Distorted Wave Eikonal Initial State Research Articles

Cusp-electron production in collisions of open-shell He-like oxygen ions with atomic targets

We report on double differential cross sections of cusp electrons obtained in MeV/u collisions of open-shell He-like oxygen ions with helium. We use zero-degree electron spectroscopy and our double measurement technique, involving ${\mathrm{O}}^{6+}(1{s}^{2})$ ground-state and ${\mathrm{O}}^{6+}(1{s}^{2},1s2s)$ mixed-state beams, to extract the cusp contribution from only the excited ${\mathrm{O}}^{6+}(1s2s)$ beam. Theoretical calculations based on the continuum distorted wave eikonal initial state are in very good agreement with the measurements. The roles of the processes of electron capture to the continuum, electron loss to the continuum, and electron loss to the continuum with simultaneous target ionization, which contribute to the cusp peak, are discussed in detail.

Dynamic effective charge in the continuum of the CDW-EIS model for ionization in ion–atom collisions: angular and energy dependence

In this work, a dynamic charge is employed in the continuum distorted wave–eikonal initial state theoretical model to describe the non-Coulomb potential of the residual target for single ionization in bare ion–multielectron atom collisions. A comparison between the well-known Belkić prescription and the effective charge depending on emission angle and energy in the final residual-target continuum state is shown. The obtained results show that this effective charge improves the description of double-differential cross sections for backward emission angles over the whole emission energy range allowing the calculation of simple differential and total cross sections.

Electron Emission Cross Section from Methane under 250 keV Proton Impact

We measure double differential cross sections (DDCS) of electrons emitted from CH4 molecules in collisions with 250 keV protons. The projectile ions are obtained from a 400 kV electron cyclotron resonance-based ion accelerator (ECRIA). We study the energy and angular distributions of the electron DDCS. The observed double and single differential and the total cross section are compared with the state-of-the-art continuum distorted wave eikonal initial state (CDW-EIS) model predictions. Two different approaches are used considering the different target descriptions: complete neglect of differential overlap (CNDO) and molecular orbital (MO) approximations. The MO model uses two different scaling parameters (d = 0.7 and 1.0). In the energy distribution of the DDCS, the carbon KLL Auger line is also observed at 240 eV. The single differential cross section (SDCS) and total cross section (TCS) are derived. Both the MO-based CDW-EIS models are in good agreement with the experimental results; however, the CNDO approach overestimates the data.

Atomic ionization by multicharged ions interpreted in terms of poles in the velocity complex space

We study the single ionization of hydrogen and helium by the impact of a highly charged Coulomb projectile. To interpret the cross section we introduce a diagonal Padé approximant. We find that the use of a Padé [, ] describes the continuum distorted wave eikonal initial state theory within its range of validity very well. The nodes of the denominator of the Padé approximant give rise to four poles in the velocity complex plane: two in the upper plane and their conjugates in the lower plane. The dependence of these poles with the projectile charge can be reasonably fitted to give a closed form for the ionization cross section, resulting in a scaling very near to that of Janev and Presnyakov. The experiments available were described very well in its entire velocity range with the use of a Padé [, ], with four poles in the upper plane and their conjugates in the lower plane. We conclude that the poles of the Padé approximant seem to have all the information of the total ionization cross section.

Classical calculations of differential electron emission in fast heavy-ion collisions with water molecules

SynopsisWe present a classical study of differential electron emission cross sections for highly-charged projectiles at υp ∼ 10 a.u. impinging on water molecules [1, 2]. Comparisons with Continuum Distorted Wave Eikonal Initial State theoretical results and with experimental data are presented. We implement a time-dependent screening effect in our model and account for the molecular target structure by means of a three-center potential.

Electron emission cross sections for collisions of heavy ions with atomic targets

A theoretical study of the double-differential cross sections (DDCS) for ejection of electron from hydrogen atom in ground state by the impact of $$\hbox {C}^{6+}$$ ion with energy values 1 and 2.5 MeV/amu is presented. For the final state, we use a continuum distorted wave that contains the product of two Coulomb distortions due to the projectile–electron and target–electron Coulombic interactions for which it is called the two-Coulomb-wave (2CW) model. In this paper, the energy and angular distributions of DDCS for electron emission from atomic hydrogen have been investigated. The ejected electrons are influenced by the combined fields of the target and the projectile ion. Comprehensive comparisons are made between the three-Coulomb-wave model (Jana et al. in Eur Phys J D 66:243, 2012) and the present 2CW model. The emitted electron, the incident projectile ion and the residual ion are considered to be in the same plane. It is found that the two-centre effect has a major influence on the observed forward–backward angular asymmetry in the angular distribution of electron emission spectra. The region of the binary encounter peak is analysed in detail. The present computed results have been compared with the available experimental results as well as other theoretical calculations based on the first Born approximation and the continuum distorted wave eikonal initial state approximation. Moreover, the present computed results are in better agreement with the available experimental data for electron emission cross sections.

Classical-trajectory Monte Carlo calculations of differential electron-emission cross sections in fast heavy-ion collisions with water molecules

A classical description of electron emission differential ionization cross sections for highly-charged high-velocity ions ($\sim$ 10 a.u.) impinging on water molecules is presented. We investigate the validity of the classical statistical mechanics description of ionization ($\hbar=0$ limit of quantum mechanics) in different ranges of electron emission energy and solid angle, where mechanisms such as soft and binary collisions are expected to contribute. The classical-trajectory Monte Carlo method is employed to calculate doubly and singly differential cross sections for C$^{6+}$, O$^{8+}$ and Si$^{13+}$ projectiles, and comparisons with Continuum Distorted Wave Eikonal Initial State theoretical results and with experimental data are presented. We implement a time-dependent screening effect in our model, in the spirit of mean-field theory to investigate its effect for highly charged projectiles. We also focus on the role of an accurate description of the molecular target by means of a three-center potential to show its effect on differential cross sections. Very good agreement with experiments is found at medium to high electron emission energies.

Reprint of: Ionization probabilities of Ne, Ar, Kr, and Xe by proton impact for different initial states and impact energies

In this contribution we present ab initio results for ionization total cross sections, probabilities at zero impact parameter, and impact parameter moments of order +1 and −1 of Ne, Ar, Kr, and Xe by proton impact in an extended energy range from 100 keV up to 10 MeV. The calculations were performed by using the continuum distorted wave eikonal initial state approximation (CDW-EIS) for energies up to 1 MeV, and using the first Born approximation for larger energies. The convergence of the CDW-EIS to the first Born above 1 MeV is clear in the present results. Our inner-shell ionization cross sections are compared with the available experimental data and with the ECPSSR results. We also include in this contribution the values of the ionization probabilities at the origin, and the impact parameter dependence. These values have been employed in multiple ionization calculations showing very good description of the experimental data. Tables of the ionization probabilities are presented, disaggregated for the different initial bound states, considering all the shells for Ne and Ar, the M-N shells of Kr and the N-O shells of Xe.

Ionization probabilities of Ne, Ar, Kr, and Xe by proton impact for different initial states and impact energies

In this contribution we present ab initio results for ionization total cross sections, probabilities at zero impact parameter, and impact parameter moments of order +1 and −1 of Ne, Ar, Kr, and Xe by proton impact in an extended energy range from 100keV up to 10MeV. The calculations were performed by using the continuum distorted wave eikonal initial state approximation (CDW-EIS) for energies up to 1MeV, and using the first Born approximation for larger energies. The convergence of the CDW-EIS to the first Born above 1MeV is clear in the present results. Our inner-shell ionization cross sections are compared with the available experimental data and with the ECPSSR results. We also include in this contribution the values of the ionization probabilities at the origin, and the impact parameter dependence. These values have been employed in multiple ionization calculations showing very good description of the experimental data. Tables of the ionization probabilities are presented, disaggregated for the different initial bound states, considering all the shells for Ne and Ar, the M-N shells of Kr and the N-O shells of Xe.

Total Ionization Cross Sections in Particle and Antiparticle Collisions with Rare Gases

In this contribution we analyze the total ionization cross sections by impact of electrons, positrons, protons and antiprotons in Ne, Ar, Kr and Xe. We compare theoretical results using the continuum distorted wave eikonal initial state approximation with a detailed compilation of the available experimental data for the four projectiles in each target. The charge and mass effects, and the convergence at intermediate energies are discussed, which are important issues for antiparticle normalization. We remark the influence of the post-collisional Auger-like electron emission, which is decisive to describe the total ionization of Kr and Xe at impact velocities above9 a.u.

Double differential distribution of electron emission in the ionization of water molecules by fast bare oxygen ions

The doubly differential distributions of low-energy electron emission in the ionization of water molecules under the impact of fast bare oxygen ions with energy of 48 MeV are measured. The measured data are compared with two quantum-mechanical models, i.e. the post and prior versions of the continuum distorted wave–eikonal initial state (CDW-EIS) approximation, and the first-order Born approximation with initial and final wavefunctions verifying correct boundary conditions (CB1). An overall excellent qualitative agreement is found between the data and the CDW-EIS models whereas the CB1 model showed substantial deviation. However, the detailed angular distributions display some discrepancies with both CDW-EIS models. The single differential and total cross-sections exhibit good agreement with the CDW-EIS models. The present detailed data set could also be used as an input for modeling highly charged ion induced radiation damage in living tissues, whose most abundant component is water. Similar measurements are also carried out for a projectile energy of 60 MeV. However, since the double differential cross-section data show similar results the details are not provided here, except for the total ionization cross-sections results.

Fully differential study of ionization in p + H2 collisions near electron—projectile velocity matching

We have performed a kinematically complete experiment on ionization of H2 by 75 keV proton impact for electrons ejected with a speed close to the projectile speed. The fully differential data are compared to a three-body distorted wave and a continuum distorted wave—eikonal initial state calculation. Large discrepancies between experiment and theory, as well as between both calculations, are found. These probably arise from a strong coupling between the ionization and capture channels, which is not accounted for by theory.

Experimental and theoretical results on electron emission in collisions between He targets and dressed Liq+ (q = 1, 2) projectiles

We investigate experimentally and theoretically the electron emission in collisions between He atoms and (q = 1, 2) projectiles at intermediate to high incident energies. We report on measured absolute values of double-differential cross-sections, as a function of the emitted electron energy and angle, at a collision energy of 440 keV u−1. The different contributions from target ionization, projectile ionization, and simultaneous target–projectile ionization are calculated with the quantum-mechanical continuum distorted wave and continuum distorted wave–eikonal initial state models, and with classical trajectory Monte Carlo simulations. There is an overall good agreement of the calculations with the experimental data for electron emission cross-sections.

Double differential cross sections for ionization of water molecules by ion impact

Single ionization from water molecules by impact of bare ions is studied. Different approximations are employed, within the post and prior versions of the continuum distorted wave–eikonal initial state model, to calculate double differential cross sections. Post–prior discrepancies are observed between theoretical results. The sensitivity of the calculations to the description of the initial bound orbitals is investigated.

Differential cross sections for single ionization of H2 by 75keV proton impact

We have calculated Triply differential cross sections (TDCS) and doubly differential cross sections (DDCS) for single ionization of H2 by 75 keV proton impact using the molecular 3 body distorted wave Eikonal initial state (M3DW-EIS) approach. Previously published measured DDCS-P (differential in the projectile scattering angle and integrated over the ejected electron angles) found pronounced structures at relatively large angles which were interpreted as an interference resulting from the two-centered potential of the molecule.

Experimental and theoretical results on electron emission from helium by the impact of bare Li3+ ions

We investigate experimentally and theoretically the ionization of helium atoms by the impact of bare Li3 + projectiles at intermediate and high incident energies. We report on measured absolute values of doubly differential cross-sections, as a function of the emitted electron energies and angles, at collision energies of 200 and 440 keV u−1. Different physical aspects of the reaction are interpreted theoretically by comparison of the data with quantum-mechanical continuum distorted wave and continuum distorted wave–eikonal initial state calculations as well as classical trajectory Monte Carlo simulations. There is an overall good agreement of the calculations with the experimental data, which improves considerably for higher collision energies.

Quantum-mechanical predictions of DNA and RNA ionization by energetic proton beams

Among the numerous constituents of eukaryotic cells, the DNA macromolecule is considered as the most important critical target for radiation-induced damages. However, up to now ion-induced collisions on DNA components remain scarcely approached and theoretical support is still lacking for describing the main ionizing processes. In this context, we here report a theoretical description of the proton-induced ionization of the DNA and RNA bases as well as the sugar–phosphate backbone. Two different quantum-mechanical models are proposed: the first one based on a continuum distorted wave–eikonal initial state treatment and the second perturbative one developed within the first Born approximation with correct boundary conditions (CB1). Besides, the molecular structure information of the biological targets studied here was determined by ab initio calculations with the Gaussian 09 software at the restricted Hartree–Fock level of theory with geometry optimization. Doubly, singly differential and total ionization cross sections also provided by the two models were compared for a large range of incident and ejection energies and a very good agreement was observed for all the configurations investigated. Finally, in comparison with the rare experiment, we have noted a large underestimation of the total ionization cross sections of uracil impacted by 80 keV protons, whereas a very good agreement was shown with the recently reported ionization cross sections for protons on adenine, at both the differential and the total scale.

The second Born approximation for the single and double ionization of atoms by electrons and positrons

Recently, Lahmam-Bennani et al (2010 J. Phys. B: At. Mol. Opt. Phys. 43 105201) have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW-EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo-states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.

Review of theories on double electron capture in fast ion-atom collisions

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.

Angular and energy differential electron emission cross sections in collisions between antiprotons and helium atoms

We present theoretical singly- and doubly-differential ionization cross sections in collisions between antiprotons and helium atoms at 50 and 100 keV impact energies. The calculations were performed within the frame work of the continuum distorted wave eikonal initial state approximation and a three-body classical trajectory Monte Carlo method. We find clear evidence for the formation of the anti-cusp in the differential distributions.