I am modelling the scattering of hydrogen atoms against each other.
In this model, one hard sphere scatters elastically off another hard sphere, they are identical with radius $r$. They meet with impact parameter $b$ and $b<r$. They scatter with angle $\theta$ and we have $b=R \cos \frac{\theta}{2}$.
If the impact parameter $b$ is a uniformly-distributed random variable, what is the distribution of $\theta$?