Pairing instability and mechanical collapse of a Bose gas with an attractive interaction

The pairing instability and mechanical collapse of Bose gas with an attractive interaction was studied. The pairing phase was found to be a saddle point and the pairing saddle point existed above the temperature of pairing instability. The system was totally unstable below the critical temperature. It was found that when fluctuations were taken into account, the critical temperature of mechanical collapse was even higher.