Radiation from Slow Electrons

Abstract

We have developed expressions describing radiation emitted by an electron in the field of a neutral atom, using as a model for the latter a point charge $\mathrm{Ze}$ surrounded by a spherical shell of radius $a$ carrying a charge $-Ze$. In the introduction we formulate the physical foundations of the problem. In section I we set up expressions for the matrix components of acceleration and give methods for evaluating the integrals involved. In section II we use results of section I to compute the intensity of radiation $J_{\nu }$ and the polarization $P$. For low velocity electrons ($V{a}^2<1\mathrm{}$, where $V$ is the energy in volt-electrons and $a$ is in angstrom units) we give simple formulas for both $J_{\nu }$ and $P$. For heavier elements $J_{\nu }$ is independent of $Z$ and is nearly proportional to $V{a}^2$, while for lighter elements $J_{\nu }$ as a function of $\mathrm{Za}$ exhibits a series of striking maxima and minima. For higher velocities we give our results for the most part graphically. We find that the criterion of applicability of bare nucleus model to neutral atoms is ${\left(\frac{Z^2}{2v}\right)}^2\ll 1$. Except for high voltages however $Z$ should be less than the nuclear charge of the actual atom. We also show that the radiation from protons in the field of our model is simply related to the radiation from electrons in the field of an unscreened nucleus. In section III we discuss how $Z$ and $a$ should be chosen in order that our model, or a nuclear model, may represent an actual atom, and make comparison with experiment finding agreement in the order of magnitude. The last part of the paper is a summary containing all the formulas of importance.