Theory of the Intensity of Scattered X-Rays

Abstract

The writer's theory of the unmodified line in the Compton Effect (Phys. Rev., 25, 314, 1925) has recently been extended by Williams (Phil. Mag. 2, 657, 1926) and the writer (Phys. Rev., 29, 206, 1927) to the case of reflection of x-rays by crystals. Both these writers assume that it is only the $U$ electrons (i.e. the electrons associated with unmodified scattering, see Phys. Rev., 26, 433, 1925) which take part in crystal reflection. In the present paper it is supposed that the $U$ electrons in a given atom scatter coherently and also according to the classical theory, so that, if $N_U$ is the number of $U$ electrons in the atom, the intensity of the x-rays scattered in a given direction is ${N_U}^2$ times the intensity scattered by a single free electron in the same direction according to Thomson's theory. In previous papers it has been assumed that the intensity of unmodified scattering is proportional to $N_U$. Now, however, because of the above assumptions, it is proportional to ${N_U}^2$. In modified scattering it is assumed that the $S$ electrons (i.e. the electrons associated with modified scattering)scatter incoherently and according tothe quantum theories of Compton,Jauncey and Breit. The modified scattering, as in previous papers, is,therefore,proportional to $N^S$, the number of $S$ electrons in the atom. Formulas are obtained for the energy of the total (i.e. unmodified plus modified) scattering coefficient and for the ratio of the modified to the total scattering coefficient in terms of the angle of scattering, the primary wave-length and the critical absorption wave-lengths of the scatterer. The theory seems to work equally well for heavy as for light elements and explains the phenomenon of excess scattering.