Quantum Theory of the Intensity of the Modified Band in the Compton Effect

Abstract

The theory of a previous paper (Phys. Rev. 25, 314, 1925), which dealt with the scattering of x-ray quanta by electrons in circular Bohr orbits, is extended to the scattering by L and M electrons and by electrons in elliptic orbits. For a certain range of positions of the electron in each orbit the mass of the whole atom is added to that of the electron and the quantum is scattered without change of wave-length. For a given type of K, L or M orbit, the ratio of the number of modified scattered quanta to that of the unmodified quanta is calculated. From this the intensity of the modified band relative to that of the unmodified line when all the K, L, and M electrons are operative in the scattering process is determined. Curves are given showing the intensity of the modified bands when Mo $\mathrm{K}\ensuremath{\alpha}$ x-rays are scattered by carbon and sulfur at 30\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{}. The theory gives for the ratio of intensity of modified band relative to unmodified.90 and 1.74 for carbon at 30\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{}, and.42 and.62 for sulfur at 30\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{}, the ratio increasing with the scattering angle and decreasing with increasing atomic number. This result tends to explain the difficulty which has been experienced in obtaining the modified band when Mo $\mathrm{K}\ensuremath{\alpha}$ x-rays are scattered by sulfur.