Theoretical Continuous X-Ray Energy and Polarization

Abstract

By the theory of Sommerfeld, relativity effects and retardation of potential being neglected, matrix elements and associated components of continuous spectrum x-radiation are computed for a variety of electron-nucleus collisions and for a distributed series of positions in the spectrum. The calculations cover values of $\frac{V}{{Z}^{2}}$ from 0.06128 to 3.356, where $Z$ is the atomic number of the nucleus, and $V$ is the bombardment potential in electrostatic units. Accuracy of calculation is 1 percent. Screening is neglected except at the long wave limit of the spectra where it is taken into account by Sauter's method. Empirical algebraic formulas are found which closely represent the rigorously calculated results. Intensity and polarization predictions for any direction of emission and any excitation conditions within the range of applicability of the theory may be readily drawn from the computed results. Elwert's proposed correction factor for rectifying the approximate spectral intensities of Sommerfeld and Maue is found effective within the limits of its restricting assumptions. Theoretical efficiencies of continuous x-ray production are calculated by combining theoretical intensities with known rates of electron energy loss in traversing matter. Thick target efficiency (a ratio, not percent) is given by $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}Z$ kv. Thin target efficiency is found to be approximately twice the thick target efficiency for any given $Z$ and kv.