Few atoms in a trap: universal behavior at the Van der Waals length scale

We present results of variational Monte Carlo calculations for the universal equations of state at the Van der Waals length scale\footnote{B. Gao, J. Phys. B \textbf{37}, L227 (2004).} for a N-atom system (N = 2 to 5) in a trap. The theory provides a systematic understanding of few atoms in a trap, including, in particular, the shape-dependence of interaction energy that becomes important at large scattering lengths. The theory also shows that atoms in a trap have significant long-range correlation for large scattering lengths, with the implication that any independent particle model, such as the Hartree-Fock approximation, is likely to fail for such systems.