minimum of the potential, but depends only on its shape. Hence it remains unchanged with change in C$_{6}$ parameter and shape independence of the one-body density profile is satisfied. Another key quantity is the pair distribution function R$_{2}$ ( r$_{ij}$ ), which determines the probability of finding the ( ij )-pair of particles at a relative separation r$_{ij}$ . The study of pair correlation is important, since the interatomic interactions play a crucial role as there are two competing interaction length scales. When the atoms try to form clusters, a strong very short range repulsion in atomic interaction comes into play. As atoms repel each other strongly at very small separations it is impossible to get some non-vanishing value of R$_{2}$ ( r$_{ij}$ ) at r$_{ij}$ = 0. We calculate it as where ψ is the many-body wavefunction and the integral over the hypervolume τ ′′ excludes integration over r$_{ij}$ . Again after a lengthy calculation we can put it in a closed form given by We plot R$_{2}$ ( r$_{ij}$ ) in Fig. 5 for the attractive interaction with different particle numbers. As mentioned earlier, pair correlation vanishes as r$_{ij}$ → 0, due to the strong interatomic repulsion and it cannot extend beyond the size of the condensate. Hence R$_{2}$ is peaked at some intermediate value of r$_{ij}$ . For weak interactions (small λ ), the correlation length is large. However as the effective attractive interaction increases, two interacting particles come closer and the pair-correlation length decreases; the pair distribution function becomes sharply peaked. It indicates stronger pair correlation in the system, in agreement with expectations. However our results are at variance with those obtained in LL model $^{8}$, which describes uniform systems with no confinement. Consequently pair correlation function 11 R$_{2}$ ( r$_{ij}$ ) = $^{√$_{2}$}$∫ 1 − 1 ( 1 − z 2 ) α ( ζ$_{0}$ ( r$_{ij}$ √ 2 1 + z )) 2 ∑ KK ′ ( h αβ K 2 α ) − 1 / $^{2}$( h αβ K ′ 2 α ) − 1 / 2 ( f$_{Kl}$f$_{K}$ ′ $_{l}$) − 1 χ$_{K}$$_{0}$ ( r ) χ$_{K}$ ′ $_{0}$( r ) P αβ K ( z ) P αβ K ′ ( z ) dz. (10) R$_{2}$ ( r$_{ij}$ ) = ∫ τ ′′ | ψ | $^{2}$dτ $^{′′}$, (9) B. Pair distribution function