We study Bose-Einstein gas for an arbitrary power low interaction $C_{ \alpha}r^{ -\alpha}$. This is done by the Hartree Fock Bogoliubov (HFB) approach at $T \le T_{ c}$ and the mean field approach at $T>T_{ c}$. Especially, we investigate the ground state property of Bose gas interacting through the Van der Waals $-C_{ 6}r^{ -6}$ plus $C_{ 3}r^{ -3}$ 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 $C_{ 3}r^{ -3}$ 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 $C_{ 3}$ and $C_{ 6}$, we confirm that the ground state of alkali atoms are stable.
Categories: cond-mat.stat-mech