Approach to chemical equilibrium in thermal models

The experimentally measured $\frac{({\mu }^{-},\mathrm{charged}\mathrm{particle})}{({\mu }^{-},\mathrm{n})}$ and ($\frac{\mathrm{p},\mathrm{n}}{\mathrm{p},{\mathrm{p}}^{\prime }}$) ratios for the emission of energetic nucleons are used to estimate the time evolution of a system of secondary nucleons produced in a direct interaction of a projectile or captured muon. The values of these ratios indicate that chemical equilibrium is not achieved among the secondary nucleons in noncomposite induced reactions, and this restricts the time scale for the emission of energetic nucleons to be about 0.7 × ${10}^{-23\mathrm{}}$ sec. It is shown that the reason why thermal equilibrium can be reached so rapidly for a particular nucleon species is that the sum of the particle spectra produced in multiple direct reactions looks surprisingly thermal. The rate equations used to estimate the reaction times for muon and nucleon induced reactions are then applied to heavy ion collisions, and it is shown that chemical equilibrium can be reached more rapidly, as one would expect.