Classical Trajectory Monte Carlo Approach Research Articles

Low-energy positronium scattering from O2

The total cross section of positronium (Ps) scattering from molecular oxygen has been measured in the velocity range 0.27--1.50 a.u. (energy range 2--61 eV) and has been found to be close to the corresponding equivelocity electron cross section above 0.87 a.u. $(20\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$, as previously found by Brawley et al., [Science 330, 789 (2010)]. However, below this value the cross section for positronium is observed to exceed that for electrons by up to a factor of 4 at the lowest energy. Measurements are compared to the predictions of low-energy resonant peaks in the elastic-scattering cross section calculated within a free-electron-gas model refined by applying corrections to the correlation energy for the interaction between Ps and the electron gas. Additionally, cross sections for ${\mathrm{O}}_{2}^{\ensuremath{-}}$ formation and positronium breakup have been calculated using a classical-trajectory Monte Carlo approach. Comparisons are made with earlier calculations and discussed in terms of both experimental and theoretical uncertainties.

Electron emission from water vapor under the impact of 250-keV protons

Absolute double differential cross sections (DDCS) of low-energy electron emission from water molecule were measured upon collisions with 250-keV protons for emission angles between 30--150 degrees. The electrons having energies between 1 and 600 eV were detected by using hemispherical electrostatic analyzer. The single differential (SDCS) and total cross section (TCS) were calculated by integrating the DDCS and SDCS, respectively. The measured DDCS, SDCS, and TCS were compared with the classical trajectory Monte Carlo (CTMC) model, using a dynamical approach in which a time-dependent screening is considered. The continuum-distorted-wave eikonal-initial state (CDW-EIS) theoretical model has also been used to explain the energy and angular distribution data. The angular distribution of the DDCS are very well reproduced by the CTMC approach. The TCS calculated by the CTMC model matches better with the measured values as compared to the CDW-EIS estimation. The forward-backward angular asymmetry parameter was also estimated to test the validity of the state-of-the-art theoretical models used. Finally the recently developed CDW-EIS calculations considering a residual target dynamic charge (DC-CDW-EIS) is shown to provide an improved agreement with the experiments compared to the CDW-EIS. The present data and interpretation should provide inputs towards energy loss calculations required for the radiobiology involved in the hadron therapy of cancer.

Net Electron Capture in Collisions of Multiply Charged Projectiles with Biologically Relevant Molecules

A model for the description of proton collisions from molecules composed of atoms such as hydrogen, carbon, nitrogen, oxygen and phosphorus (H, C, N, O, P) was recently extended to treat collisions with multiply charged ions with a focus on net ionization. Here we complement the work by focusing on net capture. The ion–atom collisions are computed using the two-center basis generator method. The atomic net capture cross sections are then used to assemble two models for ion–molecule collisions: An independent atom model (IAM) based on the Bragg additivity rule (labeled IAM-AR), and also the so-called pixel-counting method (IAM-PCM) which introduces dependence on the orientation of the molecule during impact. The IAM-PCM leads to significantly reduced capture cross sections relative to IAM-AR at low energies, since it takes into account the overlap of effective atomic cross sectional areas. We compare our results with available experimental and other theoretical data focusing on water vapor (H2O), methane (CH4) and uracil (C4H4N2O2). For the water molecule target we also provide results from a classical-trajectory Monte Carlo approach that includes dynamical screening effects on projectile and target. For small molecules dominated by a many-electron atom, such as carbon in methane or oxygen in water, we find a saturation phenomenon for higher projectile charges (q=3) and low energies, where the net capture cross section for the molecule is dominated by the net cross section for the many-electron atom, and the net capture cross section is not proportional to the total number of valence electrons.

Classical simulation of spin-tagged collisional ionization at near-threshold energies

In this paper, we develop a spin dependent classical trajectory Monte Carlo approach to investigate the spin-tagged collisional ionization process. With the help of anti-symmetrized Gaussian wave packets, an effective interaction potential between the two spin-tagged electrons is derived to mimic the spin associated quantum effect of Pauli exclusion principle. Our model is applied to investigate the spin dependent collisional ionization of e–H system. The results are in good agreement with experimental data, ab initio quantum-mechanical calculations as well as a variety of characteristics of the Wannier theory for near-threshold ionization. In contrast, the popular Fermionic molecular dynamics model overestimates the total ionization cross section as high as ten times and predicts a totally inversed ionization spin asymmetry contrary to experimental results. Further applications of our model to laser-assisted collisional ionization are demonstrated and some interesting results are presented.

Positronium formation from positron impact on hydrogen and helium targets

Charge-exchange cross sections are presented for collisions of positrons with hydrogen and neutral and singly ionized helium targets using a variant of the classical trajectory Monte Carlo approach. As a check on the method a comparison is made with the corresponding proton results. An extended error analysis is presented. Reasonable agreement with available experimental data is found, and the charge-exchange cross section for positrons on ${\text{He}}^{+}$ is predicted.

Classical treatment of ion-H2O collisions with a three-center model potential

We present calculations of cross sections for one- and two-electron processes in collisions of ${\mathrm{H}}^{+}$, He${}^{2+}$, and ${\mathrm{C}}^{6+}$ with water molecules in the framework of the Franck-Condon approximation. We employ an independent-electron method and a classical trajectory Monte Carlo approach. Anisotropy effects related to the structure of the target are explicitly incorporated by using a three-center model potential to describe the electron-H${}_{2}$O${}^{+}$ interaction. We derive scaling laws with respect to the projectile charge. We also estimate cross sections for molecular fragmentation subsequent to electron removal.

Electric-field-induced dissociation of heavy Rydberg ion-pair states

A classical trajectory Monte Carlo approach is used to simulate the dissociation of H(+)⋅⋅⋅F(-) and K(+)⋅⋅⋅Cl(-) heavy Rydberg ion pairs induced by a ramped electric field, a technique used experimentally to detect and probe ion-pair states. Simulations that include the effects of the strong short-range repulsive interaction associated with ion-pair scattering are in good agreement with experimental results for Stark wavepackets probed by a ramped field, demonstrating that many of the characteristics of field-induced dissociation can be well described using a quasi-classical model. The data also show that states with a given value of principal quantum number (i.e., binding energy) can dissociate over a broad range of applied fields, the exact field being governed by the initial orbital angular momentum and orientation of the state.

Total cross sections for ionizing processes induced by proton impact on molecules of biological interest: A classical trajectory Monte Carlo approach

In the current work, we present a study of ionizing interactions between protons and molecular targets of biological interest like water vapour and DNA bases. Total cross sections for single and multiple ionizing processes are calculated in the independent electron model and compared to existing theoretical and experimental results for impact energies ranging from 10 keV/amu to 10 MeV/amu. The theoretical approach combines some characteristics of the classical trajectory Monte Carlo method with the classical over-barrier framework. In this “mixed” approach, all the particles are described in a classical way by assuming that the target electrons are involved in the collision only when their binding energy is greater than the maximum of the potential energy of the system projectile–target. We test our theoretical approach on the water molecule and the obtained results are compared to a large set of data and a reasonable agreement is generally observed specially for impact energies greater than 100 keV, except for the double ionization process for which large discrepancies are reported. Considering the DNA bases, the obtained results are given without any comparison since the literature is till now very poor in terms of cross section measurements.

Data on cross-sections for Stark broadening of radio recombination lines: non-perturbative all-multipole classical calculations

The Stark broadening of hydrogen radio recombination lines (RRLs), observed from galactic H II regions, is controlled by inelastic collisions with charged particles. There is a dramatic discrepancy—up to several hundred percent—between cross-sections of inelastic electronic collisions (causing the radiative transitions between the Rydberg levels) calculated by various authors. This dramatic discrepancy in cross-sections leads to a significant discrepancy in spectral line widths of RRLs. In this paper, we address two problems: (i) whose results for the cross-sections of the radiative transitions between the Rydberg levels are the most reliable and should be recommended to astrophysicists-observers for their analysis of the measured profiles of RRLs? (ii) How can one allow for all major processes relevant to the Stark broadening of RRLs (transitions between discrete levels, ionization, charge exchange) within a single/unified theoretical approach? For this purpose, we employed calculations in frames of the classical trajectory Monte Carlo approach. We obtained the results for a broad range of velocities of the charged particles (both electrons and protons), including the region most difficult for the analytical description, where the velocities of both the incident particle and the atomic electron have the same order of magnitude. By benchmarking analytical and semi-empirical results of other authors to our calculations (which are non-perturbative and do not use the dipole approximation), we have found which one is the most accurate and should be recommended to astrophysicists-observers for their analysis of the measured profiles of RRLs.

Collisional survival of antiprotonic helium atoms

We investigate the collisional survival of antiprotonic p ̄ He + atomcules in pure helium from a detailed ab initio analysis of their intermolecular interaction. After averaging over classical p̄ orbits, we attribute the collisional stability of thermalized atomcules to the existence of a high activation barrier due to Pauli repulsion. Our model predicts the reduction of the barrier for outer p̄ orbits, thus accounting for the quenching of high n states by He atoms. We also investigate the thermalization stage of newly formed atomcules from a classical trajectory Monte Carlo approach. Our results support the destruction of the states with n⩾41, as well as the strong depopulation of all n<41 layers, with a quenching rate of 50% at least. Assuming a statistical distribution of newly formed atomcules with respect to their initial angular momentum, we account for the 3% observed trapping fraction of metastable states.

Classical study of single-electron capture and ionization processes inAq++(H,H2)collisions

Using a classical method, cross sections in ${A}^{q+}+(\mathrm{H},{\mathrm{H}}_{2}) (q=1,\dots{},8)$ collisions are obtained for impact energy ranges $9 {\mathrm{keV}\mathrm{}\mathrm{amu}}^{\ensuremath{-}1}--6.4 {\mathrm{MeV}\mathrm{}\mathrm{amu}}^{\ensuremath{-}1}$ (ionization), $--600 {\mathrm{KeV}\mathrm{}\mathrm{amu}}^{\ensuremath{-}1}$ (electron capture). For bare ion impact on H, comparison to experiment and to the results of accurate semiclassical calculations shows that total and partial cross sections, as well as transition probabilities, obtained with the classical trajectory Monte Carlo approach, are more accurate than usually assumed. From the characteristics of the mechanisms, we are led to use our data as estimates for the case of dressed-ion impact at the higher nuclear velocities. We successfully apply a very simple model for ${\mathrm{H}}_{2}$ targets, in which the relevant quantities are the charge of the projectile and the vertical ionization potential of the molecule. For practical purposes, we give scaling laws to benchmark $({\mathrm{H}}^{+},{\mathrm{He}}^{2+})$ cases, and for ionization we relate them, at higher $v,$ to the behavior of the transition probabilities.

Theoretical description of fast kinetic electron emission in ion-surface collisions

We present a microscopic description of the emission of fast electrons in glancing-angle ion-surface collisions. We employ a classical trajectory Monte Carlo approach that treats the primary production of kinetic electrons in close collisions and their subsequent transport through the surface region on the same footing. Dynamic image interactions and multiple scattering are explicitly included. As an application, we analyze the ejected electron spectra over a broad range of electron energies and emission angles for 0.2--0.5-MeV/u Li ions interacting with SnTe(001) surfaces. Good agreement is found with experiment for the shape of the spectrum of forward-ejected electrons containing prominent structures such as the convoy electron peak and the binary ridge.

Transport of fast electrons near surfaces

We have developed a microscopic model to study emission of fast electrons is glancing-angle ion-surface collisions using a classical trajectory Monte Carlo approach. Our model accounts for dynamic image interactions and multiple scattering near the surface. We show that a sizeable fraction of the convoy peak is produced by ionization of electrons transiently bound to the impinging ion. Properties of the collision kernels near the surface are discussed. Good agreement is found with our recent coincidence experiments for 0.2–0.5 MeV/u Li ions interacting with SnTe(001) surfaces.

Electron removal from atomic hydrogen by collisions with fully stripped oxygen ions

Cross sections for charge transfer and impact ionization in ${\mathrm{O}}^{8+}$ + H collisions have been calculated in the range of collision velocities (0.1-10) \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ cm/sec. At the lower velocities, up to 1.2 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ cm/sec, charge-transfer cross sections were determined by means of the perturbed-stationary-state method in the impact-parameter approximation with a selective basis set of adiabatic one-electron two-center orbitals. The charge-transfer cross section increases monotonically in this region, attaining a value of 8 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$ at 1.2 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ cm/sec. Rotational coupling was found to be an important mechanism which contributes significantly to the large cross sections in the molecular regime. Thus the present results are at least a factor of 2 larger than previous Landau-Zener calculations. Above 2.2 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ cm/sec, a classical-trajectory Monte Carlo approach was used to compute both charge-transfer and ionization cross sections. At velocities above 5 \ifmmode\times\else\texttimes\fi{} ${10}^{8}$ cm/sec, ionization becomes the dominant electron-removal process.