  A two-component van der Waals gas model is proposed to describe the hadronic
stages of the evolution of a nuclear fireball in the cooling stage. At the
first stage of hadronization, when mesons dominate, a two-component meson model
($\pi^0$ and $\pi^+$ -mesons) with an effective two-particle interaction
potential of a rectangular well is proposed. At the late-stage hadronization,
when almost all mesons have decayed, a two-component nucleon model of protons
and neutrons is proposed with the corresponding effective rectangular nucleon
potential. The saddle point method has been applied for analytical calculations
of the partition function. This made it possible to uniformly obtain analytical
expressions for both the pressure and density, taking into account the finite
dimensions of the system, and the analytical expressions for chemical
potentials. It is assumed that the proposed models and derived formulas can be
used to analyze experimental data connected to the quantitative characteristics
of the particle yields of different types in the final state from the hadronic
stages of the evolution of a nuclear fireball, as well as to determine the
critical parameters of the system in high-energy nucleus-nucleus collisions.
