Classical Trajectory Monte Carlo Model Research Articles

Classical trajectory Monte Carlo model calculations for ionization of atomic hydrogen by 75-keV proton impact

Cross sections differential with respect to the energy loss and scattering angle of the projectile have been calculated for ionization of atomic hydrogen by 75-keV proton impact using the classical trajectory Monte Carlo method. The results are compared with the experimental data measured by Laforge et al. [Phys. Rev. Lett. 103, 053201 (2009)] and Schulz et al. [Phys. Rev. A 81, 052705 (2010)], as well as with the predictions of several quantum-mechanical theoretical models. The analysis of the deviations between the classical and the quantum-mechanical results shows that the three-body fragmentation dynamics cannot be understood purely classically; for the description of the process the quantum-mechanical treatment of the interplay between the electron-projectile and the projectile--target-nucleus interaction is unavoidable.

Electron loss from 0.74- and 1.4-MeV/u low-charge-state argon and xenon ions colliding with neon, nitrogen, and argon

Absolute total-, single-, and multiple-electron-loss cross sections are measured for $({\mathrm{Ar}}^{+}\ensuremath{-},$ ${\mathrm{Ar}}^{2+}\ensuremath{-},$ ${\mathrm{Xe}}^{3+})\ensuremath{-}(\mathrm{Ne},$ ${\mathrm{N}}_{2},$ Ar) collisions at 0.74 and 1.4 MeV/u. In addition, a many-body classical trajectory Monte Carlo model was used to calculate total- and multiple-electron-loss cross sections for ${\mathrm{Ar}}^{+}$ impact. For ${\mathrm{N}}_{2}$ and Ar targets, excellent agreement between the measured and calculated cross sections is found; for the Ne target the experimental data are approximately 40% smaller than the theoretical predictions. The experimental data are also used to examine cross-section scaling characteristics for electron loss from fast, low-charge-state, heavy ions. It is shown that multiple electron loss increased the mean charge states of the outgoing argon and xenon ions by 2 and 3 respectively. The cross sections decreased with increasing number of electrons lost and scaled roughly as the inverse of the sum of the ionization potentials required to sequentially remove the most weakly bound, next most weakly bound, etc., electrons. This scaling was found to be independent of projectile, incoming charge state, and target. In addition, the experimental total loss cross sections are found to be nearly constant as a function of initial projectile charge state. As a function of impact energy, the theoretical predictions yield an ${E}^{\ensuremath{-}1/3}$ behavior between 0.5 and 30 MeV/u for the total loss cross sections. Within error bars, the data are consistent with this energy dependence but are also consistent with an ${E}^{\ensuremath{-}1/2}$ energy dependence.

Kαx-ray satellite lines of Si induced in collisions with 1–3-MeV protons

The Ka x-ray emission spectra of Si bombarded by 1-3-MeV protons were measured with a crystal spectrometer in Johansson geometry, enabling energy resolution below the natural linewidth of the measured Kα line. The KαL 1 and KαL 2 (KαL 1 , 2 ) x-ray satellite lines appearing in these spectra as a result of the radiative decay of atomic states with one hole in the K shell and one or two in the L subshells were precisely measured. The energies and intensities of the main components that could be resolved within the satellite lines are given. It has been demonstrated that the latter do not depend on proton energy and are essentially the same as in photon-induced spectra. The overall KaL 1 satellite intensity relative to the Ka diagram line has been used to deduce the L-shell ionization probabilities induced in near-central proton collisions. The experimental values were compared to the theoretical values calculated with the semiclassical approximation, with the three-body classical trajectory Monte Carlo model, and the classical binary-encounter-based geometrical model.

Charge Transfer in Ionic and Molecular Systems

first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessEditorial Charge Transfer in Ionic and Molecular Systems by Marie-Christine Bacchus-Montabonel Laboratoire de Spectrométrie Ionique et Moléculaire, UMR 5579, CNRS et Université Lyon I, 43 Bd. du 11 Novembre 1918, 69622 Villeurbanne Cedex, France Int. J. Mol. Sci. 2002, 3(3), 114; https://doi.org/10.3390/i3030114 Received: 5 February 2002 / Published: 28 March 2002 (This article belongs to the Special Issue Charge Transfer in Ionic and Molecular Systems) Download Download PDF Download PDF with Cover Download XML Download Epub Versions Notes Charge transfer reactions are fundamental processes present in almost all areas of physics, chemistry and biochemistry. Most of the time, these reactions are taking place in the condensed phase and solvent effects are determinant. Nevertheless, studies in the gas phase provide direct understanding of the intrinsic behaviour of the ions and are essential for the modeling of more complex mechanisms.Investigations of charge exchange reactions in ion-atom, ion-molecule and, more recently, ion-ion collisions are of fundamental as well as of practical interest. These reactions are of great importance in a variety of research fields, such as the description of many astrophysical and terrestrial environments, controlled thermonuclear fusion or ion accelerator technology. For example, the interaction of solar wind ions with cometary gases, auroral ions with planetary atmospheres, and stellar wind ions with the interstellar medium involves the formation of excited states of collision partners with the resultant visible, UV an X-ray emission. Both description of thermal and ionization balance of astrophysical plasmas and modeling of ion transport and radiative cooling processes in the diverter region of current large Tokamak fusion plasma devices require information on the relevant electron capture processes.Experimental methods such as single and double translational energy spectroscopy, energy gain spectroscopy, photon spectroscopy, Auger electron spectroscopy or recoil ion momentum spectroscopy combined with theoretical approaches, from the classical trajectory Monte-Carlo model, or the simple Landau-Zener model, to very accurate atomic or ab-initio molecular expansion methods within either time-dependent or time-independent collisional treatments, provide efficient tools for these studies. A large survey of these approaches is presented in this special issue, emphasizing recent results and developments of single-electron capture processes as well as multiple-electron capture reactions, essentially double-electron capture with regard to the complexity of the many-body problem involved, on ion-atom and ion-molecule collisions in the low-energy regime. Share and Cite MDPI and ACS Style Bacchus-Montabonel, M.-C. Charge Transfer in Ionic and Molecular Systems. Int. J. Mol. Sci. 2002, 3, 114. https://doi.org/10.3390/i3030114 AMA Style Bacchus-Montabonel M-C. Charge Transfer in Ionic and Molecular Systems. International Journal of Molecular Sciences. 2002; 3(3):114. https://doi.org/10.3390/i3030114 Chicago/Turabian Style Bacchus-Montabonel, Marie-Christine. 2002. "Charge Transfer in Ionic and Molecular Systems" International Journal of Molecular Sciences 3, no. 3: 114. https://doi.org/10.3390/i3030114 Find Other Styles Article Metrics No No Article Access Statistics For more information on the journal statistics, click here. Multiple requests from the same IP address are counted as one view.

Double-electron removal from H2 by slow, highlycharged Xe23+ ions

A five-body classical trajectory Monte Carlo model has been used tostudy double-electron removal from H2 by collisions with highlycharged ions. The final-state correlations betweenionized protons and projectile are calculated forXe23+ impact on H2 at collision energies rangingfrom 2.6 eV u-1 to 2.6 keV u-1. In thecentre-of-mass frame of the recoiling protons, as theprojectile energy decreases the proton energydistribution broadens considerably and also shifts tolower energies relative to that for an isolated moleculeFranck-Condon transition. At low collision energies theprotons are found to be scattered to the forwarddirection with large transverse momenta opposite to thatof the projectile. The strong forward momenta are asignature of three-body dynamics with the protonsCoulomb exploding against the projectile on the incomingportion of the trajectory. Investigation of thecentre-of-mass momenta of the protons reveals asignificant anisotropy of the proton angulardistributions. At the lowest collision energies, thereis a strong preference for the protons to be alignedparallel to the projectile direction. This behaviour,combined with their low centre-of-mass energies, impliesthat the protons are formed along the electric fieldvector of the incoming projectile concurrent withstretching of the molecular bond. The bond stretching isimportant only when the collision time is long (tens offemtoseconds) compared with the dissociation time of themolecule.

Capture and detachment in3He2++H−collisions

We report theoretical cross sections for capture and detachment in collisions between 3He2+ ions and negative hydrogen ions H- calculated in a range of laboratory collision energies extending from 150 eV to 2 MeV for the incident 3He2+ projectile. Calculations have been carried out within the semiclassical impact parameter method using a 30-state two-center atomic orbital expansion. Additional estimates of the same cross sections have also been obtained with the help of the classical trajectory Monte Carlo model. These results are compared with available experimental and theoretical cross sections. ©2000 The American Physical Society.

Five-body calculations ofD2fragmentation byXe19+impact

A five-body classical trajectory Monte Carlo model has been developed to study fragmentation of diatomic molecules after double electron removal by highly charged ion impact. A systematic study of the final-state deuteron energy and momentum spectra has been conducted for Xe19+ + D-2 collisions at impact energies ranging from 1 eV/u to 100 keV/u. At the highest projectile energies, the fragment energies and momenta are determined by the Coulomb explosion of the doubly-ionized molecule via the known Franck-Condon transition for the isolated molecule. The deuterons are emitted back-to-hack with nearly equal energies. At the lowest projectile energies, the final state behavior is due mainly to the collisional momentum transfer from the slow-moving projectile. The deuterons are strongly scattered in the direction opposite to the transverse momentum of the projectile with energies far greater than those produced in the Franck-Condon transition. At energies around 150 eV/u, both slow and fast deuterons are predicted. This is due to the vector addition of the collisional momentum transfer to the center of mass of the molecule with that due to the two-body Coulomb breakup of the dissociating ions. [S1050-2947(99)01009-4].

Double electron removal and fragmentation model of theH2molecule by highly charged ions

A five-body classical trajectory Monte Carlo model has been developed to study double electron removal from ${\mathrm{H}}_{2}$ by collisions with highly charged ions at impact energies ranging from 1 eV/u to 1 GeV/u. The longitudinal and transverse final-state correlation between ejected electrons is calculated for double ionization of ${\mathrm{H}}_{2}$ by impact of ${\mathrm{Se}}^{28+}$ at 3.6 MeV/u and ${\mathrm{U}}^{92+}$ at 1 GeV/u; the electron-electron interaction is dynamically included during the collision when one of the electron's total energy becomes positive. Relativistic corrections are incorporated to reflect the Lorentz contraction of the projectile's electric field. The cross section dependence on the alignment of the ${\mathrm{H}}_{2}$ molecular axis was investigated. Here, transfer ionization of ${\mathrm{H}}_{2}$ by ${\mathrm{O}}^{8+}$ at 500 keV/u is found to have a maximum for the molecular axis aligned perpendicular to the projectile velocity, while no orientation dependence is found for double ionization at 500 keV/u. In contrast, a minimum in the cross section at $90\ifmmode^\circ\else\textdegree\fi{}$ is found for 1-GeV/u ${\mathrm{U}}^{92+}{+\mathrm{H}}_{2}$ collisions. A systematic study of the energy partitioning between the two product ${\mathrm{H}}^{+}$ ions has been made for ${\mathrm{Xe}}^{54+}{+\mathrm{H}}_{2}$ from 1 eV/u to 1 MeV/u. Large deviations from Franck-Condon behavior are found for impact energies $E\ensuremath{\lesssim}10$ keV/u. At low energies the proton energies are very energetic with the main contribution arising from collisional transfer from the projectile, while the proton energy spectrum at high impact energy is due to the Coulomb explosion of the isolated molecule.

Fragmentation of H2 and HD Molecules by C6+ Impact

A five-body classical trajectory Monte Carlo model has been developed to study fragmentation of H2 and HD after double electron removal collisions by highly charged ions. The theoretical model includes all two-body Coulomb interactions in the post-collision regime. A systematic study of the energy partitioning between the nuclei has been made for C6+ impact from 1 eV/u to 1 MeV/u. Major deviation from isolated molecule Franck-Condon behavior is found for impact energies E ≤ 1 keV/u. At the lowest impact energies the target ions are very energetic with a strong contribution being from collisional transfer from the projectile. The target ion energy spectra at high impact energy is due to the Coulomb explosion of the isolated doubly ionized molecule in the known Franck-Condon transition, resulting in a distinct separation of the energy peaks for the HD isotope. At energies around 10 eV/u to 1 keV/u, or projectile charge divided by speed of q/v ≈ 30–300, both slow and fast target ions are observed which result from the competition between the momentum transfered during the collision with that from the Coulomb dissociation of the two ions.

Electron capture from coherent elliptic Rydberg states

Experimental relative cross sections for electron capture by singly charged ions (Na{sup +}) from coherent elliptic states of principal quantum number n=25 are presented. An interval of reduced impact velocities from about 1{endash}2 is covered. Absolute reaction cross sections could not be determined precisely, but the eccentricity of the coherent elliptic states and their orientation relative to the ion-impact velocity were varied to expose the dependence of the electron-capture process on the initial motion of the electron. The dependencies on eccentricity and orientation are generally strong and they vary sharply with impact velocity. Qualitatively, the observations agree fairly well with classical trajectory Monte Carlo (CTMC) calculations, as expected for the large quantum numbers involved, but significant deviations of a systematic nature do remain, showing that some aspects of the capture reactions studied are described poorly by classical physics as represented by the CTMC model. {copyright} {ital 1997} {ital The American Physical Society}

Extension of classical trajectory Monte Carlo calculations to ion–Rydberg-atom collisionsin a magnetic field

Theoretical electron transfer cross sections for 1.3--130 eV/amu singly charged ions colliding with Rydberg atoms (n=28, m=2) in a magnetic field up to 4 T are presented. Both paramagnetic and diamagnetic interactions are taken into account for the initial state and the collision. Cross sections are calculated within the classical trajectory Monte Carlo model. A method to create a classical ensemble of electrons in a nonseparable Hamiltonian allows the initial quantum stationary states to be modeled. The effect of the magnetic field on electron capture is analyzed in terms of the field-induced alteration of the initial state, as well as the direct influence on the collision dynamics.

Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms.

A quasiclassical-trajectory Monte Carlo (QTMC-EB) model is proposed to extend the classical-trajectory Monte Carlo (CTMC) method to targets having more than one electron. Quasiclassical stability is achieved via constraining potentials that enforce lower energy bounds on the one-electron dynamics. Cross sections for all possible electronic rearrangements (single and double electron transfer, single and double ionization, and transfer ionization) in ${\mathrm{H}}^{+}$+H, ${\mathrm{H}}^{+}$+He, ${\mathrm{He}}^{2+}$+He, and ${\mathrm{Li}}^{3+}$+He collisions are calculated with this model and with the previously proposed model (QTMC-KW) of Kirschbaum and Wilets [Phys. Rev. A 21, 834 (1980)]. The results are compared with accurate experimental data. The regime of validity for the two-electron targets is found to be similar to that of the usual CTMC model for one-electron targets. \textcopyright{} 1996 The American Physical Society.

Plasma as a high-charge-state projectile stripping medium

The classical trajectory Monte Carlo model has been used to computationally study the charge-state distributions that result from interactions between a high-energy, multielectron projectile and neutral and fully ionized targets. These studies are designed to determine the properties of a plasma for producing highly stripped ions as a possible alternative to gas and foil strippers that are commonly used to enhance the charge states of energetic ion beams. The results of these studies clearly show that a low-atomic-number, highly ionized plasma can yield higher charge states than a neutral target of the same density. The effect is principally attributable to the reduction in the number of available electron-capture channels. In this article, we compare the charge-state distributions that result during passage of a 20-MeV Pb projectile through neutral gas and fully ionized (singly charged) plasma strippers and estimate the effects of multiple scattering on the quality of the beam.

K-shell vacancy production by direct Coulomb ionization in 47-MeV Ca17++Ar collisions.

Calculations employing the independent-electron approximation suggest that direct Coulomb ionization is the dominant mechanism for Ar K-vacancy production by 47-MeV ${\mathrm{Ca}}^{17+}$, rather than K-K vacancy sharing as proposed by Schlachter et al. [J. Phys. B 21, L291 (1988)]. Using electron-capture probabilities for zero impact parameter given by the classical-trajectory Monte Carlo model, good agreement with the experimental charge-state distribution for multielectron capture in coincidence with Ar and Ca K x rays is achieved.

Classical and quantal models for ion-atom collisions

As part of a project for the evaluation of the classical trajectory Monte Carlo model for charge exchange and ionisation, a comparative study of classical and quantal cross sections for reactions between He 2+ ions and neutral lithium ions is described.

A classical trajectory Monte Carlo model for the injection of electrons into gaseous argon

Using about 2.5×106 classical trajectories, we have performed a Monte Carlo calculation of the response of electrons injected from a gold cathode into gaseous argon. The fraction of electrons which reach the anode F2 was computed as a function of the applied electric field E, the density of the argon gas N, and the excess energy of the injected electrons ℰ. The dependence of F2 on E/N is in good overall agreement with experiment, and the dimensionless parameter E/(Nℰσ), where σ is the momentum transfer cross section, can be used to classify the results. A statistical model of the electron’s motion in the absence of the potential energy function predicts fairly accurately the average number of atom–electron collisions required for the fate of the electron to be decided and shows that the energy loss processes are the most important input to the theory. The results are discussed in terms of the potential energy function and are compared with earlier theoretical work.