Classical Dynamics of Particles and Systems · Problem 9-50

Motion in a Noninertial Reference Frame — Marion & Thornton

Physics — Mechanics · scattering-cross-section

Problem

A fixed force center scatters a particle of mass

m

according to the force law

F(r) = k/r^3

. If the initial velocity of the particle is

u_0

, show that the differential scattering cross section is

\sigma(\theta) = \frac{k\pi^2(\pi - \theta)}{mu_0^2\theta^2(2\pi - \theta)^2\sin\theta}