Numerical Calculations of the Reflection of Electrons by Metals

The specular reflection of electrons by metallic surfaces is considered. It is assumed that the potential energy of an electron is constant ($=-V_0$) in the interior of the metal, and account is taken of the image force acting on an electron outside the metal (Nordheim's problem). The reflection coefficient $R$ is computed for the range of values of $V_0$ which is of interest in connection with real metals, and for the range of values of energy of the electrons in which $R$ has appreciable values. In the Appendix there are given some values of the function $\frac{{\Gamma }^{\prime }\mathrm{}\left(\mathrm{iy}\right)\mathrm{}}{\Gamma \mathrm{}\left(\mathrm{iy}\right)\mathrm{}}$, for real values of $y$, which were computed incidentally.