Beth cross sections for the sodium isoelectronic sequence

Bethe cross sections for the excitation of Na-like ions to the 3²P1/2, 3²P3/2, 4²P1/2, and 4²P3/2 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 ²P3/2 states are affected far more by relativistic effects than those to the ²P1/2 states. The asymptotic ionization cross sections for the neutral Na atom and Fe¹⁵⁺ 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 ${{σ}}ᵢₒₙ(Na)={{β}}^{{-}2}(2.51{ln[{{{β}}²}{(1{-}{{β}}²)}]{-}{{β}}²}+ 26.3)×{}{10}^{{-}20} {cm}²,$ ${{σ}}ᵢₒₙ({Fe}¹⁵⁺)={{β}}^{{-}2}(0.209 {ln[{{{β}}²}{(1{-}{{β}}²)}]{-}{{β}}²}+1.64)×{}{10}^{{-}20} {cm}²,$ where ${β}$ 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 Fe¹⁵⁺ is a factor of 2 to 3 larger than the Coulomb-Born results by Rudge and Schwartz and by Bely in the asymptotic region.