Eikonal Initial State Approximation Research Articles

Electron emission from CH4 molecules in collisions with fast bare C ions

We present the energy and angular distributions of electron emission from a ${\mathrm{CH}}_{4}$ molecule in collisions with fast bare C ions with energies 3.5 and 5.5 MeV/u. The absolute double differential cross sections (DDCS) are measured for the ejected electrons having energies from 11 eV to 330 eV for $3.5\ensuremath{-}\mathrm{MeV}/\mathrm{u}$ projectiles and from 5 eV to 330 eV for 5.5 MeV/u bare C ions. The emission is measured in the angular range from ${20}^{\ensuremath{\circ}}$ to ${160}^{\ensuremath{\circ}}$. The forward-backward angular asymmetry, the single differential cross sections (SDCS), and the total cross section are deduced from the measured DDCS values. The energy and angular distributions of the DDCS and SDCS are compared with those calculated using a theoretical model based on the prior form of the continuum distorted wave--eikonal initial state (CDW-EIS) approximation. The dynamics of the process is considered within the CDW-EIS approximation, while the initial orbitals of the molecular target are represented using the complete neglect of the differential overlap approximation. The calculations are found to be in very good agreement with the measured cross sections. The angle dependence of the carbon K-LL Auger emission and the total Auger emission cross section are also derived for both projectile energies.

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.

Theoretical investigation of the fully differential cross sections for single ionization of He in collisions with 75-keV protons

We present a theoretical investigation of the single ionization of He in collisions with ${\mathrm{H}}^{+}$ projectile ions at 75-keV impact energy. Using the frameworks of the independent-electron model and the impact parameter picture, fully differential cross sections (FDCS) are evaluated in the continuum distorted-wave with eikonal initial-state approximation (CDW-EIS). Comparisons are made to the recent measurements of Schulz et al. [Phys. Rev. A 73, 062704 (2006)] and Arthanayaka et al. [J. Phys. B: At. Mol. Opt. Phys. 49, 13LT02 (2016)]. Strong influence of the internuclear interaction and effects of target core polarization due to the presence of the projectile ion are observed. Comparing the present results to experimental data and other theoretical predictions, it has been found that the CDW-EIS method qualitatively reproduces structures in the FDCS. Projectile coherence effects are investigated by representing the projectile beam as a Gaussian wave packet. Evidence of interference effects due to projectile-electron and projectile-target core interactions are discussed and the need for further theoretical investigations is proposed.

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.

Single ionization and capture cross sections from biological molecules by bare projectile impact*

We report calculations on single differential and total cross sections for single ionization and single electron capture from biological targets, namely, vapor water and DNA nucleobasese molecules, by bare projectile impact: H+, He2+, and C6+. They are performed within the Continuum Distorted Wave – Eikonal Initial State approximation and compared to several existing experimental data. This study is oriented to the obtention of a reliable set of theoretical data to be used as input in a Monte Carlo code destined to micro- and nano- dosimetry.

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.

Electron emission in ionization of He and Ne by fast dressed oxygen ions and projectile-charge-state dependence

The double-differential cross sections (DDCS) of low-energy electrons emitted at forward, backward, and perpendicular directions are reported for collisions of 3.75 MeV/u ${\mathrm{O}}^{q+}$ ($q=5$, 6, 7, 8) projectiles with He and Ne targets. The measured DDCS are found to be deviating from the ${q}^{2}$ dependence throughout the entire energy region. The effect of projectile electrons, for the dressed ions, as a function of the impact parameter is clearly noticeable for large as well as low-impact parameter collisions. We also present a theoretical calculation based on the prior form of the continuum distorted wave--eikonal initial state approximation, in which the projectile-active electron interaction is modeled with the Green-Sellin-Zachor potential. This particular representation of the potential has been proven to give good qualitative results for projectiles with residual electrons. In addition to the total DDCS, the individual contributions from target ionization, projectile electron loss, and simultaneous ionization processes are also calculated. The total DDCS obtained from these calculations are shown to be in excellent agreement with the experimental observations.

Differential cross sections for single ionization of Li in collisions with fast protons andO8+ions

We study the process of single ionization of Li in collisions with H$^+$ and O$^{8+}$ projectile ions at 6 MeV and 1.5-MeV/amu impact energies, respectively. Using the frameworks of the independent-electron model and the impact parameter picture, fully (FDCS) and doubly (DDCS) differential cross sections are evaluated in the continuum distorted-wave with eikonal initial-state approximation. Comparisons are made with the recent measurements of LaForge \textit{et al} [J. Phys. B \textbf{46} 031001 (2013)] for the DDCS and Hubele \textit{et al} [Phys. Rev. Lett. \textbf{110} 133201 (2013)] for the FDCS, respectively. For O$^{8+}$ impact inclusion of the heavy particle (NN) interaction in the calculations is crucial and effects of polarization due to the presence of the projectile ion have also to be taken into account for getting very good agreement with the measured data. Our calculation reproduces the satellite peak structure seen in the FDCS for the Li(2s) measurement, which we explain as being formed by a combination of the binary and NN interactions.

Track structure of protons and other light ions in liquid water: Applications of the LIonTrack code at the nanometer scale

The LIonTrack (Light Ion Track) Monte Carlo (MC) code for the simulation of H(+), He(2+), and other light ions in liquid water is presented together with the results of a novel investigation of energy-deposition site properties from single ion tracks. The continuum distorted-wave formalism with the eikonal initial state approximation (CDW-EIS) is employed to generate the initial energy and angle of the electrons emitted in ionizing collisions of the ions with H2O molecules. The model of Dingfelder et al. ["Electron inelastic-scattering cross sections in liquid water," Radiat. Phys. Chem. 53, 1-18 (1998); "Comparisons of calculations with PARTRAC and NOREC: Transport of electrons in liquid water," Radiat. Res. 169, 584-594 (2008)] is linked to the general-purpose MC code PENELOPE/penEasy to simulate the inelastic interactions of the secondary electrons in liquid water. In this way, the extended PENELOPE/penEasy code may provide an improved description of the 3D distribution of energy deposits (EDs), making it suitable for applications at the micrometer and nanometer scales. Single-ionization cross sections calculated with the ab initio CDW-EIS formalism are compared to available experimental values, some of them reported very recently, and the theoretical electronic stopping powers are benchmarked against those recommended by the ICRU. The authors also analyze distinct aspects of the spatial patterns of EDs, such as the frequency of nearest-neighbor distances for various radiation qualities, and the variation of the mean specific energy imparted in nanoscopic targets located around the track. For 1 MeV/u particles, the C(6+) ions generate about 15 times more clusters of six EDs within an ED distance of 3 nm than H(+). On average clusters of two to three EDs for 1 MeV/u H(+) and clusters of four to five EDs for 1 MeV/u C(6+) could be expected for a modeling double strand break distance of 3.4 nm.

CDW-EIS calculation for ionization and fragmentation of methane impacted by fast protons

Ionization of the CH4 molecule in collision with energetic protons has been investigated by applying the continuum distorted wave with eikonal initial state approximation extended for multi-centre collisions. Total and double differential net and q-fold ionization cross sections have been evaluated which show good agreement with experimental data. Electron distribution characteristics to the structure of the molecule have been revealed in the impact parameter dependence of ionization probabilities. Dissociation of the molecule has also been considered. Present results for the production of CH ions (n = 1–4) are in good agreement with the available experimental data.

Antiproton, proton and electron impact multiple ionization of rare gases

We present a study on multiple ionization of Ne, Ar, Kr and Xe by antiproton, proton and electron impact. Four different aspects are involved in this work. First, the theoretical calculations of ionization probabilities by impact of antiprotons and protons, in an extended energy region (25 keV to 10 MeV), using the continuum distorted-wave eikonal initial state approximation and the first Born approximation. Second, the inclusion of Auger-type post-collisional contributions through experimental photoionization branching ratios. These contributions to multiple ionization are very important in the high-energy region. Third, the comparison with the available experimental data on multiple ionization by protons and antiprotons in the extended energy range, and by electrons for high-impact velocities, where proton, antiproton and electron impact results are expected to converge. It is also the energy region where direct ionization does not explain the experimental results, and the post-collisional ionization is the main contribution to multiple ionization. And fourth, total ionization cross sections are calculated and compared with the antiproton, proton and electron experimental data, showing the importance of Auger-type multiple ionization for heavy targets even at the level of total cross sections. Gross and count cross sections are scrutinized.

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.

New approach on molecular ionization by ion impact: the CDW-EIS-SVIM model

We have extended the continuum distorted wave eikonal initial state approximation for single ionization of atoms by ion impact to the molecular case where a model potential for the molecular target is introduced. The continuum wavefunctions of the ejected electrons are then calculated in the static-exchange potential field generated by the residual molecular ion. The Schwinger variational iterative method was used in the calculation of these continuum wavefunctions. We apply this model to the single ionization of the hydrogen molecule (H2) by different bare projectiles. Doubly differential cross sections are calculated and compared with available experimental data for intermediate impact energies.

Multiple electron emission from noble gases colliding with proton beams, including postcollisional effects

The process of multiple electron ionization of Ne and Ar noble gases produced by impact of proton beams is studied in the framework of the independent-electron model. The role played by different mechanisms is analyzed, including intershell Auger and intrashell Coster-Kronig electron emission, which follow the production of vacancies due to direct interaction of the projectile with the target electrons. The present results, obtained with the continuum distorted wave--eikonal initial state (CDW-EIS) approximation, confirm previous predictions given by a different theoretical model. Semiempirical approximations are introduced by using analytical single-ionization probabilities with adjustable parameters determined from CDW-EIS total cross sections. The small computational time required to calculate multiple ionization cross sections with these semiempirical approximations and the good agreement found with existing experimental data and with results obtained with more elaborated theoretical models make them good candidates to study electron emission from complex targets.

Multi-ionization of helium and lithium using the independent electron and independent event models with intrinsic CDW

Cross sections for the multi-ionization of He and Li are presented for impact energies in the range of 50 to 1000 keV/amu. These are calculated using the eikonal initial state approximation to represent the input and exit channels of the active electrons. The ionization process is simulated in a variety of ways, most notably an attempt to account for the effects of electron correlation via the inclusion of a continuum density of states (CDS) term. Inadequacies, of the CDW formulation at small impact parameters, and of the models themselves, are discussed and conclusions are drawn on what repercussions this has for the cross sections calculated.

CDW-EIS model for single-electron capture in ion–atom collisions involving multielectronic targets

A generalization of the continuum distorted wave eikonal initial state (CDW-EIS) approximation, for the description of single-electron capture in ion–atom collisions involving multielectronic targets is presented. This approximation is developed within the framework of the independent electron model taking particular care of the representation of the bound and continuum target states. Total cross sections for single-electron capture from the K-shell of He, Ne and Ar noble gases by impact of bare ions are calculated. Present results are compared to previous CDW-EIS ones and to experimental data.

Post–prior discrepancies in the continuum distorted wave–eikonal initial stateapproximation for ion–helium ionization

We have explored post–prior discrepancies within continuum distortedwave–eikonal initial state theory for ion–atom ionization. Although there are nopost–prior discrepancies when electron–target initial and final states are exactsolutions of the respective Hamiltonians, discrepancies do arise for multielectronictargets, when a hydrogenic continuum with effective charge is used for the finalelectron–residual target wavefunction. We have found that the prior versioncalculations give better results than the post version, particularly for highlycharged projectiles. We have explored the reasons for this behaviour and foundthat the prior version shows less sensitivity to the choice of the final state.The fact that the perturbation potentials operate upon the initial statesuggests that the selection of the initial bound state is relatively moreimportant than the final continuum state for the prior version.