Attractive Boson and the Gas-Liquid Condensation

We calculate a grand partition function of the attractive Bose gas in the infinite space within some approximations. Using the idea of the Yang-Lee zeros, it is proved that the gas-liquid condensation occurs before the conventional condition of the Bose-Einstein condensation is satisfied. Further, it is pointed out that Bosons with a zero momentum play a role of a trigger to this gas-liquid condensation. We discuss its implication to the trapped atomic gas.