Attractive inter-particle force in Van der Waals model of hadron gas in the grand canonical ensemble

We generalize derivation of partition functions of the grand canonical ensemble for the multicomponent van der Waals gas of interacting particles by hardcore potentials to the case of the attractive large-distance mean field. The formulas obtained by the saddle point method for the thermodynamic potentials with the transparent non-relativistic limit to the case of conserving large number of particles for different gas components like neutrons and protons of nuclear matter can be used for analysis of experimental data for the particle number ratios in nucleus-nucleus collisions at high excitation energies.