Continuum Distorted Wave-eikonal Initial State Research Articles

Interference pattern signatures in fully differential cross sections for single ionization of H2 molecules by fast protons

Electron interference signatures present in fully differential cross sections for single ionization by 6 MeV protons in H2 molecules are investigated. We employ a molecular version of the continuum-distorted wave-eikonal initial state model, where all the interactions present in the exit channel are considered on an equal footing. Calculations of fully differential cross sections are performed for different electron and projectile kinematical conditions and the range of validity of the theoretical approach is discussed. Furthermore, we explore the presence of interference patterns in differential cross sections for both aligned and randomly oriented targets in asymmetric coplanar geometries.

Fully differential cross sections for ion–atom impact ionization in the presence of a laser field

We study fully differential cross sections (FDCS) for single ionization of helium by ion impact in the presence of a laser field. The field is assumed to have linear polarization, to be weak compared to the typical atomic field, and we use a frequency corresponding to a CO2 laser. We employ the continuum distorted wave-eikonal initial state (CDW-EIS) to describe our FDCS in the laser background. Analysing our numerical results we explore the dependence of the FDCS on the laser field properties as well as on the ionized electron parameters.

Two center Electron Emission in fast Collisions of Bare C and F Ions with He and H2 and CDW-EIS Mode

We report the energy and angular distributions of the electron double differential cross sections (DDCS) for two collision systems: 6 MeV/u C6+ on H2 and 4 MeV/u F9+ ions on He. The electrons having energies between 1 and 500 eV are detected at about ten different emission angles between 30° and 150°. The measured data is compared with the state-of-the art continuum distorted wave-eikonal initial state (CDW-EIS) and the first Born (B1) models. In case of molecular H2 target a molecular wave function as been used for the calculations of the cross section of H2. A comparative study has been presented for the spectral shape for the atomic (He) and molecular (H2) target.

Young Type Interference Effect on the Forward-Backward Asymmetry Parameter in Electron Emission from H2 Under Fast Ion Impact

We have investigated the double differential distribution of electron emission from molecular hydrogen in collisions with fast bare carbon ions in order to investigate the effect of Young type interference on the forward-backward angular asymmetry. The asymmetry parameter, derived from the cross sections for complementary forward and backward angles, shows an oscillatory behaviour as a function of electron velocity which is absent in atomic target such as He. It is shown that the asymmetry parameter which is based on the DDCS of H2 only, can be used as self normalizing way of the obtaining the Young type interference in an inversion symmetric homo-nuclear diatomic molecule like H2. The measured energy and angular distributions as well as the asymmetry parameter are compared with a molecular CDW-EIS (continuum distorted wave-eikonal initial state) model.

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.

Forward backward asymmetry in electron emission from H2by fast carbon ions and Young type interference effect

We have investigated the effect of Young type interference on the forward backward angular asymmetry in electron emission from molecular hydrogen in collisions with fast bare carbon ions. The asymmetry parameter shows an oscillatory behaviour as a function of electron velocity which is absent in atomic target such as He. It is shown that the asymmetry parameter which is based on DDCS from H2only can be a tool to investigate the Young type interference. The measured energy and angular distributions as well as the asymmetry parameter are compared with a molecular CDW-EIS (continuum distorted wave-eikonal initial state) model.

Fully differential cross sections for 3.6 MeV u−1 AuZ+P+ He collisions

Recent experimental data for fully differential cross sections (FDCS) have been compared to various continuum-distorted-wave eikonal-initial-state (CDW-EIS) models without much success, despite good agreement with double-differential cross sections. We present theoretical results from a four-body problem for FDCS of 3.6 MeV/u AuZ+P + He collisions, ZP = 24, 53, with ejected electron energy of 4 eV. Theoretical results for the inclusion and omission of the internuclear potential are given. Results are an improvement on current CDWEIS calculations for these collisions, especially in the Au24+case.

A multi-scale ab initio theoretical study of the production of free radicals in swift ion tracks in liquid water

Using a multi-scale theoretical approach from first principles, we show that the production of HO2 radicals in liquid water can be understood from the initial Coulomb explosion of doubly ionized water molecules. Based on the separation of time scales, we used three different theoretical models, each one associated with a specific time scale. The initial ∼1 fs of water radiolysis is taken care of with a Monte Carlo code whose basic ingredients are cross-sections. These have been calculated in the present work using the continuum distorted wave eikonal initial state (CDW-EIS) model framework. Our calculated cross-sections nicely demonstrate that double ionization of water molecules is one major event compatible with the experimental HO2 molecular rate production. The subsequent tens of fs following the double ionization of one water molecule of the liquid medium have been described with microscopic ab initio Car–Parrinello molecular dynamics simulations. Dynamics shows that the water Coulomb explosion leads to the formation of two H3O+ ions and an atomic oxygen atom. The final stage of the Coulomb explosion (up to the ms timescale) has been modelled with a chemical Monte Carlo code, assessing that the production of HO2 results from the O + OH → HO2 reaction in the liquid phase.

Electron emission from fragmentation of CO2 by fast proton impact

Single ionization of CO2 by 6 MeV proton impact has been studied by measuring in coincidence the momentum vectors of the emitted electron and the charged nuclear fragment CO+2, CO+ or O+, respectively. The experimental data have been compared with the predictions of a state of the art CDW–EIS (continuum distorted wave–eikonal initial state) calculation for molecular orbitals. A good qualitative agreement is observed even though the vibrational motion of the molecule is not taken into account in the model. The low-energy electron spectra show a rich structure which may be attributed to the presence of molecular excitation channels which undergo radiationless decay, via autoionization and also via predissociation. This interpretation is supported by photoionization studies of CO2.

Influence of the electron binding energy in the distortion of the initial state in ion-atom collisions

In this work, we propose a modified continuum distorted wave (CDW) theory for ion-atom ionization that incorporates an electron effective-mass model for the bound electron-projectile distortion in the entrance channel. Distorted wave theories have been shown to be adequate when the projectile impact energy is high enough but, as the projectile velocity decreases, both CDW and continuum distorted wave--eikonal initial state (CDW-EIS) approximations exhibit remarkable discrepancies when compared with the available experimental data, in particular for highly charged ion impact. Our modified CDW approximation incorporates the active electron binding energy in the distorted wave description of the initial state. We found very good agreement with experimental data in a single ionization doubly differential cross section for multiply charged projectiles and impact energies as low as 50 keV∕amu.

Highly charged particle impact ionization of He

Absolute experimental measurements have been reported for the fully differential cross section (FDCS) for single ionization of helium by 3.6 MeV/u AuQ+ (Q = 24, 53) ions. These absolute measurements are not in very good agreement with CDW-EIS (continuum distorted wave-eikonal initial state) calculations which are normally in excellent agreement with doubly differential cross-section measurements. We have recently introduced the 3DW-EIS approach which is a fully quantum mechanical approach. In addition, we have used a Hartree–Fock distorted wave for the outgoing electron instead of approximating the ejected electron as a Coulomb wave with an effective charge. For the case of low-energy C6+ ionization of helium, the 3DW-EIS model was in better agreement with absolute experimental data than the CDW-EIS approximation. The purpose of this paper is to investigate the validity of the 3DW-EIS model for more highly charged ions. Our theoretical results for the single ionization of helium by highly charged gold particles are in poor agreement with experimental results. The experiment displays unique forward peak structures in the FDCS that were not seen in the theoretical approach. We consider possible mechanisms to account for this forward peak structure.

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.

Magnetically quantized continuum distorted‐wave theory in atomic and molecular collisions

AbstractThe continuum distorted‐wave eikonal initial‐state (CDW‐EIS) theory of Crothers and McCann (J Phys B 1983, 16, 3229) used to describe ionization in ion–atom collisions is generalized (G) to GCDW‐EIS to incorporate the azimuthal angle dependence of each CDW in the final‐state wave function. This is accomplished by the analytic continuation of hydrogenic‐like wave functions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keVu−1, the total ionization cross‐section falls off, with decreasing energy, too quickly in comparison with experimental data. The idea behind and motivation for the GCDW‐EIS model is to improve the theory with respect to experiment by including contributions from nonzero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Ion–Atom/Argon—Calculation of ionization cross sections by fast ion impact for neutral target atoms ranging from hydrogen to argon

A FORTRAN 90 program is presented which 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 hydrogen up to and including argon. The code is applicable for the case of both high and low Z projectile impact in fast ion–atom collisions. The theoretical models provided for the program user are based on two quantum mechanical approximations 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. The codes presented here extend previously published codes for single ionization of target hydrogen [Crothers and McCartney, Comput. Phys. Commun. 72 (1992) 288], target helium [Nesbitt, O'Rourke and Crothers, Comput. Phys. Commun. 114 (1998) 385] and target atoms ranging from lithium to neon [O'Rourke, McSherry and Crothers, Comput. Phys. Commun. 131 (2000) 129]. Cross sections for all of these target atoms may be obtained as limiting cases from the present code. Program summary Title of program: ARGON Catalogue identifier: ADSE Program summary URL: http://cpc.cs.qub.ac.uk/cpc/summaries/ADSE Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computer for which the program is designed and others on which it is operable: Computers: Four by 200 MHz Pro Pentium Linux server, DEC Alpha 21164; Four by 400 MHz Pentium 2 Xeon 450 Linux server, IBM SP2 and SUN Enterprise 3500 Installations: Queen's University, Belfast Operating systems under which the program has been tested: Red-hat Linux 5.2, Digital UNIX Version 4.0d, AIX, Solaris SunOS 5.7 Compilers: PGI workstations, DEC CAMPUS Programming language used: FORTRAN 90 with MPI directives No. of bits in a word: 64, except on Linux servers 32 Number of processors used: any number Has the code been vectorized or parallelized?: Parallelized using MPI No. of bytes in distributed program, including test data, etc.: 32 189 Distribution format: tar gzip file Keywords: Single ionization, cross sections, continuum-distorted-wave model, continuum-distorted-wave eikonal-initial-state model, target atoms, wave treatment Nature of physical problem: The code calculates total, and differential cross sections for the single ionization of target atoms ranging from hydrogen up to and including argon by both light and heavy ion impact. Method of solution: ARGON allows the user to calculate the cross sections using either the CDW or CDW-EIS [J. Phys. B 16 (1983) 3229] models within the wave treatment. Restrictions on the complexity of the program: Both the CDW and CDW-EIS models are two-state perturbative approximations. Typical running time: Times vary according to input data and number of processors. For one processor the test input data for double differential cross sections (40 points) took less than one second, whereas the test input for total cross sections (20 points) took 32 minutes. Unusual features of the program: none

Three-body Coulomb dynamics in hydrogen ionization by protons and antiprotons at intermediate collision velocities

We consider ionization of atomic hydrogen with emission of low-energy electrons by proton and antiproton impact in the range of impact velocities 3 a.u.{<=}v{sub p}{<=}6 a.u., where the electron capture by protons is already of minor importance but the differences in hydrogen ionization due to proton and antiproton impact can still be substantial. By calculating various differential cross sections within the first and second Born and continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approximations we attempt to analyze the dynamics of hydrogen ionization by protons and antiprotons. We discuss in some detail the role of (i) the interaction between the projectile and the target nucleus and (ii) multiphoton exchanges between the projectile and the target electron. Profound charge-sign effects are suggested by CDW-EIS and second Born calculations for the fully differential emission pattern. Although after the integration over the electron emission angles these effects substantially diminish, they still remain noticeable even in the total ionization cross section suggesting, in particular, that protons are more effective, compared to antiprotons, in producing soft electron emission from hydrogen in the range of collision velocities under consideration.

CDW-EIS theoretical calculations of projectile deflection for single ionization in highly charged ion–atom collisions

We present continuum distorted wave-eikonal initial state (CDW-EIS) theoretical calculations for the projectile deflection in single ionization of helium by heavy-ion impact as a function of ionized electron energies. These calculations account for the helium passive electron shielding in the internuclear interaction improving standard CDW-EIS theory. The results are compared with recent experimental results by impact of 100 MeV/amu C6+ and 3.6 MeV/amu Au53+. For highly charged projectiles there is a poor quantitative agreement between theory and experiment. However, this refined calculation does share some qualitative features with the data. In particular the variation of the effective charge of the residual He+ ion from Zeff=1 to Zeff=2 when going from small to large projectile scattering angles is able to represent a shoulder observed in the double differential cross sections. Important qualitative differences are observed at the level of triple differential cross sections.

Saturation effects in highly charged ion interaction with thin carbon foils

We present a set of experimental values for relative cross sections of Auger electron production in carbon foils for projectile charges QP ranging from 6 to 39 and fixed projectile velocity 19.2 atomic units. We deduce the 1s single and double ionisation cross sections and their relative variation with respect to the projectile charge. The cross section saturates for the largest projectile charges. However, the comparison of the experimental data with continuum distorted wave-eikonal initial state (CDW-EIS) and classical trajectory Monte Carlo (CTMC) calculations shows that this saturation effect is not well reproduced by the calculations. We suggest that the observed saturation effect in 1s-shell ionisation could be due to multiple electron effects not included in these models based on independent electron approximation. We have then simulated the backward electron emission yield γB taking into account this strong saturation effect for the 1s shell. We obtained a better agreement for both the emission yield γB and the stopping power. The electron emission simulation gives some insight on the relative contribution of valence and 1s-shell to saturation effects.

Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothersand McCann (Crothers D S F and McCann J F 1983 J. Phys. B: At. Mol. Phys.16 3229) used to describe ionization in ion–atom collisions is generalized (G)to GCDW-EIS, to incorporate the azimuthal angle dependence into thefinal-state wavefunction. This is accomplished by the analytic continuation ofhydrogenic-like wavefunctions from below to above threshold, using paraboliccoordinates and quantum numbers including magnetic quantum numbers, thusproviding a more complete set of states. At impact energies lower than 25 keVu−1, the total CDW-EIS ionization cross section falls off, with decreasingenergy, too quickly in comparison with experimental data by Crothers andMcCann. The idea behind and motivation for the GCDW-EIS model is toimprove the theory with respect to experiment, by including contributionsfrom non-zero magnetic quantum numbers. We also therefore incidentallyprovide a new derivation of the theory of continuum distorted waves forzero magnetic quantum numbers while simultaneously generalizing it.

Postcollision interaction and two-center effects in ionizing collisions

Momentum distributions of the recoil target ion and the ejected electron have been calculated for 75-keV ${\mathrm{H}}_{2}^{+}+\mathrm{He}$ collisions by applying the classical trajectory Monte Carlo (CTMC) and the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) theory. A qualitative agreement was found between the calculated centroid values of the momentum distributions and the corresponding experimental data published recently by An et al. [Phys. Rev. A 63, 030703 (2001)]. The presence of postcollision interaction effects in the momentum distributions was analyzed repeating the CTMC calculations with a short-range model potential between the electron and the projectile ion as a function of the interaction length. The role of two-center effects was investigated by comparing the CDW-EIS results with those obtained in the first-Born approximation.

Energy straggling of protons through thin solid foils

The energy straggling of protons penetrating thin foils is theoretically and experimentally investigated for intermediate and high impact velocities. We calculate separately the contributions due to the interaction of the projectile with valence and core electrons. The energy straggling originated in the valence band is evaluated within the dielectric formalism, using the Mermin-Lindhard dielectric response function. The contribution coming from the core ionization is calculated with the continuum-distorted-wave--eikonal-initial-state (CDW-EIS) approximation. The predictions of the model are compared with recent measurements for Al, Zn, and Au targets. In addition, experimental results of straggling for Si are presented. The transmission method is used to measure the straggling, and experimental data are corrected to consider roughness effects. Theoretical values are in good agreement with the experiments in the whole range of energies considered. At low energies the binary interaction with valence electrons is the dominant mechanism, while the inner-shell contribution becomes the most important one as the energy increases.