose Gases near Feshbach Resonances

The lowest order constrained variational method [Phys. Rev. Lett. 88, 210403 (2002)] has been generalized for a dilute (in the sense that the range of interatomic potential is small compared with inter-particle spacing) uniform gas of bosons near the Feshbach resonance using the multi-channel zero-range potential model. The method has been applied to Na (F=1, m_F=1) atoms near the $B_0=907$G Feshbach resonance. It is shown that at high densities, there are significant differences between our results for the real part of energy per particle and the one-channel zero-range potential approximation. We point out the possibility of stabilization of the uniform con densate for the case of negative scattering length.