Hertzian Dipole Radiation via the Weizsacker-Williams Model

This problem is a continuation of an earlier note on the Weizsäcker-Williams method [1]. The basic idea of the method is that if a rapidly moving electron is sufficiently perturbed, it will emit α = e/h̄c photons per unit bandwidth during per formation time t0, where the latter is the time it takes for the radiation to pull one wavelength ahead of the charge. Thus, the photon number spectrum of the radiation is