Phase diagram and binding energy of interacting Bose gases
  From the many-body T-matrix the condition for a medium-dependent bound state and its binding energy is derived for a homogeneous interacting Bose gas. This condition provides the critical line in the phase diagram in terms of the medium-dependent scattering length. Separating the Bose pole from the distribution function the influence of a Bose condensate is discussed and a thermal minimum of the critical scattering length is found. 
M. M\"annel, K. Morawetz, M. Schreiber, P. Lipavsk\'y