Beth cross sections for the sodium isoelectronic sequence

Abstract

Bethe cross sections for the excitation of Na-like ions to the $3^{2}P_{\frac{1}{2}}$, $3^{2}P_{\frac{3}{2}}$, $4^{2}P_{\frac{1}{2}}$, and $4^{2}P_{\frac{3}{2}}$ states from the ground state are computed from the relativistic Hartree-Fock wave functions. As the nuclear charge is increased, excitation cross sections to the $^{2}P_{\frac{3}{2}}$ states are affected far more by relativistic effects than those to the $^{2}P_{\frac{1}{2}}$ states. The asymptotic ionization cross sections for the neutral Na atom and ${\mathrm{Fe}}^{15+}$ ion are computed from a sum rule, i.e., by subtracting the sum of discrete excitation cross sections from the total inelastic-scattering cross section obtained from the sum rule. The ionization cross sections thus obtained are ${\ensuremath{\sigma}}_{\mathrm{ion}}(\mathrm{Na})={\ensuremath{\beta}}^{\ensuremath{-}2}(2.51{\mathrm{ln}[\frac{{\ensuremath{\beta}}^{2}}{(1\ensuremath{-}{\ensuremath{\beta}}^{2})}]\ensuremath{-}{\ensuremath{\beta}}^{2}}+ 26.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20} {\mathrm{cm}}^{2},$ ${\ensuremath{\sigma}}_{\mathrm{ion}}({\mathrm{Fe}}^{15+})={\ensuremath{\beta}}^{\ensuremath{-}2}(0.209 {\mathrm{ln}[\frac{{\ensuremath{\beta}}^{2}}{(1\ensuremath{-}{\ensuremath{\beta}}^{2})}]\ensuremath{-}{\ensuremath{\beta}}^{2}}+1.64)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20} {\mathrm{cm}}^{2},$ where $\ensuremath{\beta}$ is the incident electron or proton speed divided by that of light. The cross section for Na is in agreement with that calculated by McGuire, but not with the electron-impact experiment by McFarland and Kinney. The ionization cross section for ${\mathrm{Fe}}^{15+}$ is a factor of 2 to 3 larger than the Coulomb-Born results by Rudge and Schwartz and by Bely in the asymptotic region.