 0  0.005  0.01  0.015  0.02  0.025  0  1  2  3  4  5  6  7 One-body density r$_{k}$ 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. FIG. 4. (Color online) One-body density distribution for the repulsive BEC with several C$_{6}$ pa- rameters, all of which correspond to the identical a$_{s}$ = 0.00433 o.u., with 10000 $^{87}$Rb atoms in the JILA trap. All quantities are in oscillator units. depends on the minimum of the well, in addition to the actual shape of the lowest eigen potential. In Table 1, we present the dependence of the position ( r$_{m}$ ) and the value ( ω$_{0}$$_{m}$ ) of the minimum of lowest eigen potential for different values of C$_{6}$ parameter, corresponding to the same a$_{s}$ . Table 1. Dependence of r$_{m}$ and ω$_{0}$$_{m}$ on C$_{6}$ (corresponding to a$_{s}$ = 0 . 00433) for A = 10000 atoms (all quantities are expressed in o.u.). C$_{6}$ r$_{m}$ ω$_{0}$$_{m}$ 5 . 0 × 10 − 11 339 . 92 48792 . 7 6 . 4 × 10 − 11 339 . 47 48668 . 7 8 . 5 × 10 − 11 339 . 04 48546 . 3 8 . 0 × 10 − 10 338 . 93 48517 . 8 We observe that, as C$_{6}$ increases, ω$_{0}$$_{m}$ decreases appreciably, while position of the minimum of effective many-body potential changes by a small amount. In the next sub-section, we will see that the shape of the ω$_{0}$ ( r ) curve remains practically unchanged. As the total condensate energy depends on the depth of the potential, as well as on its shape (stiffness), we observe that the ground state energy decreases gradually with increase in C$_{6}$ $^{29}$. Thus the shape independence hypothesis is violated for the total energy. However, the one-body density distribution is given by the many-body wave function, which is independent of the 10