  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.
