Classical Trajectory Monte Carlo Model Research Articles

Interaction of Protons with Noble-Gas Atoms: Total and Differential Cross Sections

We present a classical treatment of the ionization and electron-capture processes in the interaction of protons with neutral noble-gas atoms, namely, Ne, Ar, Kr, and Xe. We used a three-body classical-trajectory Monte Carlo (CTMC) method to calculate the total (TCS) and differential (DCS) cross sections of single-electron processes. The Garvey-type model potential was employed in the CTMC model to describe the collision between the projectile and the target, accounting for the screening effect of the inactive electrons. The TCSs are evaluated for impact energies in the energy range between 0.2 keV and 50 MeV for a number of sub-shells of the targets. The ionization DCS are evaluated for an impact energy of 35 keV, focusing on the outer sub-shells only. We found that our ionization and electron-capture TCSs are in very good agreement with the previous theoretical and experimental data for all targets. Moreover, we presented single (SDCS)- and double (DDCS)-differential cross sections as a function of the energy and ejection angle of the ionized electron for all collision systems.

Wavelength Dependence of Atomic Excitation for Ar Subject to Intense Midinfrared Laser Pulses

We report experimental and theoretical investigations of wavelength dependence of Rydberg state excitation (RSE) process of Ar subject to intense laser fields. By simultaneously measuring ionization and RSE yields of Ar atoms subject to strong laser fields at a series of wavelengths, we obtain the wavelength scaling law of the ratio of Ar* over Ar+ with respect to the laser intensity, and this result can be well reproduced by a nonadiabatic model, but not by the classical-trajectory Monte Carlo model. Our results indicate that the nonadiabatic corrections of the photoelectron tunneling exit and tunneling probability play a significant role at shorter wavelengths. Analysis shows that the wavelength dependence phenomenon is due to the interplay of the nonadiabatic effect, wave-packet diffusion and Coulomb focusing effect of the liberated electron.

The optimized field amplitude ratio for nonsequential double ionization by counter-rotating two-color circularly polarized fields

With a classical trajectory Monte Carlo model, we systematically study the laser intensity and field amplitude ratio dependence of nonsequential double ionization by counter-rotating two-color circularly polarized fields (800 and 1600[Formula: see text]nm). The results show that the optimized field amplitude ratio changes with the laser intensity, which is attributed to the shift of the most probable amplitude ratio of electron returning with the laser intensity. Moreover, the laser intensity-dependent double ionization probability curve shows a remarkable dip in the transition region between the nonsequential and sequential channels. It can be well explained by the reduction of the probability of electron returning with the increase of the laser intensity.

Controlling Magnetic and Electric Nondipole Effects with Synthesized Two Perpendicularly Propagating Laser Fields

Nondipole effects are ubiquitous and crucial in light-matter interaction. However, they are too weak to be directly observed. In strong-field physics, motion of electrons is mainly confined in transverse plane of light fields, which suppresses the significance of nondipole effects. Here, we present a theoretical study on enhancing and controlling the nondipole effect by using the synthesized two perpendicularly propagating laser fields. We calculate the three-dimensional photoelectron momentum distributions of strong-field tunneling ionization of hydrogen atoms using the classical trajectory Monte Carlo model and show that the nondipole effects are noticeably enhanced in such laser fields due to their remarkable influences on the sub-cycle photoelectron dynamics. In particular, we reveal that the magnitudes of the magnetic and electric components of nondipole effects can be separately controlled by modulating the ellipticity and amplitude of driving laser fields. This novel scenario holds promising applications for future studies with ultrafast structured light fields.

C6+ -impact ionization of uracil at MeV/u impact energies: The role of the multiple-ionization channel

In this work, total and differential ionization cross sections of uracil ionized by ${\mathrm{C}}^{6+}$ projectiles are calculated by extending an adaptative classical trajectory Monte Carlo model recently introduced in the ion-${\mathrm{H}}_{2}\mathrm{O}$ collisions context. Calculated cross sections are contrasted and benchmarked against available experimental and theoretical data at impact energies in the MeV/u range. Present results are found in good agreement with the reported experimental data at different levels of differentiability. In addition, the electron emission contributions arising from single and multiple electron ionization are explicitly determined and their partial dominance analyzed in terms of the specific angular and/or energetic ranges.

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.

Nonadiabatic strong field ionization of noble gas atoms in elliptically polarized laser pulses.

We present theoretically obtained photoelectron momentum distributions (PMDs) for the strong field ionization of argon in an elliptically polarized laser field at a central wavelength of 400 nm. Three different theoretical approaches, namely, a numerical solution of the time-dependent Schrödinger equation (TDSE), a nonadiabatic model, and a classical-trajectory Monte Carlo (CTMC) model are adopted in our calculations. From the TDSE calculations, it is found that the attoclock offset angle (most probable electron emission angles with respect to the minor axis of the laser's polarization ellipse) in the PMD increases with rising ATI order. While this result cannot be reproduced by the CTMC model, the nonadiabatic model achieves good agreement with the TDSE result. Analysis shows that the nonadiabatic corrections of the photoelectron initial momentum distribution (in both longitudinal and transverse directions with respect to the tunneling direction) and nonadiabatic correction of the tunneling exit are responsible for the ATI order-dependent angular shift.

Target electron removal in C5+ + H collision

We present target ionization and charge exchange cross sections in a collision between C5+ ion and H atom. We treat the collision dynamics classically using a four-body classical trajectory Monte Carlo (CTMC) and a four-body quasi-classical Monte Carlo (QCTMC) model when the Heisenberg correction term is added to the standard CTMC model via model potential. The calculations were performed in the projectile energy range between 1.0 keV/amu and 10 MeV/amu. We found that the cross sections obtained by the QCTMC model are higher than that of the cross sections calculated by the standard CTMC model and these cross sections are closer to the previous experimental and theoretical data. Moreover, for the case of ionization, we show that the interaction between the projectile and the target electrons plays a dominant role in the enhancement of the cross sections at lower energies.

Excitation cross sections in a collision between two ground-state hydrogen atoms

We present excitation cross sections in collision between two ground state hydrogen atoms using a four-body classical trajectory Monte Carlo model. Calculations were performed for impact energies in the range between 1.0 keV and 100 keV where the cross sections are highly relevant to the interest of the fusion research. Beside the total excitation cross sections for target and projectile we also present partial excitation cross sections into the 2s and 2p states of the target. The partial excitation cross sections are compared with the previously obtained theoretical and experimental results.

Cross section scaling for the ionization of H2O by highly charged ions

SynopsisA classical trajectory Monte Carlo model that explicitly considers the ten electrons of the H2O molecule is used to study electron production in collisions involving bare ions. Present results are contrasted to the reported experimental data and to other theoretical results obtained by means of distorted wave models. Focus is made on the energy range 100 (keV/amu)/ZP-1000 (keV/amu)/ZP along which a simple scaling for the net cross section is introduced.

The role of multiple ionization in fast highly charged ions collisions on H2O

SynopsisAn adaptive classical trajectory Monte Carlo model that explicitly considers the eight electrons cor-responding to the valence molecular orbitals of the H2O molecule is introduced. In this dynamical model, the electrons’ binding energies change throughout the collision ensuring the proper energy deposition by the projectile for multiple electron removal. Present results are relevant to the ion-therapy program, specially at irradiation planning stages in which detailed information on the electronic emission spectra are needed as input data.

Strong-field tunneling ionization in the relativistic regime

We study the photoelectron energy and momentum distributions of strong-field tunneling ionization in the relativistic regime. Using the relativistic strong-field approximation, we have derived the position of the tunnel exit, the initial momentum distributions at the tunnel exit, and the instantaneous ionization rate when the electron tunnels through the Coulomb barrier in the relativistic regime. Since the tunneling electron energy is of the order of 1% of the rest of its mass, those nonadiabatic tunneling coordinates are quite different from the nonrelativistic case. We further incorporate the nonadiabatic relativistic tunneling coordinates into the classical trajectory Monte Carlo model and have calculated photoelectron energy and momentum distributions by accurately considering the field distribution in the focus of relativistic femtosecond laser pulses. We show that the nonadiabatic tunneling effect and the focal field distribution are very crucial to modeling strong-field ionization in the relativistic regime because the quiver radius of electrons can be as large as the beam waist.

Angular momentum distribution in strong-field frustrated tunneling ionization

Using the classical-trajectory Monte Carlo model, we have theoretically studied the angular momentum distribution of frustrated tunneling ionization (FTI) of atoms in strong laser fields. Our results show that the angular momentum distribution of the FTI events exhibits a double-hump structure. With this classical model, we back traced the tunneling coordinates, i.e., the tunneling time and initial transverse momentum at tunneling ionization. It is shown that for the events tunneling ionized at the rising edge of the electric field, the final angular momentum exhibits a strong dependence on the initial transverse momentum at tunneling. While for the events ionized at the falling edge, there is a relatively harder recollision between the returning electron and the parent ion, leading to the angular momentum losing the correlation with the initial transverse momentum. Our study suggests that the angular momentum of the FTI events could be manipulated by controlling the initial coordinates of the tunneling ionization.

Energy-dependent angular shifts in the photoelectron momentum distribution for atoms in elliptically polarized laser pulses

We measure the photoelectron momentum distributions from atoms ionized by strong elliptically polarized laser fields at the wavelengths of 400 and 800 nm, respectively. The momentum distributions show distinct angular shifts, which sensitively depend on the electron energy. We find that the deflection angle with respect to the major axis of the laser ellipse decreases with the increase of the electron energy for large ellipticities. This energy-dependent angular shift is well reproduced by both numerical solutions of the time-dependent Schr\odinger equation and the classical-trajectory Monte Carlo model. We show that the ionization time delays among the electrons with different energies are responsible for the energy-dependent angular shifts. On the other hand, for small ellipticities, we find the deflection angle increases with increasing the electron energy, which might be caused by electron rescattering in the elliptically polarized fields.

Control of the yield of surviving Rydberg atoms in strong-field ionization with two-color laser fields

We theoretically investigate the controllable yield of neutral excited atoms surviving in the tunneling ionization process using two-color fields with parallel and orthogonal polarizations. Using the classical-trajectory Monte Carlo model, we show that the yield of the surviving Rydberg atoms after tunneling ionization can be modulated by varying the relative phase of the two frequency components. Tracing back to the initial tunneling coordinates at the tunnel exit of the electrons that contribute to the surviving atoms, we find the distribution of these coordinates shifts with the relative phase and the polarization configuration of the two-color fields. The orthogonally polarized two-color field counterintuitively tends to recapture more electrons than the two-color field with parallel polarizations.

Classical trajectory Monte Carlo model calculations for ionization of the uracil molecule by impact of heavy ions

The ionization of the uracil molecule induced by heavy-ion impact has been investigated using the classical trajectory Monte Carlo (CTMC) method. Assuming the validity of the independent-particle model approximation, the collision problem is solved by considering the three-body dynamics of the projectile, an active electron and the molecule core. The interaction of the molecule core with the other two particles is described by a multi-center potential built from screened atomic potentials. The cross section differential with respect to the energy and angle of the electrons ejected in the ionization process has been calculated for an impact of 3.5 MeV u−1 ions. Total electron emission cross sections (TCS) are presented for () and projectiles as a function of the impact energy in the range from 10 keV u−1 to 10 MeV u−1. The dependence of the TCS on the charge state of the projectile has been investigated for 2.5 MeV u−1 () and () ions. The results of the calculations are compared with available experimental data and the predictions of other theoretical models: the first Born approximation with correct boundary conditions (CB1), the continuum-distorted-wave–eikonal-initial-state approach (CDW-EIS), and the combined classical-trajectory Monte Carlo–classical over-the-barrier model (CTMC-COB).

Classical-trajectory Monte Carlo model calculations for the antiproton-induced ionization of atomic hydrogen at low impact energy

The three-body dynamics of the ionization of the atomic hydrogen by 30 keV antiproton impact has been investigated by calculation of fully differential cross sections (FDCS) using the classical trajectory Monte Carlo (CTMC) method. The results of the calculations are compared with the predictions of quantum mechanical descriptions: The semi-classical time-dependent close-coupling theory, the fully quantal, time-independent close-coupling theory, and the continuum-distorted-wave-eikonal-initial-state model. In the analysis particular emphasis was put on the role of the nucleus-nucleus (NN) interaction played in the ionization process. For low-energy electron ejection CTMC predicts a large NN interaction effect on FDCS, in agreement with the quantum mechanical descriptions. By examining individual particle trajectories it was found that the relative motion between the electron and the nuclei is coupled very weakly with that between the nuclei, consequently the two motions can be treated independently. A simple procedure is presented by which the NN interaction effect can be included into the calculations carried out without it.

Development and evaluation of a many-electron–multicenter classical-trajectory Monte Carlo model in charge-exchange processes involving collisions of multiply charged ions and CO

A many-electron--multicenter classical-trajectory Monte Carlo model is developed and tested in charge-exchange studies involving projectiles with charges from $+$3 to $+$10 and the CO molecule. The present model is contrasted against simpler single-center and independent-atom approaches. Total and state-selective charge-exchange cross sections are presented and are compared to recent data from the Jet Propulsion Laboratory where available.

Cross sections for bare and dressed carbon ions in water and neon

The paper presents calculated cross sections for bare and dressed carbon projectiles of charge states q (0 to 6) with energies 1–104 keV u–1 impacting on molecular water and atomic neon targets. The cross sections of water are of interest for radiobiological studies, but there are very few experimental data for water in any phase, while those for liquid water are non-existent. The more extensive experimental database for the neon target made it possible to test the reliability of the model calculations for the many-electron collision system. The current calculations cover major single and double electronic interactions of low and intermediate energy carbon projectiles. The three-body classical trajectory Monte Carlo (CTMC) method was used for the calculation of one-electron transition probabilities for target ionization, electron capture and projectile electron loss. The many-electron problem was taken into account using statistical methods: a modified independent event model was used for pure (direct) and simultaneous target and projectile ionizations, and the independent particle model for pure electron capture and electron capture accompanied by target ionization. Results are presented for double differential cross sections (DDCS) for total electron emission by carbon projectile impact on neon. For the water target, we present the following: single differential cross sections (SDCS) and DDCS for single target ionization; total cross sections (TCS) for electron emission; TCS for the pure single electronic interactions; equilibrium charge state fractions; and stopping cross sections. The results were found to be in satisfactory agreement with the experimental data in many cases, including DDCS and SDCS for the single target ionization, TCS for the total electron emission and TCS for the pure single electron capture. The stopping cross sections of this work are consistent with the other model calculations for projectile energies ≥800 keV u–1, but smaller than the other calculations at lower energies. The discrepancy arises from the inclusion of all carbon charge states and coupling between electron capture and target ionization channels, while other models use an average projectile charge. The CTMC model presented here provides a tool for cross section calculations for low and intermediate energy carbon projectiles. The calculated cross sections are required for Monte Carlo track structure simulations of full-slowing-down tracks of carbon ions. The work paves the way for biophysical studies and dosimetry at the cellular and subcellular levels in the Bragg peak area of a therapeutic carbon ion beam.

State-selective electron capture in He++ H2collisions at intermediate impact energies

State-selective single electron capture in collisions of He${}^{+}$ with H${}_{2}$ molecules is investigated using the cold-target recoil-ion momentum spectroscopy technique. The energy range considered is 6.25 keV/amu (projectile velocity ${v}_{p}$ $=$ 0.5 a.u.) to 50 keV/amu (${v}_{p}$ $=$ 1.41 a.u.). In addition, we explore the transverse recoil momentum distributions that provide direct access to the angular scattering of the receding projectile. The present experimental data are contrasted to the theoretical results obtained by means of the classical trajectory Monte Carlo model with which we find good overall agreement in the energy range explored.