Ground state property of Bose-Einstein gas for arbitrary power low interaction

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We study Bose-Einstein gas for an arbitrary power low interaction Cαr⁻α. This is done by the Hartree Fock Bogoliubov (HFB) approach at T ≤ Tc and the mean field approach at T>Tc. Especially, we investigate the ground state property of Bose gas interacting through the Van der Waals -C₆r⁻⁶ plus C₃r⁻³ interactions. We show that the ground state under this interaction is stable if the ratio of coupling constants is larger than that of the critical curve. We find that the C₃r⁻³ term plays an important role for the stability of the ground state when the density of atoms becomes sufficiently large at low temperature. Further, using the numerical values of C₃ and C₆, we confirm that the ground state of alkali atoms are stable.