Thermodynamics, Statistical Physics, and Quantum Mechanics

320 SOLUTIONS

5.68 Rayleigh Scattering (Tennessee)

a) The formula for the total cross section is

We write where is the solid angle. The differential

cross section is obtained by taking a functional derivative with respect to

There remains only the integral, which is eliminated by the delta

function for energy conservation:

where the vector differs from only in direction.

b) With the assigned choice of the matrix element we write our differential

cross section as

where the factor S is the average over initial polarizations and the sum
over final polarizations. There are two possible polarizations, and both are
perpendicular to the direction of the photon. These averages take the form

The factor 1/2 is from the average over initial polarization. The angle is
between the directions of and