[en] The theory of inner-shell Coulomb ionization by heavy charged particles, of atomic number small compared to the target atomic number, is developed through the extension of work by Brandt and his coworkers for K shells to L shells. In slow collisions relative to the characteristic times of the inner shell electrons, the quantum-mechanical predictions in the plane-wave Born approximation (PWBA) can exceed experimental cross sections by orders of magnitude. The effects of the perturbation of the atom by and the Coulomb deflection of the particle during collisions are included in the theory. The perturbed atomic states amount to a binding of the inner-shell electrons to the moving particle in slow collisions, and to a polarization of the inner shells by the particle passing at large impact parameters during nonadiabatic collisions. These effects, not contained in the PWBA, are treated in the framework of the perturbed stationary state (PSS) theory for slow collisions and in terms of the harmonic oscillator model of Ashley, Brandt, and Ritchie for stopping powers in fast collisions. The effect of the Coulomb deflection of the particle in the field of the target nucleus on the cross sections is incorporated in the semiclassical approximation of Bang and Hansteen. Except for the lightest target atoms, the contribution of electron capture by the particles to inner-shell ionizations is shown to be negligible. The theory as developed earlier for the K shell, and here for L shells, agrees well with the vast body of experimental data on inner-shell Coulomb ionization by heavy charged particles

[en] Throughout all these workshops and again at this conference, the effective charge has been utilized to analyze stopping power data. How does Z₁/sup *//Z₁ apply in explanation of quantities relevant to our understanding of penetration of charged particles through matter, but other than stopping powers? The quantity that I would like to consider is the inner-shell ionization cross section. I will restrict myself to K-shell x-ray production cross sections by H and He ions because these comprise the data base that I have. This data base was gathered from the literature for another project and it consists of circa 6600 cross sections. 5 figs

[en] Theories for electron capture from inner shells by fully stripped ions are compared with experiments for K-shell vacancy production. The recently developed theory goes beyond the Oppenheimer-Brinkman-Kramers (OBK) approximation since it accounts for the perturbed stationary-state (PSS) and relativistic (R) effects in the description of inner shells as well as for the Coulomb (C)-deflection of the projectile ions; at high velocities of these ions, the theory merges with the second Born approximation. Agreement with a vast amount of data is obtained without introduction of semiempirical scaling factors. The scheme of calculations, which are cast in terms of the OBK cross sections of Nikolaev only for convenience, is presented through a sample evaluation of electron capture cross sections

[en] L subshell ionisation cross section of Au induced by 8-15 MeV Si^2+,3+,4+ ions have been measured. The data are compared with the theoretical predictions of the ECPSSR, and efficacy of incorporating the intra shell (IS) coupling into ECPSSR is examined. The effect of simultaneous multiple ionisation on the data is discussed qualitatively

[en] The influence of the energy loss of slow projectiles during inelastic collisions on the inner-shell ionization cross sections is treated analytically. The result agrees with available experimental cross sections for K-shell ionization by protons. Residual trends in the data may gauge the quality of wave functions employed in calculations of Coulomb ionization cross sections

[en] The low-velocity stopping power formula of Lindhard and Scharff (1961) was rederived; when scaled with a different definition of the TF unit of length for the projectile-target quasimolecule, it agreed with the semiempirical fits of Andersen and Ziegler (1977) up to v₁ = 2/3 - the agreement was no worse than seen in previous comparisons of these fits with the calculations of Echenique et al. (1981, 1986). Bethe's high-velocity stopping power was employed with a semitheoretical function for the average ionization potential - this function was constructed to equal 15 eV for hydrogen. The Andersen-Ziegler fits were found to converge to this high-velocity formula; measurements with GeV-protons stopped in the lightest targets are needed to verify the universal utility of Bethe' stopping power in the high-velocity limit. Further work in progress will search for an expedient but more justified (if not simpler) L for all proton velocities

[en] When Z¹ << Z², inner-shell ionization of a target atom of atomic number Z² by a projectile of atomic number Z¹ occurs predominately via removal of an inner-shell electron to the target atom continuum (direct ionization). Electron capture contributes then insignificantly to the ionization, and thus the predictions of perturbativein-Z¹/Z² theories of direct ionization can be tested through comparison with measured ionization cross sections. We present such a comparison with the recently reported data for K-shell ionization of the Z²=22, 26, 28, and 30 elements by 60-150 keV protons (Z¹=1). These ionization cross sections were inferred from x-ray production measurements using Krause's fluorescence yields

[en] Experimental cross sections for K-shell x-ray production by hydrogen and helium ions (Z₁ = 1,2) in target atoms from beryllium to uranium (Z₂ = 4--92 ) are tabulated as compiled (7418 cross sections) from the literature (161 references were found) with the search for the data terminated in January 1988. These cross sections are compared with predictions of the first Born approximation and ECPSSR theory for inner-shell ionization. The ECPSSR accounts for the energy loss (E) and Coulomb deflection (C) of the projectile ion as well as for the perturbed stationary state (PSS) and relativistic (R) nature of the target's inner-shell electron.While the first Born approximation generally overestimates the data by orders of magnitude, the ECPSSR theory is confirmed to be, on the average, in agreement with the experiment to within 10%--20%. For light and heavy target atoms, however, systematic and opposite deviations are found in the low projectile-velocity regime. These deviations are associated with the influence of multiple outer-shell ionizations on the fluorescence yields of light elements, particularly in ionization by helium ions, and with the inaccuracy of the ECPSSR theory in the reproduction of relativistic calculations for ionization of heavy elements. The remaining discrepancies at moderate projectile velocities are prima facie attributed to inadequacies of a screened hydrogenic description for the K-shell electron

[en] The Coulomb-deflection factor, defined as the ratio of the Coulomb to plane-wave Born cross sections, is derived for slow but classically moving ions, and found to be in agreement with the data for K-shell ionization. When the half distance of closest approach in a head-on collision, d, is comparable to the important impact parameters (approx.1/q₀, where q₀ is the minimum momentum transfer), this factor simplifies to exp(-πdq₀) as it has been employed in the inner-shell-ionization theory. When the impact parameters are small on the scale of the projectile de Broglie wavelength, as they are in nuclear phenomena, the Coulomb-deflection factor tends to exp(-2πdq₀). An extension of our results to screened Coulomb repulsion gives good agreement with the semiclassical calculations and the data for K-shell excitation in Ne⁺-Ne collisions

[en] The repulsion between positively charged projectiles and the nucleus of target atoms gives rise to a Coulomb-deflection factor that reduces the inner-shell-ionization cross sections calculated for straight-line particle trajectories. In the monopole approximation to the repulsion, this factor depends on the function G₀(x) = [x dK/sub i/x(y)/dyVertical Bar/sub y/ = x]², where K/sub i/x is the Bessel function of imaginary order. Through identities between Bessel functions of complex order and argument we have, in this addendum to an earlier paper [W. Brandt and G. Lapicki, Phys. Rev. A 20, 465 (1979)], reduced the evaluation of G₀(x) to computed functions. Values of G₀(x) and its integrals as they appear in the theory of K- and L-shell ionizations are tabulated. The monopole approximation is compared with results based on the standard approximation G(x) = 1 which describes the experimental data