Problem 6.7

A particle with kinetic energy \(T\) is deflected by a spherical potential well of radius \(R\) and depth \(U_{0},\) i.e. by the field in which the potential energy of the particle takes the form \[ U=\left\{\begin{aligned} 0 & \text { for } r>R \\ -U_{0} & \text { for } r<R, \end{aligned}\right. \] where \(r\) is the distance from the centre of the well. Find the relationship between the aiming parameter \(b\) of the particle and the angle \(\theta\) through which it deflects from the initial motion direction.