the system begins its cooling stage. The depth in the hot zone to which nucleon 1 has penetrated is $d_1 = (vt+z)/2$, and the depth to which nucleon 2 has penetrated is $d_2 = (vt-z)/2$. We neglect the decrease in velocity of the nucleons as they travel through the hot zone. This is an acceptable approximation because in the end we are interested only in those nucleons which suffer a small energy loss in traversing the hot matter.

We construct the phase space distribution as follows:

> $H(x,N)$ = probability that the nucleon has momentum fraction $x$ after making N collisions;\
> $S(N,d)$ = probability that the nucleon has made $N$ collisions after penetrating to a depth $d$;\
> $\sum_{N=0}^{\infty} H(x,N) S(N,d)$ = probability that the nucleon has momentum fraction $x$ after penetrating to a depth $d$.

The distribution functions are normalized to unity. $$\begin{aligned}
\int_{0}^{1} \frac{dx}{x} \, H(x,N) &=& 1 \\
\sum_{N = 0}^{\infty} \, S(N,d) &=& 1\end{aligned}$$ The phase space density of nucleon $i$ is then taken to be $$\frac{dp_{zi}}{2\,\pi} \, f_i (z,p_{iz},t) =
\gamma \, n_0 \, \frac{dx_i}{x_i} \sum_{N_i = 0}^{\infty}
\, H(x_i,N_i) \, S(N_i,d_i) \, ,$$ where $n_0$ is the average baryon density in a nucleus, 