Question

A particle with kinetic energy T is deflected by a spherical potential well of radius R and depth U_o, i.e. by the field in which the potential energy of the particle takes the form

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 θ through which it deflects from the initial motion direction.

Answer 1

See the diagram on the next page. In the region where potential is nonzero, the kinetic energy of the particle is, by energy conservation,

T + U and the momentum of the particle has the magnitude.

On the boundary the force is radial, so the tangential component of the momentum does not change :