Note on the Quantum Theory of the Unmodified Line in the Compton Effect

Abstract

Disappearance of the unmodified line.—According to the theory developed in two previous papers (Phys. Rev. 25, 314 and 723) it is shown that the unmodified line should disappear at a scattering angle $\phi$ given by vers $\phi =(3+2\mathrm{}\surd 2)\left(\frac{{{\lambda }_0}^2}{{\lambda }_s}\right)\left(\frac{\mathrm{mc}}{h}\right)$ where ${\lambda }_0$ is the wave-length of the primary x-rays and ${\lambda }_s$ the K critical absorption wave-length of the scattering substance. This formula shows that there is an unmodified line for all values of $\phi$ when Mo $\mathrm{K}\alpha$ rays are scattered by carbon and heavier elements, but when scattered by boron and lithium this line should disappear at 147° and 60° respectively. Ratio of the energies in the modified and unmodified lines.—The theory of the previous papers gives the ratio of the number of electrons in orbital positions $U$ such as to scatter unmodified rays in a direction $\phi$ to the number of electrons in orbital positions $M$ such as to scatter modified rays. A formula for the ratio of the probability of an electron scattering when in the $U$ position to that when in the $M$ position is given together with a simpler method for calculating the number of electrons in the $M$ position to the number in the $U$ and $M$ positions for elliptic orbits.