is probably not necessary. We care only about the probability that a nucleon-nucleon collision leads to a significant amount of energy release in the sense of conversion of initial kinetic energy to meson mass. We are essentially basing our results on the total inelastic cross section, the average meson multiplicity, kinematics, and entropy. Our analysis would be better if we had a handle on the width of the multiplicity distribution, averaged over the initial state isospin and summed over the final state isospin.

Star Burst Probabilities
========================

In this section we put together the ingredients developed in the last two and compute the number of star bursts which may become nucleation sites or seeds for plasma formation and growth.

The nucleon-nucleon collisions may be referred to as primary-primary, primary-secondary, and secondary-secondary, depending on whether the nucleons have scattered from thermalized particles in the hot zone (secondary) or not (primary). The easiest contribution to obtain is the primary-primary. All integrations and summations can be done analytically with the result $$\frac{dN^{\rm prim-prim}_{\rm in}}{ds} =
4\pi R^2 \sigma_{\rm in}(s) \left(\frac{\lambda \gamma n_0}
{w}\right)^2 \, \left[1-\left(1+w\,\frac{vt_0}{\lambda}\right)\,
\exp{\left(-\frac{vt_0}{\lambda}\right)}\right] \,
\delta (s-4E_0^2) \, .$$ The formulas for the primary-secondary and secondary-secondary contributions can be simplified to 