one-body density and pair distribution function are not. In conclusion, the present work focuses on the one-body density and pair-correlation aspects of the zero temperature weakly interacting trapped Bose gas. The use of correlated many-body approach takes care of the effect of finite-size, where quantum fluctuation is important and gives a realistic picture of correlation properties. Due to the use of a realistic interatomic interaction and consideration of finite number of atoms in the trap, our results deviate from the earlier results $^{4,8}$, but exhibit realistic aspects which are relevant to exper- iments. Our calculation is performed for a two-body potential (van der Waals potential), whose parameters can be adjusted to give both positive and negative scattering lengths, for Rb atoms in the JILA trap. Thus, our results are realistic and can be experimentally verified in future. Our calculations also verify the validity of the shape-independent approximation in dilute BECs for one-body density and pair-distribution functions. This is in contrast with the earlier observed shape dependence for ground state energies $^{29}$. 14 IV. CONCLUSION FIG. 7. (Color online) Plot of two-body correlation function against r$_{ij}$ in o.u. for repulsive BEC with several indicated C$_{6}$ parameters, all of which correspond to identical a$_{s}$ = 0.00433 o.u. with 10000 $^{87}$Rb atoms in JILA trap. (The portion near the origin is magnified in the inset to show that the pair distribution function vanishes inside the hard core. The same is true for Fig. 5.)  0  0.05  0.1  0.15  0.2  0.25  0.3  0  1  2  3  4  5  6  7  8  9  10 Pair distribution function r$_{ij}$ C$_{6}$ = 5.0 x 10 -11 o.u. C$_{6}$ = 6.489755 x 10 -11 o.u. C$_{6}$ = 8.5 x 10 -11 o.u. C$_{6}$ = 8.0 x 10 -10 o.u.  0 0.0001  0 0.01