Hyperspherical lowest-order constrained-variational approximation to resonant Bose-Einstein condensates

We study the ground-state properties of a system of N harmonically trapped bosons of mass m interacting with two-body contact interactions, from small to large scattering lengths. This is accomplished in a hyperspherical coordinate system that is flexible enough to describe both the overall scale of the gas and two-body correlations. By adapting the lowest-order constrained-variational method, we are able to semiquantitatively attain Bose-Einstein condensate ground-state energies even for gases with infinite scattering length. In the large-particle-number limit, our method provides analytical estimates for the energy per particle E0/N ≈ 2.5N 1/3h̄ω and two-body contact C2/N ≈ 16N 1/6 √ mω/h̄ for a Bose gas on resonance, where ω is the trap frequency.