Atomic Bose gas with a negative scattering length

We derive the equation of state of a dilute atomic Bose gas with an interatomic interaction that has a negative scattering length and argue that two continuous phase transitions, occurring in the gas due to quantum degeneracy effects, are preempted by a first-order gas-liquid or gas-solid transition, depending on the details of the interaction potential. We also discuss the consequences of this result for future experiments with magnetically trapped spin-polarized atomic gases such as lithium and cesium