We study a dilute Bose gas of atoms whose scattering length $a$ is large compared to the range of their interaction. We calculate the energy density $E$ of a homogeneous Bose-Einstein condensate (BEC) to second order in the low-density expansion, expressing it in terms of $a$ and a second parameter ${\Lambda }_{*}$ that determines the low-energy observables in the three-body sector. The second-order correction to $E$ has a small imaginary part that reflects the instability due to three-body recombination. In the case of a trapped BEC with large negative $a$, we calculate the coefficient of the three-body mean-field term in $E$ in terms of $a$ and ${\Lambda }_{*}$. It can be very large if there is an Efimov state near threshold.

• Received 24 August 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.040401