Hyperspherical-LOCV Approximation to Resonant BEC

Abstract

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 (LOCV) method, we are able to semi-quantitatively 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 $E_0/N\approx 2.5N^{1/3}\hslash \omega$ and two-body contact $C_2/N\approx 16N^{1/6}\sqrt{m\omega /\hslash }$ for a Bose gas on resonance, where $\omega$ is the trap frequency.