A General Quantum Theory of the Wave-Length of Scattered X-rays

Corpuscular quantum theory of the scattering of x-rays.—The theory previously presented gave for the change of wave-length due to scattering, assuming each quantum scattered by a single free electron, $\delta {\lambda }_F=\left(\frac{h}{\mathrm{mc}}\right) \mathrm{vers} \varphi =.\mathrm{}0242\mathrm{} \mathrm{vers} \varphi$, where $\varphi$ is the angle between the primary and scattered ray. This theory is now extended to scattering by bound electrons. If the scattering electron is not ejected from the atom, no energy is transferred and no change of wave-length occurs; but if the electron is removed, the change of wave-length must lie between $\delta {\lambda }_B={\lambda }^2({\lambda }_s-\lambda )$ and $\infty$, where $\lambda$ is the incident wave-length and ${\lambda }_s$ the critical ionization wave-length for the scattering electron in its original orbit. If we restrict the theory by assuming that the final momentum possessed by the residual atom is that acquired during the absorption from the incident beam, of the energy $\frac{\mathrm{hc}}{{\lambda }_s}$ required to remove the electron from the atom, and that the electron, now free, receives the impulse resulting from the deflection of the quantum, the resulting change of wave-length is $\delta \lambda =\delta {\lambda }_B+\delta {\lambda }_F$. Comparison with experimental results shows that the restricted theory accounts satisfactorily for scattering by the lighter elements and also for the scattering of tungsten rays by Mo if for heavy elements $\delta {\lambda }_F$ is taken to be zero. Criticism of the "tertiary radiation" hypothesis, which leads to the expression $\delta \lambda ={\lambda }^2({\lambda }_s-\lambda )$, shows that it does not account for the large percentage of polarization, for the large relative intensity and for the homogeneity of the scattered x-rays.