The Mass Absorption Coefficient of theKShell According to the Dirac Relativistic Theory of the Electron

Abstract

Taking as model an atom containing two non-interacting electrons and a fixed nucleus with charge $\mathrm{Ze}$, the mass absorption coefficient is calculated by use of the proper functions of the Dirac relativistic equation. $Z$ is determined so as to make the lowest energy level agree with the experimental value determined from the K absorption edge. The numerical calculation presented difficulty because of lack of tables of complex gamma functions. The relativistic coefficient is found to be from 0 to 40 percent smaller than the non-relativistic coefficient calculated by Nishina and Rabi, the greatest difference occurring for the heavy elements and short wave-lengths; it agrees slightly worse with experiment than the non-relativistic coefficient. The difference between theory and experiment is least for the heavy atoms, as would be expected, since for the heavy atoms (large $Z$) the neglected electronic interaction-field is small in comparison with the nuclear field. The variation of the relativistic coefficient with wave-length is complicated, but in the range $\frac{1}{2}{\lambda }_k$ to ${\lambda }_k$ (${\lambda }_k=$ wave-length of $K$ absorption edge) it is more nearly linear with ${\lambda }^3$ than the non-relativistic coefficient. The importance of using the relativistic equation for heavy atoms and short x-ray wavelengths is emphasized by these results, which also show that the model chosen is too approximate, even for the heavy elements.