The Spatial Distribution of Photoelectrons

The perturbation of a hydrogen-like atom by a plane polarized electromagnetic wave is considered on the basis of Dirac's equation, and perturbed wave functions are obtained. These functions lead by a method similar to that used by Sommerfeld in his "Wellenmechanisches Ergänzungsband" to a formula for the spatial distribution of the photoelectrons. To the first approximation this formula differs from that given by a factor 5/9 in the second term. The angle between the average direction of the emission of the photoelectrons and the electric vector of the incident wave appears therefore to be equal to $\frac{h\nu }{\mathrm{cmv}}$ instead of the value $\left(\frac{9}{5}\right)\left(\frac{h\nu }{\mathrm{cmv}}\right)$ given. The factor 5/9 follows from the consideration of the normalizing factors for the spherical harmonics, which were not introduced by Sommerfeld. A second approximation has also been obtained showing the influence of electron spin. This approximation differs from that obtained by Carrelli in that the spin and some other terms not considered by Carrelli and also the factor 5/9 appear.