Classical Electrodynamics · Problem 15.3

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · bremsstrahlung-hard-sphere-relativistic

Problem

Treat Problem 15.2 without the assumption of nonrelativistic motion, using (15.2) and assuming the elastic impact is of negligible duration. Show that the cross section for photon emission is now d2σdΩ d(ℏω)=R24πe2ℏcβ2ℏω[sin⁡2θ(1−βcos⁡θ)2+1β3ln⁡(1+β1−β)−2β2]\frac{d^2\sigma}{d\Omega\, d(\hbar\omega)} = \frac{R^2}{4\pi}\frac{e^2}{\hbar c}\frac{\beta^2}{\hbar\omega}\left[\frac{\sin^2\theta}{(1-\beta\cos\theta)^2} + \frac{1}{\beta^3}\ln\left(\frac{1+\beta}{1-\beta}\right) - \frac{2}{\beta^2}\right]

Browse the problem library