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

We study the system of a dilute homogeneous bose gas with an attractive interaction within the variational wave-function approach. We find that the pairing phase is unstable against fluctuations in pairing. The system can collapse due to this pairing instability in addition to the well-known 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|as| 3)2/9, where n is the density and as is the scattering length.