is solved subject to appropriate boundary conditions to get E$_{R}$ and the hyperradial wave function ζ$_{0}$ ( r ). The many-body wave function can be constructed in terms of ζ$_{0}$ ( r ) and χ$_{K}$$_{0}$ ( r ) $^{24}$. Now in order to study the correlation properties of the interacting Bose gas we choose a realistic interatomic potential having a strong repulsive core at a small separation and an attractive tail at large atomic separations. This is approximately represented by the van der Waals potential with a hard core of radius r$_{c}$ and a 1 r 6 attractive tail, viz. V ( r$_{ij}$ ) = ∞ , for r$_{ij}$ ≤ r$_{c}$ and − C$_{6}$ r 6 ij for r$_{ij}$ > r$_{c}$ . The effective interaction is characterized by the s -wave scattering length ( a$_{s}$ ), which depends strongly on r$_{c}$ $^{23}$. Usually the potentials are chosen to be purely attractive or purely repulsive according to whether a$_{s}$ is negative or positive respectively. In our many-body calculation, we solve the zero-energy two-body Schr¨ odinger equation with V ( r$_{ij}$ ) to obtain a$_{s}$ $^{19,23}$. The value of r$_{c}$ is adjusted so that a$_{s}$ has the values corresponding to the JILA experiments $^{25,26}$. A typical value of r$_{c}$ is of the order of 10 − 3 o.u. In atomic units this is a few tens of Bohr, which is larger than the atomic radius. Note that r$_{c}$ is expected to be larger than the atomic radius, as the van der Waals potential with the hard core of radius r$_{c}$ is the effective potential which produces the correct experimental zero-energy scattering cross-section (given by a$_{s}$ ). We define the one-body density, as the probability density of finding a particle at a distance ⃗ r$_{k}$ from the center of mass of the condensate where ψ is the full many-body wave function and the integral over the hypervolume τ ′ excludes the variable ⃗ r$_{k}$ . After a lengthy but straightforward calculation we arrive at a closed form given by 6 R$_{1}$ ( ⃗ r$_{k}$ ) = ∫ τ ′ | ψ | $^{2}$dτ ′ (7) III. RESULTS A. One-body density