and a set of (3 N − 1) ‘hyperangles’, consisting of 2 N polar angles of N Jacobi vectors and ( N − 1) angles defining their relative lengths $^{20}$. In the hyperspherical harmonics expansion method (HHEM) the N -body Schr¨ odinger Equation (2) is solved by expanding ψ in the complete set of hyperspherical harmonics (HH), which are the eigenfunctions of the N - dimensional Laplace operator (analogous to the spherical harmonics in three dimension) $^{20}$. Substitution of this in Eq. (2) and projection on a particular HH results in a set of coupled differential equations. However imposition of symmetry of the wave function and calculation of the matrix elements are such formidable tasks that a practical solution for A > 3 is nearly impossible. Moreover due to the fact that the degeneracy of the HH basis increases very rapidly with the increase in the grand orbital quantum number K $^{20}$, a convergent calculation using HHEM with the full HH basis is extremely computer intensive. This is the price one pays for keeping all many-body correlations . On the other hand, a typical experimental BEC is designed to be extremely dilute to eliminate the possibility of molecule formation through three-body collisions. Hence we assume that the probability of three and more particles to come within the range of interatomic interaction is negligible and the effect of the two-body correlations will be adequate for the full many-body wave function. Moreover, only two-body interactions are relevant. Therefore, ψ can be expressed in terms of Faddeev components ψ$_{ij}$ of the ( ij ) interacting pair 21 Since only two-body correlations are important, ψ$_{ij}$ is a function of the interacting-pair sep- aration r$_{ij}$ = ⃗ x$_{i}$ − ⃗ x$_{j}$ and r only. Hence it can be expanded in the subset of HH needed for the expansion of the two-body interaction V ( ⃗ r$_{ij}$ ). This subset is called the potential harmonics (PH) basis $^{21}$. This results in a dramatic simplification in the analytic and com- putation works and it has been used upto 14000 bosons in the trap $^{18}$. In this procedure, a realistic interatomic interaction can be used. Such an interaction has a strongly repulsive core. Hence ψ$_{ij}$ must be vanishingly small for small values of r$_{ij}$ . But the first ( K = 0) term of the PH basis is a constant $^{20}$. Hence to reproduce the short-range behaviour of ψ$_{ij}$ correctly, a large number of PH basis functions is needed, which slows down the rate of convergence considerably. Hence, we introduce a ‘short-range correlation function’ in the PH expansion basis $^{22}$. In the zero temperature BEC, the kinetic energy of the interacting pair is practically zero. Therefore, the two-body collision process is determined entirely by 4 ψ = ∑ i<j ψ$_{ij}$ ( ⃗ r$_{ij}$, r ) . (4)