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

Abstract

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.

17 pages, LaTeX, 3 figures