Pairing Instability and Mechanical Collapse of a Bose Gas with an Attractive Interaction

We study the pairing instability and mechanical collapse of a dilute homogeneous bose gas with an attractive interaction. The pairing phase is found to be a saddle point, unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instability and mechanical collapse are higher than the BEC temperature of an ideal bose gas with the same density. When fluctuations are taken into account, we find that the critical temperature of mechanical collapse is even higher. The difference between the collapse temperature and the BEC temperature is proportional to $(n|a_s|^3)^{2/9}$, where $n$ is the density and $a_s$ is the scattering length.