 0  0.01  0.02  0.03  0.04  0.05  0.06  0.07  0.08  1  2  3  4  5  6  7 One-body density r$_{k}$ a$_{s}$ = 2.09 x 10 -4 o.u., PHEM a$_{s}$ = 2.09 x 10 -4 o.u., GP a$_{s}$ = 43.3 x 10 -4 o.u., PHEM a$_{s}$ = 43.3 x 10 -4 o.u., GP FIG. 1. (Color online) One-body density distribution as a function of r$_{k}$ (in o.u.) for a repulsive BEC with A=10000 bosons. The choice of a$_{s}$ = 0.00433 o.u. corresponds to $^{87}$Rb experiment in the JILA trap. PHEM corresponds to our present many-body results and GP corresponds to mean-field results. FIG. 2. (Color online) One-body density distribution as a function of r$_{k}$ (in o.u.) for an attractive interaction ( a$_{s}$ = − 1 . 836 × 10 − 4 o.u. for $^{85}$Rb atoms in the JILA trap), for various indicated values of particle numbers.  0  0.1  0.2  0.3  0.4  0.5  0.6  0  1  2  3  4  5  6  7 One-body density r$_{k}$ A = 100 1000 2400 2470 having a sharper peak, as the net interaction increases. The peak at k = 0 becomes more pronounced with increase in effective repulsion, whereas for weak interaction it develops a long-range tail in the momentum space. The momentum is being redistributed to higher k values. The width of the low-momentum peak for a$_{s}$ = 0 . 00433 o.u. and A = 10000 is about 0 . 7 µ m − $^{1}$. We have remarked earlier that with recent progress in creating atomic clouds with large dipole moment, interest has been shifted to longer range interaction instead of taking only 8