Classical Trajectory Monte Carlo Calculations Research Articles

Classical and semi-classical treatments of Li3+, Ne10++H(1s) collisions

We perform molecular close-coupling and impact-parameter classical trajectory Monte Carlo calculations of total and partial cross sections for capture and ionization in collisions of highly charged ions on H(1s). We first consider Li3++H(1s) as a benchmark to ascertain the complementarity of the methods, and then Ne10++H(1s), which has been scarcely studied up to now, and has recently become of interest for fusion plasma research.

Dynamics of formation ofK-hole fractions of sulfur projectiles inside a carbon foil

The $K\ensuremath{\alpha}$ and $K\ensuremath{\beta}$ satellite and hypersatellite x-ray lines emitted by highly ionized sulfur projectiles passing with energies from $65\phantom{\rule{0.3em}{0ex}}\text{MeV}$ up to $122\phantom{\rule{0.3em}{0ex}}\text{MeV}$ through carbon foils of thickness of $15\text{\ensuremath{-}}210\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}{\mathrm{g}\phantom{\rule{0.3em}{0ex}}\text{cm}}^{\ensuremath{-}2}$ have been recorded using a Si(Li) detector. The additional hypersatellite $K{y}^{h}$ peak proves that for such high energies of the sulfur ions very high subshells ($4p$ and $5p$) could be occupied. In order to study the dynamics of formation of $K$-shell vacancy fractions of sulfur projectiles passing through a carbon foil the dependence of sulfur $K$ x-ray production cross sections on foil thickness has been examined separately for each recorded line using the three component model. For each projectile energy the values of $K$-shell hole production cross sections and $K$-shell electron capture cross sections (both common for all recorded x-ray lines in the case of each projectile energy) have been fitted, as well as the specific values (for each recorded x-ray line) of $K$-shell hole filling cross sections, which are directly connected with average lifetimes of appropriate states of sulfur ions. The obtained ``experimental'' values of $K$-shell vacancy production cross sections are much higher than the theoretical predictions. This suggests that apart from the ionization process the excitation from $K$ shell into higher shells is responsible for a production of $K$-shell vacancies, which has been confirmed by recent classical trajectory Monte Carlo calculations.

Protonium formation in collisions of antiprotons with hydrogen molecular ions

Protonium formation in molecular collisions, , is theoretically investigated. Within the framework of the adiabatic approximation, the four-body problem can be treated as three-body collisions on a single adiabatic (Born–Oppenheimer) potential energy surface (PES), in the same manner as chemical reaction problems. The adiabatic potential energies of the system are calculated for various configurations. A classical trajectory Monte Carlo calculation is carried out for the collisions on the adiabatic PES. It is found that the dissociative dynamics plays a critical role in protonium formation, and consequently the molecular target is much more effective in protonium formation than the atomic-hydrogen target.

H+–He(1s2) collisions: CTMC calculations of single ionisation and excitation cross sections

The processes of helium single ionisation and excitation by proton impact are reviewed for the collision energy region relevant to He beam fusion edge plasma diagnostics (proton energy 10<E<50keV). Classical trajectory Monte Carlo (CTMC) calculations have been performed and compared with the existing data. Obtained results for single ionisation are close to available experimental data, while for excitation they are larger by up to a factor of two. For excitation into high quantum numbers, the n−3 scaling law is verified by our CTMC calculations.

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.

Comment on “Laser-assisted formation of antihydrogen”

In a recent paper, Whitehead, McCann, and Shimamura [Phys. Rev. A 64, 023401 (2001)] presented classical-trajectory Monte Carlo (CTMC) calculations of the effects of laser fields on the cross section for antihydrogen formation in collisions of antiprotons with positronium. They also use the same method to calculate the photoionization rate of isolated positronium in a strong field. The purpose of this Comment is to point out (i) the criteria for validity of the quasiclassical approximation are not satisfied for all the conditions used; (ii) some of their numerical results do not agree with the values obtained with a corroborated code; (iii) the ambiguity of a cross section when the target can ionize even before the projectile arrives; and (iv) the essential effect of quantum-mechanical tunneling on the strong-field ionization rate. A recently published method allowing tunneling in a CTMC calculation [J. S. Cohen, Phys. Rev. A 64, 043412 (2001)] is used for (iv). It is concluded that the laser effect on formation of antihydrogen may be much greater than that found by Whitehead et al., but the pulse must be better characterized for quantitative predictions.

Shifts in electron capture to the continuum at low collision energies: Enhanced role of target postcollision interactions

Measurements of electron velocity distributions emitted at $0\ifmmode^\circ\else\textdegree\fi{}$ for collisions of 10- and 20-keV ${\mathrm{H}}^{+}$ incident ions on ${\mathrm{H}}_{2}$ and He show that the electron capture to the continuum cusp formation, which is still possible at these low impact energies, is shifted to lower momenta than its standard position (centered on the projectile velocity), as recently predicted. Classical trajectory Monte Carlo calculations reproduce the observations remarkably well, and indicate that a long-range residual interaction of the electron with the target ion after ionization is responsible for the shifts, which is a general effect that is enhanced at low nuclear velocities.

Liouville master equation for multielectron dynamics: Neutralization of highly charged ions near a LiF surface

We present a simulation of the neutralization of highly charged ions in front of a lithium fluoride surface including the close-collision regime above the surface. The present approach employs a Monte Carlo solution of the Liouville master equation for the joint probability density of the ionic motion and the electronic population of the projectile and the target surface. It includes single as well as double particle-hole (de)excitation processes and incorporates electron correlation effects through the conditional dynamics of population strings. The input in terms of elementary one- and two-electron transfer rates is determined from classical trajectory Monte Carlo calculations as well as quantum-mechanical Auger calculations. For slow projectiles and normal incidence, the ionic motion depends sensitively on the interplay between image acceleration towards the surface and repulsion by an ensemble of positive hole charges in the surface (``trampoline effect''). For ${\mathrm{Ne}}^{10+}$ we find that image acceleration is dominant and no collective backscattering high above the surface takes place. For grazing incidence, our simulation delineates the pathways to complete neutralization. In accordance with recent experimental observations, most ions are reflected as neutral or even as singly charged negative particles, irrespective of the charge state of the incoming ions.

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.

Projectile and targetionization in MeV u-1 collisions of Xe ions with N2

Experimental cross sections are presented for single andmultiple electron stripping from Xe18+ projectiles incollisions with N2 at energies 2.0-9.3 MeV u-1. Thedata are compared to 2-30 MeV u-1 n-body classicaltrajectory Monte Carlo calculations that explicitly include electrons on both centres. Two-centre electron-electron (e-e) and electron-screened nuclear interactions contribute to theionization reactions. The computations are in reasonable accordfor the total stripping cross section but underestimate thehigher stages of multiple electron loss. An energy depositionmodel gives improved agreement with experiment. The energydependence of the total stripping cross section is close to E-0.5. Calculations are also presented for target ionizationby Xe+, Xe8+ and Xe18+ at 10 and20 MeV u-1. Projectile and target ionization crosssections are found to be comparable. Cross sections for projectile stripping by ionized targets are also calculated andfound to be relatively insensitive to the ionization stage ofthe target. This latter observation is attributed to thecompensating contributions between the two-centree-e and electron-screened nuclear interactions.

A quasiclassical approach to electron impactionization

A quasiclassical approximation to quantum mechanical scatteringin the Møller formalism is developed. While keeping thenumerical advantage of a standard classical trajectory MonteCarlo calculation, our approach is no longer restricted to usingstationary initial distributions. This allows one to improve theresults by using better suited initial phase space distributionsthan the microcanonical one and to gain insight into thecollision mechanism by studying the influence of differentinitial distributions on the cross section. A comprehensiveaccount of results for single, double and triple differentialcross sections for atomic hydrogen will be given, in comparisonwith experiment and other theories.

Simultaneous projectile-target ionization: a novel approach to (e, 2e) experiments on ions.

A kinematically complete experiment for simultaneous ionization of a projectile and target has been performed for 3.6 MeV/u C2+ on He collisions measuring the final vector momenta of the He1+ recoil ion and of two electrons (projectile, target) in coincidence with the emerging C3+ projectile. The feasibility of an event-by-event separation of the various reaction channels, among them the ionization of C2+ by the interaction with a quasifree target electron, is demonstrated in agreement with six-body classical trajectory Monte Carlo calculations, paving the way to kinematically complete electron-ion scattering experiments.

Dynamics of the fragmentation ofD2by fast protons and slow highly chargedXe26+

Using recoil-ion momentum spectroscopy, combined with a multihit detector system, the full momentum vectors of both fragment ions produced by fragmentation of ${\mathrm{D}}_{2}$ by fast 50-kV protons and slow (9.56--0.191 keV/u) ${\mathrm{Xe}}^{26+}$ ions have been measured. The data are kinematically complete, and make it possible to separate the laboratory momentum of the center of mass of the molecule from the momentum of each fragment in the center-of-mass system of the molecule. Using this separation, we find that, for higher collision velocities, the overall reaction can be described as double-electron capture, followed in a second and separate step by a Coulomb explosion of the doubly charged ${\mathrm{D}}_{2}$ molecule. For the lowest collision velocities, however, the projectile remains in the vicinity of the molecule during the fragmentation, and this clean separation of steps is lost. The projectile is found to extract internal energy from the molecule, thus leading to less energetic fragments in the center-of-mass system of the molecule. This effect causes a distortion in the spherical momentum images, as shown by the two-dimensional momentum distributions in the collision plane. The experimental results are found to be in good agreement with five-body classical trajectory Monte Carlo calculations.

Collisional excitation of H2 by grains in C-type shocks

We have performed classical trajectory Monte Carlo calculations of the probabilities of rovibrational excitation and dissociation of molecular hydrogen in collisions with a surface, modelled as MgO. The results show that, in C-type shock waves, states of high excitation energy are populated predominantly in collisions with charged grains, rather than with much more abundant neutral species. The intensities of rovibrational transitions of H2 have been calculated for a series of models of C-type shocks, considered to be relevant to molecular outflow sources. We compare the column densities of excited states of H2 and the intensities of representative rovibrational transitions, calculated excluding and including collisions with grains.

Multiple Scattering of the Emitted Electrons in Intermediate Velocity C+ + Ne Collisions: Search for Fermi-Shuttle Acceleration in Experiment and CTMC Calculations

We report a combined experimental and theoretical study of an intermediate velocity collision system. Our aim is to investigate the possibility of emitting electrons which are accelerated by the Fermi-shuttle mechanism due to double and triple scattering effects. Electron emission in the 20–2000 eV energy range and in the full angular range of 0°–180° were measured by the impact of 150 keV/u C+ ions on Ne atoms. Classical trajectory Monte-Carlo (CTMC) calculations, show structures belonging to both the projectile-target (P-T) and the target-projectile (T-P) types of double scattering, and signatures for the triple P-T-P scattering. However, T-P and P-T-P shoulders together, calculated by CTMC at forward angles, form a structureless monotonic spectrum. This finding is in agreement with experiment.

Three-body effects in the fragmentation of D_{2} by slow, highly-charged xenon

Kinematically complete data and five-body classical trajectory Monte Carlo calculations are presented for fragmentation of ${\mathrm{D}}_{2}$ by slow ${\mathrm{Xe}}^{26+}$ ions. For strongly perturbing collisions, two types of three-body effects are identified. The largest, due to interactions between the undissociated molecule and the dipole field of the projectile, is compatible with a two-step fragmentation picture. A smaller effect, due to quadrupolelike and higher multipole interactions between the dissociating fragments and the projectile field, extracts internal energy from the exploding molecule and is incompatible with a two-step picture.

Velocity dependence of single-electron capture for the 0.4–5-keV/amuAr8+−Cs(6s)collision system

The single-electron capture (SEC) process which occurs in ${\mathrm{Ar}}^{8+}$-$\mathrm{Cs}(6s)$ collisions is experimentally studied, in the 0.4--5-keV/amu energy range, by optical spectroscopy in the near UV and visible wavelength range (200--600 nm). The classical-trajectory Monte Carlo (CTMC) method is also used to determine the state-selective electron-capture cross sections. For high collision energies, strong lines corresponding to $\ensuremath{\Delta}n=1$--4 transitions from $n=7$ to 13 states with large angular momentum values of Ar VIII and $\ensuremath{\Delta}n=0$ transitions from $n=5$ states are observed. For low collision energies, together with the lines observed for high collision energies, lines corresponding to transitions from states with low-$l$ values $(10s,$ $11s,$ and $13s)$ are detected. Production cross sections for the most populated levels $(n=9,$ 10, and 11) are determined and compared with the previous experimental data of Martin et al. [Phys. Rev. A 46, 1316 (1992)] and Denis et al. [Phys. Rev. A 50, 2263 (1994)], and with the CTMC calculations. From molecular structure calculations which are performed for the ${{\mathrm{Ar}}^{7+}+\mathrm{Cs}{}}^{+}$ molecular system, our results are analyzed in terms of dynamical couplings between the relevant molecular channels involved in the electron-capture process. Polarization degrees for SEC lines corresponding to transitions between high-$l$ values states are also measured. The comparison with those calculated from the CTMC results provides information about the Zeeman sublevel distributions.

Classical trajectory Monte Carlo calculations of electron capture and ionization in collisions of multiply charged ions with elliptical Rydberg atoms

We have performed classical trajectory Monte Carlo (CTMC) studies of electron capture and ionization in multiply charged (Q=8) ion-Rydberg atom collisions at intermediate impact velocities. Impact parallel to the minor and to the major axis, respectively, of the initial Kepler electron ellipse has been investigated. The important role of the initial electron momentum distribution found for singly charged ion impact is strongly disminished for higher projectile charge, while the initial spatial distribution remains important for all values of Q studied.

Multiple ionization in fast ion-atom collisions: simultaneous measurement of recoil momentum and projectile energy loss

We report on the first experiment that measures simultaneously the full momentum vector of recoil ions and projectile energy loss and scattering angle in ion-atom collisions. We studied multiple ionization in the collisions of 0.83-MeV/u O7+ with Ne. Recoil ions ( Ne(q+), q = 1-8) were detected in coincidence with single capture to O6+. The results give the first experimental evidence for the increase of the average electron energy with increasing recoil charge state q. The average ejection angle shows a dramatic decrease with q. Results are compared with n-electron classical trajectory Monte Carlo calculations.

Large angular-momentum changing in a short half-cycle pulse interaction with a Rydberg atom

We show that, in contrast to multiphoton absorption in atoms, the remote region from a nucleus is dominant in the process of a half-cycle pulse interaction with a Rydberg atom, and that this interaction produces a very large change in the angular momentum of the electron. We have found good agreement between classical trajectory Monte Carlo, semiclassical, and quantum-mechanical calculations for the energy distribution of the electron.