Time-dependent distortion in calculations of K-shell ionization for incident protons and helium and lithium ions

Time-dependent distortion of the initial electronic state in response to the motion of the projectile is employed in calculations of total and differential cross sections for the direct-Coulomb, {ital K}-shell-ionization process within the semiclassical approximation. Selected targets are chosen from Al through Ag for incident protons and helium and lithium ions in the velocity region that corresponds to energies of 0.175 through 5.0 MeV/u for a Cu target. The distortion is taken to include both energy and wave function (via polarization) of the initial-state {ital K}-shell electron. Discussion is presented with regard to the appearance of nonorthogonal basis states. The results of calculations for the total {ital K}-shell-ionization cross section in comparison with experimental data show good agreement for protons incident on targets from Ti through Cu. Some differences are noted for Al and Ag targets, and systematically larger discrepancies with projectile atomic number are obtained for He and Li projectiles. It is found that the introduction of temporally dependent distortion causes drastic changes in the behavior of the scattering amplitude at low velocities that have not been generally appreciated. Time-dependent binding gives rise to a large suppression of the cross section (over that induced by the well-known introduction of a constant increase in binding), while time-dependent polarization leads to a large enhancement. An explanation of this behavior is suggested. Possible causes of the differences between theoretical and experimental values of the cross section are considered. Some observations apropos of the introduction of temporally dependent quantities in approximate calculations are made.