A one-parameter, polarized, variational wave function, correlated to a projectile, is described and used as the initial state in calculations of inner-shell excitation probabilities and ionization cross sections for collisions with heavy charged particles. The Rayleigh-Ritz variational principle is used to determine the parameter. The minimized energy gives the binding effect as a function of projectile position. Existing computer codes can be adapted to incorporate the variational wave function. Early treatments of polarization as a negative binding effect give results remarkably similar to the new ones. The new results do not show the abrupt cessation of the polarization effect caused by the use of an impact-parameter cutoff in the original description. The polarization of the wave function does not give a negative binding effect. Agreement with measured K-shell ionization cross sections is improved.

Theoretical calculations for the proton-induced K-shell ionization probability in which the ground-state electron wave function is allowed to be polarized under the influence of the incident projectile are described. These calculations extend the results of a previous theoretical model in which the wave function is allowed only a spherically symmetric distortion. The model is based upon lowest-ord...

The excitation of electronic transitions in matter by a group of swift ions traveling close together and at nearly the same velocity may depend on the spatial configuration of ions making up the cluster. We have studied theoretically the effect of configuration on the interactions of clusters with an electron gas and in collision with single atoms (vicinage effect). The latter case is explored with a classical harmonic-oscillator model and with quantum-mechanical perturbation theory. We discuss similarities between the vicinage function for energy loss of a swift cluster in an electron gas and that for the same cluster colliding with a system of noninteracting atoms at condensed-matter density. The aligning effect of the wake potential on the trailing ion of a discluster penetrating a solid target, as first observed by Gemmell et al., is not expected to occur in cluster collisions with single atoms, and does not occur in collisions with gases at ordinary pressures. Aligning forces comparable with those in solids require target densities of the same order of magnitude as those occurring in condensed matter. The data of Lurio, Anderson, and Feldman taken in a search for vicinage effects in inner-shell excitation are discussed. The effect of wake fluctuations on cluster energy loss is shown to be negligible under ordinary conditions. We evaluate the effect of residual molecular ionic structure on cluster energy loss.

K-shell x-ray production measurements are reported for protons, deuterons and alpha particles incident on thin foils of copper, niobium, silver and antimony. In the velocity range of the experiments, which correspond to 100-600 keV/u, the energy of ionization was as large as 10% of the bombarding energy. The inferred dependence of the excitation process on the projectile mass, atomic number and energy is compared with theoretical estimates of a low-velocity ionization threshold, the binding effect and the Coulomb-deflection effect. Precision of measurement is not great enough to discern unambiguously the threshold effect, but the binding and Coulomb-deflection effects are clearly distingui shed.

Expressions are derived using the semiclassical Coulomb approximation for probabilities for $2s\ensuremath{-}2p$ excitation during a collision between a target atom and a proton. Results of calculations are presented. For proton energies above 1 MeV the transition probabilities are less than \ensuremath{\sim}0.03. Unlike excitation from one atomic shell to another, our intrashell results are largely independent of the target atomic charge ${Z}_{2}$ and binding-energy difference $\ensuremath{\Delta}{E}_{2s2p}$. The shapes of our impact-parameter distributions, when scaled to the atomic radius, are similar for various targets. However, for a given target, the dependence of the $m=0$ and $m=\ifmmode\pm\else\textpm\fi{}1$ amplitudes on both impact parameter $B$ and $\ensuremath{\Delta}{E/}_{2s2p}$ is quite different, indicating that the polarization of light emitted in subsequent $2p\ensuremath{-}1s$ transitions may vary with both $B$ and $\ensuremath{\Delta}{E}_{2s2p}$. Furthermore, near $B=0$ the probabilities are sensitive to $\ensuremath{\Delta}{E}_{2s2p}$, which varies with the charge state of the target atom. Consequently, the authors suggest that dependences of collision cross sections and probabilities on the atomic charge state may be investigated by considering impact-parameter dependence or polarization fractions in $2s\ensuremath{-}2p$ atomic excitation by ion impact.

Results of calculations performed in the plane-wave Born approximation for the atomic states of the M-shell are presented in the form of the excitation function I31(η,W), the universal function F31(η/θ2,θ), and the direct Coulomb ionization cross sections. A description of vacancy filling leading to x-ray production cross sections from incident carbon ions on 79Au, 82Pb, and 83Bi are compared with...

The dependence of the direct ionization cross section on a single scaled velocity variable makes ionization of a given subshell a universal phenomenon common to all particle-atom Coulomb ionization collisions. Constructing universal plots of a wide range of data has led to a refined description of the direct Coulomb ionization process. The sources of this universality lie in the PWBA, the lower limit of the momentum transfer and a description of the atomic states which has a scaling length. Universality is exact in the low velocity limit but the cross section develops a parametric dependence on the target binding energy as velocity increases. This dependence is usually ignored, but for some cases it is significant.

Experimental $K$-shell ionization cross sections of $_{13}\mathrm{Al}$ and $_{28}\mathrm{Ni}$ are reported for ions of $_{1}^{1}\mathrm{H}$, $_{1}^{2}\mathrm{H}$, $_{2}^{4}\mathrm{He}$, $_{3}^{6}\mathrm{Li}$, and $_{3}^{7}\mathrm{Li}$ with kinetic energies in the range from 2 to 36 MeV, and of $_{28}\mathrm{Ni}$ for ions of $_{6}^{12}\mathrm{C}$, $_{8}^{16}\mathrm{O}$, and $_{9}^{19}\mathrm{F}$ in the range from 4 to 90 MeV. The theory of direct Coulomb $K$-shell ionization, as developed in an earlier paper [Phys. Rev. A 7, 983 (1973)] for projectiles of atomic number ${Z}_{1}$, small compared to the target atomic number ${Z}_{2}$, and of velocities ${v}_{1}$ small compared to the target $K$-shell electron velocity ${v}_{2K}$, i.e., ${v}_{1}\ensuremath{\ll}{v}_{2K}$, is extended to intermediate velocities ${v}_{1}\ensuremath{\simeq}{v}_{2K}$. New effects appear. They add to the ${Z}_{1}^{2}$-proportional cross sections one derives from linear-response theories for direct ionizations. They are attributed to the polarization of the target $K$ shell in the field of the projectile, and to electron capture by the projectile. Guided by the perturbed stationary-state theory of atomic collisions, the polarization effects are incorporated so that the theory retains the unifying aspects of the cross sections derived in the plane-wave Born approximation, but the variables now contain the nonlinear effects as scaling factors. Electron-capture cross sections are added. When ${v}_{1}\ensuremath{\gg}{v}_{2K}$, such contributions subside, and one retrieves the cross sections of the linear-response approximation. The theory predicts $K$-shell ionization cross sections for projectiles with $\frac{{Z}_{1}}{{Z}_{2}}<0.5$ at all velocities in a comprehensive manner. It agrees with experimental data covering six orders of magnitude for collisions partners with $\frac{{Z}_{1}}{{Z}_{2}}$ ranging from 0.03 to 0.3 and $\frac{{v}_{1}}{{v}_{2K}}$ from 0.07 to 2.