AtomicL-shell ionization by protons: Dirac-Hartree-Slater calculation of cross sections

Coulomb ionization of the $L$ subshells of Au and U by slow protons has been calculated in the relativistic plane-wave Born approximation (PWBA), with Dirac-Hartree-Slater (DHS) wave functions. Semiclassical corrections for binding-energy change and Coulomb deflection are applied as developed by Brandt and Lapicki. Considerable improvement is attained in these ab initio relativistic PWBA calculations with DHS wave functions, as compared with earlier classical, semiclassical, and PWBA results based on screened hydrogenic wave functions. The predicted subshell ionization cross sections agree well with experimental data. The effect of relativity tends to cancel partially the effects of binding and Coulomb deflection. The calcualted energies at which minima occur in $\frac{{\sigma }_{L_1}}{{\sigma }_{L_2}}$ and $\frac{{\sigma }_{L_3}}{{\sigma }_{L_2}}$ cross-section ratios also agree well with observation. Predicted total $L$ x-ray-production cross sections agree extremely well with experiment. The $\frac{L\alpha }{L\gamma }$ and $\frac{L\alpha }{L\beta }$ x-ray emission rates for $p$+Au agree with measurements if $L$ fluorescence and Coster-Kronig yields are adjusted in accordance with recent relativistic theory.