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 \(\left(\theta<\frac{\pi}{2}\right)\).