The Polarization Factor in X-Ray Reflection

Abstract

The polarization factor for the reflection of polarized x-ray radiation. An x-ray beam consisting of a multiplicity of superposed polarized radiations with non-coincident planes of polarization will exhibit the same scattering distribution in a plane normal to the beam as will a beam consisting of two plane polarized components, suitably intense, whose planes of polarization are mutually perpendicular. The customary polarization factor $\frac{1}{2}(1+{cos}^{2}2\theta )$ does not apply to reflection of polarized radiation and should be replaced by $\frac{{sin}^2\alpha +P{cos}^2\alpha +(P{sin}^2\alpha +{cos}^2\alpha ){cos}^{2}2\theta }{1+P}$ In this quantity $P$ is the primary polarization ratio and $\alpha$ is an angle defining the orientation of the tube with respect to the plane of reflection. For the orientation most often employed the new polarization factor reduces to $\frac{(P+{cos}^{2}2\theta )}{\mathrm{}(1+P)\mathrm{}}$. Radiation from a tube so oriented that $\alpha$ is 45° will be reflected with the same intensity as an equally intense unpolarized radiation, the polarization factor assuming the familiar form $\frac{1}{2}(1+{cos}^{2}2\theta )$. This orientation is recommended for future investigations, since it necessitates no knowledge of the primary polarization. A new method for measuring the polarization of homogeneous x-rays is presented.