We study the properties of Bose-Einstein condensates with the realistic van der Waals two-body interaction for large numbers of trapped atoms, solving the many-body Schrödinger equation by the potential harmonic expansion method. The effect of different $C_6$ parameters has been critically examined, starting from very few to 14 000 atoms to analyze and justify the idea of a shape-independent approximation. It is found that the condensate properties almost remain unchanged when the number of atoms are quite small $(\sim 100)$, in good agreement with earlier results of Blume and Greene [Phys. Rev. A 63, 063601 (2001)], but we observe the appreciable effect of a long attractive tail when $N$ is large, even in the low-density limit. The above reference considered only 20 atoms which is far from a real experimental situation. Our calculation gives a realistic scenario which justifies the use of a shape-dependent two-body interaction in many-body theories.

• Received 28 July 2008

DOI:https://doi.org/10.1103/PhysRevA.78.063608