Classical Mechanics (Kibble & Berkshire) · Problem 10.18

The angular momentum principle — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · collisions

Problem

Equal masses Show that, when the particles are of equal mass, the elastic scattering formulae take the simple form

\theta_1 = \tfrac{1}{2}\psi \qquad \theta_2 = \tfrac{1}{2}\pi - \tfrac{1}{2}\psi \qquad \theta = \tfrac{1}{2}\pi \qquad \frac{E_1}{E_0} = \cos^2\tfrac{1}{2}\psi \qquad \frac{E_2}{E_0} = \sin^2\tfrac{1}{2}\psi

where

\psi

is the scattering angle in the ZM frame. In the scattering of neutrons of energy

E

by neutrons at rest, in what directions should the experimenter look to find neutrons of energy

\frac{1}{4}E

? What other energies would be observed in these directions?