Surface Effect in Secondary and Photoelectric Emission

Abstract

The secondary emission yield of metals by the surface effect $\delta$ is expressed in terms of the surface photo-electric yield $y\left(\omega \right)$ for a radiation of frequency $\omega$ and angle of incidence of $invcos\frac{1}{2}\left(5^{\frac{1}{2}-1\mathrm{}}\right)$ which is about 52°. It is shown that $\delta \sim {\left(2\mathrm{}\pi \alpha E_p\right)}^{-1\mathrm{}}\int {{\omega }_1}^{{\omega }_2}\frac{y\left(\omega \right)d\omega }{\omega }$, where $E_p$ is the primary energy in atomic units, $\alpha =\frac{1}{137}$, ${\omega }_1$ is the threshold frequency, and ${\omega }_2$ depends on the energy of the primary and may be replaced by $\infty$. For a square-well potential model for a metal, $\delta \sim \frac{{10}^{-3\mathrm{}}}{E_p}$ with a relative error of order $\left(\frac{E_F}{E_p}\right)\ln \left(\frac{E_p}{E_F}\right)$, where $E_F$ is the Fermi energy.