The properties of the uniform Bose gas are studied within the optimized variational perturbation theory (Gaussian approximation) in a self-consistent way. It is shown that the atomic Bose-Einstein condensate with a repulsive interaction becomes unstable when the gas parameter $\gamma =\rho a^3$ exceeds a critical value ${\gamma }_{crit}\approx 0.01$. The quantum corrections beyond the Bogoliubov-Popov approximation to the energy density, chemical potential, and pressure in powers of $\sqrt{\gamma }$ expansions are presented.

• Received 11 January 2008

DOI:https://doi.org/10.1103/PhysRevA.77.033626