Stability of the homogeneous Bose-Einstein condensate at large gas   parameter
  The properties of the uniform Bose gas is studied within the optimized variational perturbation theory (Gaussian approximation) in a self-consistent way. It is shown that the atomic BEC with a repulsive interaction becomes unstable when the gas parameter gamma=rho a^3 exceeds a critical value gamma_{crit} ~ 0.01. The quantum corrections beyond the Bogoliubov-Popov approximation to the energy density, chemical potential and pressure in powers of gamma expansions are presented. 
Abdulla Rakhimov, Chul Koo Kim, Sang-Hoon Kim, and Jae Hyung Yee