Lets study the rate as a function of the angle of the photon from the z axis, . The rate will be independent of the azimuthal angle. We see that the rate is proportional to . We still must sum over the two independent transverse polarizations. For clarity, assume that and the photon is therefore emitted in the x-z plane. One transverse polarization can be in the y direction. The other is in the x-z plane perpendicular to the direction of the photon. The x component is proportional to . So the rate is proportional to .
If we assume that then only the term remains and the rate is proportional to . The angular distribution then goes like .
Jim Branson 2013-04-22