Classical Trajectory Monte Carlo 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.

Classical-trajectory model for ionizing proton-ammonia molecule collisions: the role of multiple ionization

We use an independent electron model with semi-classical approximation to electron dynamics to investigate differential cross sections for electron emission in fast collisions of protons with ammonia molecules. An effective potential model for the electronic orbitals is introduced, and utilized in the context of the classical-trajectory Monte Carlo (CTMC) approach for single-electron dynamics. Cross sections differential in electron emission angle and energy are compared with experimental data. Compared to previous scattering-theory based quantum-mechanical results the time-dependent semi-classical CTMC approach provides results of similar quality for intermediate and high ionized electron energies. We find some discrepancies in the total cross sections for q-fold ionization between the present model and independent-atom-model calculations. The double ionization cross sections are considerably larger than recent experimental data which are derived from coincidence counting of charged fragments. The calculated triple ionization cross sections exceed the experimental coincidence data for q = 3 by several orders of magnitude at intermediate energies.

Determining the Orbital Angular Momentum of a Vortex Beam Using Strong Field Ionization

While interferometric methods exist for classifying vortex states of light, these techniques usually require destroying the beam of interest to determine the light’s OAM. A recent two-color pump-probe experiment employed strong field ionization and beam sculpting to classify vortex beams. Here, we propose an alternative strong-field method for distinguishing OAM states of light which does not require beam sculpting and instead utilizes a noncollinear terahertz standing wave to probe ionized electrons. We then use classical trajectory Monte Carlo (CTMC) methods to simulate strong-field ionization of helium under this configuration with the terahertz field both on and off. We find that the resulting electron momenta distributions can be used to extract the OAM of the beam, as long as the vortex beam spot size does not exceed 1/4 the terahertz pulse’s wavelength.

Calculation of Ionization, Excitation and Electron Capture Cross Sections for Be4+ + H(2s,2p) Collisions.

A computational study of Be4+ + H(2s,2p) collisions has been carried out employing the Classical Trajectory Monte Carlo (CTMC) method for the impact energy range from 20 keV/u to 1000 keV/u. The integral n partial cross sections for H(n) excitation and Be3+(n) electron capture and, the total ionization and electron capture cross sections are calculated and compared to recent semiclassical results. A general good agreement is observed for the n partial and total electron capture and ionization cross sections. The comparative study of the three inelastic processes show no significant differences between both excited targets.

Interaction of electrons and positrons with two-dimensional artificially generated proton lattice and with carbon lattice

A many-body classical trajectory Monte Carlo (CTMC) method is applied in the study of scattering probabilities of electrons and positrons after interacting with a two-dimensional (2D) artificially generated, uniform lattice, composed of fixed protons. We used different lattice parameters between the protons for different simulations, where the projectiles have kinetic energies of 500 and 1000 eV. We found a very strong focusing of electrons and a very strong defocusing of the positrons at lower lattice parameters. Furthermore, we found, these effects get weaker with increasing lattice parameters. Interesting changes took place at lattice parameters 2 and 3 au. which are close to the lattice parameter between carbon atoms in graphene of value 2.68 au. We also performed a simulation of a defective lattice by removing some protons and noticed distinguishable changes in the spectra compared to the spectra of an ideal lattice. This comparison may open a way for the detection of lattice defects in real samples.

Impact ionization of highly charged ion-atom collisions considering strong magnetic field and plasma screening effect

The impact ionization process of target is a crucial issue in the study of Heavy Ion Beam (HIB)-driven Magnetized Inertial Fusion (MIF). The collision systems between heavy projectile ions (Xeq+, Biq+, Uq+) and light target atoms/ions (H, D, T, 3He, 3He+, 11B) are promising candidate reactions for fusion power. In this study, the impact ionization process in medium-energy (ranges 1–100 MeV/u) is studied numerically based on the extended Classical-trajectory Monte Carlo (CTMC) method, where the effects of projectile charge state, external magnetic field and plasma screening on the single ionization process are considered. The results show that the existed external magnetic field results in a decrease of the yield of ionized high-energy electrons, whereas the yield of backward emitted electrons is increased. The effect of plasma screening on the ionization process is shown to be determined by the competition between the screening charge of projectile ion and the target nucleus. Thus, a significant decrease of ionization cross section is found in the low energy region since the screening charge of projectile ion is dominant. However, the screening effect of target nucleus charge is dominant in high energy region, where a significant increase of ionization cross sections is found.

Charge transfer and ionization cross-sections in collisions of singly charged lithium ions with helium and nitrogen atoms

We present a non-perturbative classical treatment of the charge transfer and ionization processes in collisions between singly charged lithium ions with helium and nitrogen atomic targets. Single capture and single ionization total cross sections are calculated using a three-body classical trajectory Monte Carlo (CTMC) method in which the interaction between the collision partners is described by a Garvey-type model potential. The cross sections are evaluated for collision energies between 20 keV and 100 MeV. In particular, we found excellent agreement between our results and the available experimental data for the case of the single capture of He(1s) by Li+ ions. In addition, our CTMC results are in a reasonable agreement with the experimental results for collision energies higher than 200 keV for single capture of N(2p) atoms by Li+. Furthermore, we present single ionization cross sections for both collision systems.

Antiproton collisions with excited positronium

We present results of calculations of several processes resulting from positronium (Ps) collisions with antiprotons: antihydrogen formation, Ps breakup, and ${n}_{\mathrm{Ps}}$-changing collisions. Calculations utilize the quantum convergent close-coupling (CCC) method and the classical trajectory Monte Carlo (CTMC) method. We identify a region of Ps principal quantum numbers ${n}_{\mathrm{Ps}}$ and Ps energies where the classical description is valid and where the CCC calculations become computationally too expensive. This allows us to present the most complete and reliable set of cross sections in a broad range of ${n}_{\mathrm{Ps}}$ and initial orbital momentum quantum numbers ${l}_{\mathrm{Ps}}$ which are necessary for experiments with antihydrogen at CERN.

The effects of Heisenberg constraint on the classical cross sections in proton hydrogen collision

The interaction between a proton and a ground state hydrogen atom is studied using a standard three-body classical trajectory Monte Carlo (CTMC) and a quasi-classical trajectory Monte Carlo (QCTMC) model where the quantum feature of the collision system is mimicked using the model potential in the Hamiltonian as was proposed by Kirschbaum and Wilets (1980 Phys. Rev. A 21 834). The influence of the choice of the model potential parameters (α, ξ) on the initial radial and momentum distribution of the electron are analyzed and optimized. We found that although these distributions may not be as close to the quantum results as the distribution of standard CTMC results, we can find the combination of the (α, ξ) where the calculated cross sections are closer to the experimental data and closer to the results obtained quantum mechanically. We show that the choice of 3 < α < 5 is reasonable. To validate our observation, we present cross sections for ionization, excitation, charge exchange (CX), and state selective CX to the projectile bound state. Calculations are carried out in the projectile energy range between 10 and 1000 keV amu−1.

Study of the effect of higher-order dispersions on photoionisation induced by ultrafast laser pulses applying a classical theoretical method

We investigated the effect of higher order dispersion on ultrafast photoionisation with Classical Trajectory Monte Carlo (CTMC) method for hydrogen and krypton atoms. In our calculations we used linearly polarised ultrashort 7 fs laser pulses, 6.5 times 10^{14} mathrm {W/cm^{2}} intensity, and a central wavelength of 800 nm. Our results show that electrons with the highest kinetic energies are obtained with transform limited (TL) pulses. The shaping of the pulses with negative second- third- or fourth- order dispersion results in higher ionisation yield and electron energies compared to pulses shaped with positive dispersion values. We have also investigated how the Carrier Envelope Phase (CEP) dependence of the ionisation is infuenced by dispersion. We calculated the left-right asymmetry as a function of energy and CEP for sodium atoms employing pulses of 4.5 fs, 800 nm central wavelength, and 4 times 10^{12}mathrm {W/cm^{2}} intensity. We found that the left-right asymmetry is more pronounced for pulses shaped with positive Group Delay Dispersion (GDD). It was also found that shaping a pulse with increasing amounts of GDD in absolute value blurs the CEP dependence, which is attributed to the increasing number of optical cycles.

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.

Projectile electron loss, excitation and de-excitation cross section database in a collision between two hydrogen atoms in the impact energy range between 50 keV–5.0 MeV, Part I: Target is in ground state

We present projectile electron loss, excitation, and de-excitation cross-sections database for H(nl)+H(1s) collision system. A four-body classical trajectory Monte Carlo (CTMC) and a quasi-classical trajectory Monte Carlo (QCTMC) methods were employed in the projectile energy range between 50 keV to 5.0 MeV.

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.

State-selective electron capture cross sections in collision between fully striped ions and ground state hydrogen atom—Classical treatment of the collision

We present a state-selective electron capture cross sections database from the ground state hydrogen atom. A standard three-body classical trajectory Monte Carlo (CTMC) and quasi-classical trajectory Monte Carlo (QCTMC) models were employed for impact energies between 10 and 200 keV/amu. The projectile ions are H+, He2+, Li3+, Be4+, B5+, C6+, N7+, and O8+. The cross sections are tabulated for each value of the final quantum numbers n, l, m, summed over m for the given n and l and over l and m for the given n. The maximum quantum number nmax is set to 4 for H+, He2+ and Li3+, as well as to 5 for Be4+, B5+, C6+, N7+ and O8+, respectively.

Classical and semiclassical calculations of state-selective cross sections for electron capture and excitation in Be4++H(2s) collisions

A computational study of ${\mathrm{Be}}^{4+}+\mathrm{H}(2s)$ collisions has been carried out. Two computational models have been employed: the classical trajectory Monte Carlo (CTMC) method and the numerical solution of the time-dependent Schr\"odinger equation (GTDSE). The integral $n$ and $nl$ partial cross sections for H excitation and electron capture, obtained with both methods, are compared at two energies: 20 and 100 keV/u. It is shown that the CTMC, with an improved hydrogenic initial distribution, provides excitation cross sections in good agreement with the numerical calculation for excitation to $\mathrm{H}(n$) with $n&gt;3$. The agreement between the corresponding $nl$ partial cross sections from both methods is less satisfactory at 100 keV/u, where there is a transition from the low-energy mechanism that involves an increase of the populations with $l$, and the high-energy mechanism, where the dipole-allowed transitions are dominant. The electron capture cross sections calculated with the CTMC method do not depend on the initial distribution and show a reasonable agreement with the GTDSE ones, which supports the use of the CTMC method to calculate electron capture cross sections into highly excited levels and total cross sections. The mechanism of the electron capture process is discussed and CTMC calculations of the ionization process are also presented.

Charge transfer in collisions of H&lt;sup&gt;+&lt;/sup&gt;, Li&lt;sup&gt;3+&lt;/sup&gt;, Be&lt;sup&gt;4+&lt;/sup&gt; and O&lt;sup&gt;7+&lt;/sup&gt; ions with He atom based on 4-classical trajectory Monte Carlo method

The classical trajectory Monte Carlo (CTMC) method is a common method to study the charge-transfer and impact-ionization cross sections for the collisions between ions and atoms, and the heavy particle collision in astrophysics and laboratory plasma environment. Here in this work, we use the 4-CTMC method to study a four-body collision process including two bound electrons, and the Hamiltonian equation of the four-body dynamic system is solved numerically. The single/double electron ionization and capture cross sections are calculated for collisions of high charge state ions (Li&lt;sup&gt;3+&lt;/sup&gt;, Be&lt;sup&gt;4+&lt;/sup&gt; and O&lt;sup&gt;7+&lt;/sup&gt;) with helium atom in a wide range of projectile energy. The calculation results show that the results from the 4-CTMC method and the experimental measurements are in better agreement in a projectile energy range of 50－200 keV/amu for proton-helium collision system. In addition, for incident ions with high charge state, the results calculated by the 4-CTMC method are in better agreement with the experimental measurements or other theoretical values in a projectile energy range of 100－500 keV/amu. Though the double ionization and capture cross sections calculated by 4-CTMC or 3-CTMC method are higher than the experimental results due to ignoring the electron correlation, the results from the 4-CTMC method are in better agreement with the experimental results.

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.

Wavelength-Dependent Features of Photoelectron Spectra from Nanotip Photoemission

If a metal nanotip is irradiated with the light of a wavelength much larger than the nanotip’s radius of curvature, optical near-fields become excited. These fields are responsible for distinct strong-field electron dynamics, due to both the field enhancement and spatial localization. By classical trajectory, Monte Carlo (CTMC) simulation, and the integration of the time-dependent Schrödinger equation (TDSE), we find that the photoelectron spectra for nanotip strong-field photoemission, irradiated by mid-infrared laser pulses, present distinctive wavelength-dependent features, especially in the mid- to high-electron energy regions, which are different from the well known ones. By extracting the electron trajectories from the CTMC simulation, we investigate these particular wavelength-dependent features. Our theoretical results contribute to understanding the photoemission and electron dynamics at nanostructures, and pave new pathways for designing high-energy nanometer-sized ultrafast electron sources.

Double differential distributions of e-emission in ionization of N2 by 3, 4 and 5 keV electron impact

We report the measurement of the absolute double differential cross sections (DDCS) of secondary electrons emitted due to the ionization of N2 molecule in collisions with fast electrons having energies between 3 and 5 keV. The emitted electrons with energies from 1–500 eV have been measured for different forward and backward emission angles. The measured DDCS have been compared with the state-of-the-art first Born approximation with correct boundary condition (CB1) model calculations as well as with the classical trajectory Monte Carlo (CTMC) method. From the measured DDCS, the single differential cross sections (SDCS) as a function of the emission energies have been computed and eventually the total ionization cross sections (TCS) have been derived. The TCS values are also compared with a semi-empirical calculation, namely, the CSP-ic (complex scattering potential-ionization contribution) model.

Dynamic charge state distributions of 5 MeV Xe20+ ions penetrating through gaseous argon target

Dynamic distribution of charge state of highly charged 131Xe20+ (Z = 54) ions penetrating through the different areal density of gaseous argon target are measured, with the energy of 5 MeV (38.2 keV/u). Two individual stages of charge state are observed: pre-equilibrium stage, where the distribution moves toward the lower charge state with increasing the density of target; equilibrium stage, where the average charge state remains constant as 3.5. The experimental average charge states are compared with the theoretical predictions by the semi-empirical formulas and the classical-trajectory Monte Carlo (CTMC) respectively. A strong dependence of the average charge on energy loss of projectiles is observed too.