Continuum Distorted Wave-eikonal Initial State Research Articles

Target dependence of slow electrons emitted in swift ion-atom collisions

Low-energy electron emission is studied for $3.6\ensuremath{-}\mathrm{MeV}/u$ ${\mathrm{Au}}^{53+}$ impact on Ne and Ar using the first-Born and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations. By using optimized effective potentials to represent the target atom, very good agreement is obtained between the CDW-EIS results and experiments. The comparison with the calculations using the first-Born approximation shows that the emission is very asymmetric, with a preferential emission into the forward direction. A detailed study of the emission from each initial orbital of the target atom reveals features in the spectra which can be related to the structure of the initial-state bound wave function.

ION-ATOM/NEON – Calculation of ionization cross sections by fast ion impact for neutral target atoms ranging from lithium to neon

The program presented calculates the total cross sections, and the electron energy spectra of the singly and doubly differential cross sections for the single target ionization of neutral atoms ranging from lithium up to and including neon. The code is applicable for the case of both high and low Z projectile impact in fast ion-atom collisions. The theoretical descriptions provided for the program user are based on two quantum mechanical models which have proved to be very successful in the study of ionization in ion-atom collisions. These are the continuum-distorted-wave (CDW) and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations respectively.

Strong double K-K transfer channel in near symmetric collision of Si+Ar at intermediate velocity range

We present a combined study of single and double K-K electron transfer cross sections along with the single and double K-shell ionization of Ar induced by Si projectiles in the energy range 0.9-4.0 MeV u-1. The charge-state dependence of the normal and hypersatellite x-rays was used to derive the cross sections for the one- and two-electron processes, respectively. The enhancement in the fluorescence yields due to multiple vacancies was measured from the energy shifts and intensity ratios of the characteristic x-ray lines to derive K-shell vacancy production cross sections from x-ray production cross sections. The ratio of double to single K-K transfer cross sections is found to be quite large for this nearly symmetric collision system, whereas the ratio of double to single ionization cross sections is quite small. The measured single K-K transfer cross sections are reproduced very well by the two-centre close-coupling calculations whereas the double K-K transfer data are underestimated by the theory based on the independent-electron approximation (IEA). The K-shell ionization cross sections are found to deviate strongly from the calculations based on the continuum distorted wave eikonal initial state (CDW-EIS) and ECPSSR models. The CDW-EIS calculations along with the IEA model grossly underestimate the double ionization cross sections. It is stressed that in the case of two-electron processes the independent-electron model breaks down and the possible role of correlations between K-electrons is discussed.

Local saddles and local maxima in double differential cross sections of single ionization in ion-atom collisions

The ejected-electron spectrum for H+ incident on H2 and He at 40 keV is examined experimentally and theoretically. The continuum-distorted-wave eikonal-initial-state (CDW-EIS) model is adopted to study the ionization process. Experimentally a 260 mm diameter hemispherical analyser with half-angle acceptance of 1.5° and energy resolution E/E of 0.012, is used to measure the velocity distribution of the emitted electrons. The analyser and the surrounding interaction region are double shielded against the Earth's magnetic field by use of µ-metal enclosures. The observations and calculations, for double differential cross sections (differential with respect to electron momentum and emission angle), are in very good agreement and show a spectrum dominated by a well defined electron capture to the continuum (ECC) peak although existence of saddle-point electrons at 0° is not confirmed.

Fisher information and uncertainty-like relationships in many-body systems

A Fortran 90 program is presented, namely Ion-Atom-Wave (IAW), which calculates total, single and double differential cross sections for the single ionization of atomic and molecular hydrogen-like targets and helium-like targets by both light-and-heavy-ion impact. The cross sections are evaluated within the continuum distorted-wave final-state (CDW) and the continuum distorted-wave eikonal-initial-state (CDW-EIS) approximations. IAW calculates cross sections within the wave treatment. This program extends a previously published program ION (D.S.F. Crothers and M. McCartney, Comput. Phys. Commun. 72 (1992) 288) which calculated the total, single and double differential cross sections for the ionization of hydrogen-like targets by fully stripped ions.

Electron and recoil-ion momenta in single ionization of He by protons

For single ionization of He atoms in collisions with fast protons we have measured and calculated, as a function of the scattering of the proton, differential reaction cross sections and mean values of the recoil momentum projected onto the transverse direction defined by the collision plane and the plane perpendicular to the proton impact velocity (the mean transverse momentum). The calculations were performed in the continuum distorted-wave eikonal initial-state (CDW-EIS) approximation. The partitioning, at a fixed scattering angle , of the total transverse recoil momentum into two mean transverse momenta, one carried by the free electron and the other by the remaining ion, is almost independent of the impact energy (250, 500 and 1000 keV). At the mean transverse electronic momentum goes to zero, but for the fraction rises smoothly and reaches 80% near 0.4 mrad. The present experimental cross sections and transverse recoil momenta are in good agreement with CDW-EIS results including the internuclear interaction.

Ion-Atom-Wave — Calculation of single ionization cross sections in ion—atom collisions

A Fortran 90 program is presented, namely Ion-Atom-Wave (IAW), which calculates total, single and double differential cross sections for the single ionization of atomic and molecular hydrogen-like targets and helium-like targets by both light-and-heavy-ion impact. The cross sections are evaluated within the continuum distorted-wave final-state (CDW) and the continuum distorted-wave eikonal-initial-state (CDW-EIS) approximations. IAW calculates cross sections within the wave treatment. This program extends a previously published program ION (D.S.F. Crothers and M. McCartney, Comput. Phys. Commun. 72 (1992) 288) which calculated the total, single and double differential cross sections for the ionization of hydrogen-like targets by fully stripped ions.

Triply differential cross section for ionization of multielectronic targets

The Continuum Distorted Wave-Eikonal Initial State (CDW-EIS) approach is used to calculate the Triply Differential Cross Section (TDCS) for ionization of multielectronic atomic targets in coincidence with the outgoing projectile direction and recoil momentum of the target. A generatrix state method is used to evaluate the transition amplitudes for a general initial atomic state. The structures presented in both TDCSs are compared standing out the double collision mechanisms. The results obtained in CDW-EIS approximation are compared with previous classical trajectories Monte Carlo (CTMC) calculations.

LMD — Calculation of longitudinal momentum distributions in the single ionization of helium by ion impact

A program is presented which calculates the final-state longitudinal momentum distributions of the ejected electron and recoil-ion for the single ionization of helium-like targets by both light and heavy-ion impact. The longitudinal momentum distributions are evaluated within a wave treatment. The continuum-distorted-wave (CDW) and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations are used throughout. The program considered here extends a previously published program ION (D.S.F. Crothers, M. McCartney, Comput. Phys. Commun. 72 (1992) 288) which calculated the total, singly and doubly differential cross sections for the ionization of hydrogen-like targets by fully stripped projectile ions.

Momentum distributions of ionization products in ion-atom collisions

Final state momentum distributions of the projectile, the recoil-ion, and the emitted electron in ion-atom ionizing collisions are examined. New theoretical results using the continuum distorted wave-eikonal initial state (CDW-EIS) approximation are reported for He ionization by proton impact at high and intermediate energies. The finite value at the kinematical threshold in the longitudinal recoil-ion momentum distribution is shown to be considerably enhanced at intermediate energies. The transverse recoil-ion momentum distribution is calculated by considering the internuclear interaction. At higher energies, the longitudinal and transverse electron momentum distributions clearly show the binary electron contribution. The calculations prompt for further experimental work in the field.

Longitudinal momentum distributions in single ionization of He by Ni24+ ions.

The longitudinal momentum distributions for the recoil ion and ejected electron in single ionization of He by 3.6 MeV/amu Ni24+ ions are presented using the continuum distorted-wave (CDW-CDW) model. The results are discussed in the context of recent continuum distorted-wave eikonal-initial state (CDW-EIS) calculations [Rodriguez et al., J. Phys. B. 28, L471 (1995)] and compared with available experimental data [Moshammer et al., Phys. Rev. Lett. 73, 3371 (1994)].

CDW-EIS calculations for recoil ion emission in proton—helium collisions

Single ionization of helium atoms in collision with high energy protons is treated theoretically in the continuum distorted-wave eikonal initial-state (CDW-EIS) approximation. The total $\langle $E$\_{\text{R}}\rangle $ and transverse $\langle $E$\_{\text{R}\perp}\rangle $ average He$^{+}$ recoil-ion-energies are calculated as functions of the laboratory proton scattering angle $\Theta \leq $ 2 mrad. Measurements (Dorner et al. 1989, Phys. Rev. Lett. 63, 147-150) of these average energies made for helium gas in equilibrium at 30 K are reasonably well reproduced to within a factor of two, by the CDW-EIS approximation. The CDW-EIS recoil-ion energy distributions are convoluted over a Maxwellian-Boltzmann distribution, to allow for the 30 K thermal motion of the target helium atoms in the experiment.

Angular asymmetry of low-energy electron emission in ion-atom collisions.

We show that two factors contribute to the forward-backward angular asymmetry in low-energy electron emission by ion impact: the deviation of the target potential from a pure Coulomb potential and the two-center effect. We perform calculations with various theories that include these two effects: the continuum-distorted-wave--eikonal-initial-state (CDW-EIS) and the CDW approximations based on distorted-wave perturbation theory and a close-coupling calculation using a discrete representation of the continuum. The various theories give consistent results on the asymmetry but discrepancies remain between theory and experiment. \textcopyright{} 1996 The American Physical Society.

Two-center electron emission in collisions of fast, highly charged ions with He: Experiment and theory.

Electron emission cross sections differential in energy and angle of the ejected electrons were measured in collisions of 5-MeV/{ital u} C{sup 6+}, O{sup 8+}, and Ne{sup 10+} ions on He. The experimental results deviate substantially from calculations based on the plane-wave Born approximation indicating that the ejected electrons are significantly affected by the two-center field of the target and projectile ion. The two-center effects were confirmed by comparison with results from the continuum-distorted-wave--eikonal-initial-state (CDW-EIS) approximation that has recently been improved by using Hartree-Fock-Slater wave functions for the ejected electrons. It is shown for nearly complete energy and angular ranges that the improved CDW-EIS method predicts cross sections in excellent agreement with experiment.

Search for saddle-point electrons using the continuum-distorted-wave eikonal initial-state model.

The continuum-distorted-wave eikonal initial-state (CDWEIS) model is used to study the ionization of hydrogen by protons of energy 10--500 keV. Ejected electron spectra are presented and discussed in the context of the saddle-point mechanism. The behavior of the ejected electron spectrum as the charge of the incident projectile is varied is also considered. It is concluded that within its range of validity, CDWEIS does not provide any evidence of the existence of saddle-point electrons.

Ionization of excited hydrogenlike ions by collisions with bare ions.

Total cross sections have been examined theoretically by using the continuum distorted wave--eikonal initial state (CDW-EIS) and the plane-wave Born approximations for the ionization of hydrogenlike ions in the excited states with the principal quantum number n\ensuremath{\le}5 in collisions with bare ions in the keV/amu to MeV/amu range. For the ionization of hydrogenlike ions up to ${\mathrm{C}}^{5+}$(1s) by ${\mathrm{H}}^{+}$ at low energies, the present CDW-EIS prediction is in good accord with close-coupling calculation, while the Born prediction leads to a considerable overestimate. A comparison is made between the present results and other theoretical predictions as well as experimental measurements.

Comment on ionisation of the first excited state of hydrogen by ion impact using the continuum distorted wave eikonal initial state approximation

The continuum distorted wave eikonal initial state (CDWEIS) approximation is used to study the ionisation of hydrogen in it's first excited state by proton and antiproton impact in the energy range 10–1000 keV. The total cross sections presented are found to be in disagreement with similar CDWEIS calculations by Fainstein, Ponce and Rivarola [6]. It is concluded that Fainstein et al. have erroneously included a constant multiplicative factor (of 2) in their calculations.

CDW-EIS theory of ionization by ion impact with Hartree-Fock description of the target

We have carried out a generalization of the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approximation for ion-impact single ionization where the interaction of the active electron with the target is represented by a Hartree-Fock potential. We apply this model to the ionization of He, Ne and Ar by proton and multiply-charged bare-ion impact. Doubly differential and total cross sections are calculated from each subshell. These cross sections summed over all subshells show a much better agreement with experimental data than those obtained from the previous formulations of the CDW-EIS approximation which use hydrogenic wavefunctions with effective charges.

Ionization of excited hydrogen atoms by collisions with bare ions.

Energy and charge dependence of total cross section for ionization of the excited states with n\ensuremath{\le}5 of hydrogen, in collisions with the bare ions up to ${\mathrm{O}}^{8+}$, has been investigated theoretically by using the continuum distorted wave--eikonal initial state (CDW-EIS) approximation. In contrast with the similar calculations of Fainstein et al. [J. Phys. B 23, 1481 (1990)], the present results show that the CDW-EIS approximation becomes identical to the Born approximation at high energies, even in the ionization of excited states. A comparison is made between the present results and other theoretical predictions.

Convergence of the multipole expansion for the doubly differential ionization cross section.

We analyze the convergence of the Legendre polynomials expansion of the doubly differential cross section (DDCS) for soft electron emission (SEE) in ion-atom collisions. This expansion has been recently employed in the analysis of the angular shape of theoretical as well as experimental data on SEE. Numerical calculations using the continuum-distorted-wave--eikonal-initial-state (CDW-EIS) approximation show that for sufficient low electron velocity, the DDCS for ionization is well described with a few terms of the expansion. Besides, we show analytically that the expansion reduces to the first three terms in the zero-emission-velocity limit, within CDW or CDW-EIS approaches.