Classical Mechanics (Kibble & Berkshire) · Problem 7.15

Non-linear oscillations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · scattering

Problem

A uniform flux of particles, each of mass

m

and speed

V

, is incident upon a fixed scatterer that exerts the repulsive radial force

\boldsymbol{F} = (m\gamma^2/r^3)\hat{\boldsymbol{r}}

. Find the impact parameter

p

as a function of the scattering angle

\theta

, and deduce the differential scattering cross section. Find the total back-scattering cross-section.