 48790  48810  48830  48850  48870  48890  332  336  340  344  348 0 (r) r 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. 8. (Color online) Plot of the effective potential (in o.u.) against r (in o.u.) for 10000 $^{87}$Rb atoms with a$_{s}$ = 0.00433 o.u.. The curve corresponding to C$_{6}$ = 5 . 0 × 10 − 11 is in its actual position. The other curves have been shifted both vertically and horizontally to coincide the minima (both in position and value). All the curves overlap completely (within numerical errors). This shows that the shape of the effective many-body potential ω$_{0}$ ( r ) is independent of the choice of ( C$_{6}$, r$_{c}$ ) for the same value of a$_{s}$ . Acknowledgement REFERENCES We would like to acknowledge helpful discussion with L. Salasnich, S.R. Jain and G. Mus- sardo. This work has been funded by the Department of Science and Technology (DST), India under grant number SR/S2/CMP/0059(2007). BC thanks the International Center for Theoretical Physics (ICTP), Trieste for hospitality and financial support, where a part of the work was done. TKD acknowledges the University Grants Commission (UGC), India for the Emeritus Fellowship. AB acknowledges the UGC, India for the Research Fellowship in Sciences for Meritorious Students and the Council of Scientific and Industrial Research (CSIR), India for a Senior Research Fellowship. 15 $^{1}$E. H. Lieb and W. Liniger, Phys. Rev. 130 , 1605 (1963). $^{2}$E. H. Lieb, Phys. Rev. 130 , 1616 (1963). $^{3}$K. Sakman et al , Phys. Rev. A 78 , 023615 (2008).