Problem 6.8

A stationary ball of radius $R$ is irradiated by a parallel stream of particles whose radius is $r$. Assuming the collision of a particle and the ball to be elastic, find: (a) the deflection angle $\theta$ of a particle as a function of its aiming parameter b; (b) the fraction of particles which after a collision with the ball are scattered into the angular interval between $\theta$ and $\theta+d \theta$ (c) the probability of a particle to be deflected, after a collision with the ball, into the front hemisphere $\left(\theta<\frac{\pi}{2}\right)$.