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We present a variational Monte Carlo (VMC) formulation for the universalequations of state at the Van der Waals length scale [B. Gao, J. Phys. B\textbf{37}, L227 (2004)] for $N$ Bose atoms in a trap. The theory illustratesboth how such equations of state can be computed exactly, and the existence andthe importance of long-range atom-atom correlation under strong confinement.Explicit numerical results are presented for N=3 and 5, and used to provide aquantitative understanding of the shape-dependent confinement correction thatis important for few atoms under strong confinement.Comment: 6 pages, 4 figure

Bose atoms in a trap: A variational Monte Carlo formulation for the universal behavior at the van der Waals length scale