content_image/331454.jpg
<img src='content_image/331454.jpg'>

contact interaction. Thus, even in the low-density limit the use of a realistic interatomic in- teraction potential in the many-body calculation has been emphasized by several authors [27- 29]. The van der Waals potential is an ideal choice as it properly takes care of the effect of realistic dipole-dipole interaction. The strength of the van der Waals interaction C$_{6}$ changes widely from a small value for H atoms to a high value for Cs atoms. Hence, to see how the one-body density is affected by the strength of the long-range tail of the two-body potential, we select three different values of C$_{6}$ in addition to the actual experimental value – one below and two above. These are (in o.u.): 5 × 10 − $^{11}$, 6 . 489755 × 10 − $^{11}$, 8 . 5 × 10 − $^{11}$, 8 × 10 − $^{10}$, the second one being the experimental value. For each value of C$_{6}$ , we calculate corresponding r$_{c}$ as before, such that a$_{s}$ has the experimental value 0.00433 o.u. For each set of ( C$_{6}$, r$_{c}$ ), we solve the many-body Schr¨ odinger equation as before. Calculated one-body density for different sets are shown in Fig. 4 for 10000 bosons. We observe that the one-body den- sity of the inhomogeneous gas for different two-body potentials are almost indistinguishble; i.e. independent of the shape of V ( r$_{ij}$ ). Our numerical calculations confirm that one-body density is absolutely determined (within numerical errors) by the parameter a$_{s}$ only. 

This is in contrast with ref. $^{29}$, where ground state energy of the condensate was found to depend on the shape of the potential. Thus the one-body density does not depend strongly on the shape of the interaction potential, while the ground state energy does. 

An explanation of the above observation is as follows. The total condensate energy 

