Thermal equilibrium in proton induced reactions

The thermal model, which has been applied successfully to inclusive cross sections in heavy ion reactions, is applied here to the (p,p′) and ($\mathrm{p},\pi$) reactions. The thermal source temperatures and velocities determined in proton induced reactions are similar to those found in heavy ion reactions, although the temperatures are cooler in proton induced reactions. Several methods can be used to estimate the number of nucleons in the thermal source, and these are found to give roughly consistent answers. Using a classical dense gas model, an estimate is made of the lifetime of the hot source. As one might expect, the lifetime is calculated to be in the ${10}^{-23\mathrm{}}$ sec range, indicating that the hot region probably does not cleanly separate from the nucleus before it cools off. A discussion of the limiting temperature behavior observed in this analysis is also given.