A Corpuscular Quantum Theory of the Scattering of X-rays by Light Elements

Corpuscular quantum theory of the scattering of x-rays.—In A. H. Compton's recent theory of the scattering of x-rays in separate quanta, a definite change in wave-length due to scattering is predicted; but in order to calculate the intensity of the scattered beam, he reasons in a not quite rigorous manner from analogy with the Doppler effect. In the present paper it is shown that the energy removed from the primary beam is of the order of magnitude of the energy falling on a sphere of the radius of the electron. It is therefore assumed that quanta of x-rays in the form of corpuscles are deflected by the electrons according to a law of force such that for corpuscles of small momentum (low frequency quanta), the distribution of the scattered rays is that expressed by the classical theory. It is found that for corpuscles of large momentum (high frequency quanta) the scattering electron recoils on collision in such a manner that the distribution of the energy of the scattered rays is modified. Curves and formulas are given showing for different radiation frequencies the theoretical values of the total energy removed from the primary beam by scattering, the energy which reappears in the scattered beam, and the energy of recoil in the scattering electrons. The formula expressing the distribution of the scattered x-rays (Eq. 17) is similiar in form to that obtained by Compton, but gives appreciably different results for very high frequency radiation such as hard $\gamma$-rays. Comparison with experimental results for the scattering of hard $\gamma$-rays shows an agreement which is probably within experimental error, and which is as good as that obtained with Compton's equations. By slightly modifying the assumptions, however, it is possible to obtain Compton's expression exactly, or to obtain other expressions differing slightly from it.