Electron Capture and Loss Cross Sections for Protons Passing through Air

Abstract

Measurements have been made of the electron-loss cross section ${\ensuremath{\sigma}}_{1}$ and the electron-capture cross section ${\ensuremath{\sigma}}_{c}$ for hydrogen beams in air. ${\ensuremath{\sigma}}_{1}$ varied from 24.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 40.8 kv to 13.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 325 kv. ${\ensuremath{\sigma}}_{c}$ varied from 20.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 31.4 kv to 2.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 122 kv. In the ranges quoted, the cross sections were well represented by the formulas, ${\ensuremath{\sigma}}_{1}=(24.54\ensuremath{-}\frac{0.866E}{{E}_{0}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}{\mathrm{cm}}^{2}$ ${\ensuremath{\sigma}}_{c}=[41.4\mathrm{exp}(\ensuremath{-}\frac{0.562E}{{E}_{0}})]\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}{\mathrm{cm}}^{2}$ where ${E}_{0}=24.8$ kv, the energy of a proton having the velocity $\frac{{e}^{2}}{\ensuremath{\hbar}}$. By extrapolation of the data, ${\ensuremath{\sigma}}_{1}$ was found to equal ${\ensuremath{\sigma}}_{c}$ at energy ${E}_{0}$.