The Scattering of X-rays by Gases and Crystals

It is shown that, in exact agreement with the wave mechanical result worked out by Wentzel and Waller and Hartree, the Raman-Compton-Jauncey formula for the scattering of x-rays by an atom deduced on the basis of classical electrodynamics may be written $I_{\phi }=I_e\left\{F^2+Z-\Sigma \stackrel{z}{r=1\mathrm{}}{E_r}^2\right\},$ where $I_{\phi }$ is the intensity scattered in a direction $\phi$ with the primary beam, $I_e$ is the scattering from a single isolated electron as calculated by Thomson, $Z$ is the atomic number, $E_r$ is the average amplitude of the waves scattered by the $r-\mathrm{t}\mathrm{h}$ electron in the atom and $F$ is the true atomic structure factor as given by $F={{\Sigma }_1}^z{E}_r$. This shows that the coherent scattering is proportional to $F^2$ and that the introduction of the average atomic structure factor $F^{\prime }$ by Jauncey is unnecessary. On the basis of Eq. ($A$), theoretical formulas for the scattering of x-rays by gases and crystals are redeveloped and the results turn out to explain all the disagreement between theories proposed by Jauncey and the writer.