Classical Mechanics (Kibble & Berkshire) · Problem 10.19

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

Physics — Mechanics · collisions

Problem

Use the elastic scattering formulae to express the energy of the scattered particle as a function of the scattering angle, and the energy of the recoiling particle as a function of the recoil angle, as follows: E1E0=1+γ2cos⁡2θ1+2γcos⁡θ1(1−γ2sin⁡2θ1)1/2(γ+1)2,E2E0=4γ(γ+1)2cos⁡2θ2.\frac{E_1}{E_0} = \frac{1 + \gamma^2\cos 2\theta_1 + 2\gamma\cos\theta_1\left(1-\gamma^2\sin^2\theta_1\right)^{1/2}}{(\gamma+1)^2}, \qquad \frac{E_2}{E_0} = \frac{4\gamma}{(\gamma+1)^2}\cos^2\theta_2. Make polar plots of E1/E0E_1/E_0 as a function of θ1\theta_1 for the case of neutrons scattered by the nuclei of hydrogen, deuterium, helium and carbon.

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