Some Properties of Unstable Particle Gases

The elastic scattering of two particles is interpreted as the formation and decay of an unstable particle. The collision cross section and the reciprocal of the scattering delay time are used to determine rates of production and destruction in a gas of interacting stable particles. By equating the two rates, a general expression for the equilibrium number density of unstable particles is obtained. This is tested for two specific types of scattering, and it is found that in resonance scattering the expression, in the limit as $\Gamma \to 0$ (stable particles), reduces to that predicted by the equations of chemical and nuclear statistical equilibrium. Dividing a real gas into an ideal stable particle gas and an ideal unstable particle gas, an equation of state for the latter is inferred from the form of the second virial coefficient. The physical and chemical "reality" of unstable particle gases is examined. It is shown that their existence implies small corrections to the equations of chemical and nuclear statistical equilibrium, as they apply to stable particle abundances.