Total Cross Sections for Inelastic Scattering of Charged Particles by Atoms and Molecules. IV. Positive Lithium Ion

Abstract

The Born cross sections for several important discrete excitations of ${\mathrm{Li}}^{+}$ from its ground state have been calculated with correlated wave functions. By extrapolation, cross sections for higher excitations have also been determined. Subtraction of the sum ${\ensuremath{\sigma}}_{\mathrm{ex}}$ of these excitation cross sections from the total inelastic-scattering cross section ${\ensuremath{\sigma}}_{\mathrm{tot}}$ obtained through a sum rule for the Bethe cross sections yields a reliable counting ionization cross section ${\ensuremath{\sigma}}_{i}$. The cross sections thus obtained are ${\ensuremath{\sigma}}_{\mathrm{tot}}={(\frac{z}{\ensuremath{\beta}})}^{2}(0.536{\mathrm{ln}[\frac{{\ensuremath{\beta}}^{2}}{(1\ensuremath{-}{\ensuremath{\beta}}^{2})}]\ensuremath{-}{\ensuremath{\beta}}^{2}}+5.216\ifmmode\pm\else\textpm\fi{}0.002)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ ${\ensuremath{\sigma}}_{\mathrm{ex}}={(\frac{z}{\ensuremath{\beta}})}^{2}(0.265{\mathrm{ln}[\frac{{\ensuremath{\beta}}^{2}}{(1\ensuremath{-}{\ensuremath{\beta}}^{2})}]\ensuremath{-}{\ensuremath{\beta}}^{2}}+2.295\ifmmode\pm\else\textpm\fi{}0.002)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ and ${\ensuremath{\sigma}}_{i}={(\frac{z}{\ensuremath{\beta}})}^{2}(0.271{\mathrm{ln}[\frac{{\ensuremath{\beta}}^{2}}{(1\ensuremath{-}{\ensuremath{\beta}}^{2})}]\ensuremath{-}{\ensuremath{\beta}}^{2}}+2.921\ifmmode\pm\else\textpm\fi{}0.004)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}$ where $\mathrm{ze}$ is the charge of the incident particle and $\ensuremath{\beta}$ is its velocity divided by that of light. The ionization cross section is in excellent agreement with experimental data in the asymptotic region (incident electron energy \ensuremath{\gtrsim} 5 keV).