Elastic Collision Cross Sections Research Articles

A Quantum Mechanical Treatment of Electron Broadening in Strong Magnetic Fields. II. Large Enhancements due to Exchange Interactions

We present a quantum treatment of atom–electron collisions in magnetic fields, demonstrating the significant importance of including the effect of exchange that arises from two interacting electrons. We find strange behaviors that are not encountered in collisions without a magnetic field. In high magnetic fields, exchange can lead to orders of magnitude enhancements of collision cross sections. Additionally, the elastic collision cross sections that involve the ground state become comparable to those involving excited states, and states with large orbits have the largest contribution to the collisions. We anticipate significant changes to spectral line broadening in neutron star surfaces and atmospheres.

Electron transport characteristics in water under electrostrictive effect

The transport characteristics of electrons are crucial for the generation and development of pulse discharge in water. In this work, we develop a physical model of electron transport that consides elastic and inelastic collision cross sections. The purpose of this study is to investigate frequency variations of elastic collisions, ionization and excitation collisions with different initial electron energy values, and to explore the characteristic of electron energy loss in water. The Monte Carlo method is employed to track structure characteristics of electron transmission and scattering under varying energy values. The results show that the electrons of lower energy (~20 eV) are significantly impacted by the water molecule scattering, hence their transmission capacities are weakened. When the incident energy of electron reaches 100 eV, the scattering deviation distance is roughly equivalent to the transmission depth, about 6–8 nm, and the maximum deviation angle <i>θ</i><sub>shift</sub> ~ 60°. When the electron incident energy is in a range of 10–1000 eV, the number of elastic collisions is much greater than the number of excitation and ionization collisions, and the number of ionization collisions and excitation collisions increases significantly with the increase of electron energy. The higher the electron incident energy, the greater the energy loss is. However, the energy loss decreases sharply with the extension of penetration distance. For the ionization collision, the average ionization energy loss, <i>W</i>, decreases rapidly with the increase of electron energy, and ultimately maintains at a level of 20–30 eV, which is consistent with the experimental results reported.

Electromagnetic interaction models for Monte Carlo simulation of protons and alpha particles

Electromagnetic interactions of protons and alpha particles are modeled in a form that is suitable for Monte Carlo simulation of the transport of charged particles. The differential cross section (DCS) for elastic collisions with neutral atoms is expressed as the product of the DCS for collisions with the bare nucleus and a correction factor that accounts for the screening of the nuclear charge by the atomic electrons. The screening factor is obtained as the ratio of the DCS for scattering of the projectile by an atom with a point nucleus and the parameterized Dirac–Hartree–Fock–Slater (DHFS) electron density, calculated from the eikonal approximation, and the Rutherford DCS for collisions with the bare point nucleus. Inelastic collisions, which cause electronic excitations of the material, are described by means of the plane-wave Born approximation, with an empirical simple model of the generalized oscillator strength (GOS) that combines several extended oscillators with resonance energies and strengths determined from the atomic configurations and from the empirical mean excitation energy of the material. The contributions from inner subshells are renormalized to agree with realistic ionization cross sections calculated numerically from the DHFS self-consistent model of atoms by means of the plane-wave Born approximation. The resulting DCS allows analytical random sampling of individual hard inelastic interactions.

Low-Energy Electron and Positron Scattering by para-Difluorobenzene.

The Schwinger multichannel method is employed in calculations of the elastic integral and differential cross sections for collisions of low-energy electrons and positrons with para-difluorobenzene (1,4-C6H4F2). The present calculations involving electron scattering have been performed using both static-exchange and static-exchange plus polarization levels of approximation. Our results indicate the presence of three resonances of π*-character in the low-energy region and a fourth resonance, of σ*-character, at higher energy levels. With respect to the positron scattering, the calculations were conducted using the static plus polarization approximation at three different polarization levels. The present calculated electron and positron cross sections show a reasonable agreement with the total cross sections measured by Makochekanwa et al. (J. Phys. B, 2004, 37, 1841). It is also important to highlight that our computed integral cross section for electron scattering indicates the presence of a Ramsauer-Townsend minimum, while the integral cross section for positron scattering indicates the presence of a virtual state.

Elastic Neutrino–Atom Scattering as a Probe of Neutrino Millicharge and Magnetic Moment

Neutrino scattering on a target at low-energy transfer is one of the basic tools for searching for neutrino electromagnetic properties. We consider the effects of the neutrino millicharge and magnetic moment on the atomic recoil spectrum in elastic neutrino–atom scattering. The results of our calculations of differential cross sections for elastic collisions of tritium neutrinos with the H, 2H, 3He, and 4He atomic targets show that the corresponding experiments can achieve sensitivity to the indicated neutrino electromagnetic characteristics by orders of magnitude better than the available measurements of elastic neutrino–electron and neutrino–nucleus collisions.

The Role of Molecular Structure in Monte Carlo Simulations of the Secondary Electron Yield and Backscattering Coefficient from Methacrylic Acid.

In this paper, we show the influence of the chemical structure of four different conformers on the secondary electron emission and backscattering of an electron beam from a gel of methacrylic acid. The conformers have different permanent dipole moments, which determines the cross sections for elastic collisions with electrons. The cross sections are used in Monte Carlo simulations of an electron beam, which enters the gel of methacrylic acid. The secondary electron yield and the backscattering coefficient are computed as a function of the beam energy.

Effect of mixing CF4 with O2 on electron characteristics of capacitively coupled plasma

Effect of mixing CF4 with O2 on electron parameters in capacitively coupled RF plasma was studied. Adding CF4 gas to fixed O2 flow, electron energy probability functions were measured by a Langmuir probe method. As the CF4 gas was added, the decrease in the probability of low energy electrons was observed. The proportion of low energy electrons decreased gradually as the CF4 gas ratio increased, respectively. From electron energy probability functions, electron densities and electron temperatures were calculated. As the CF4 gas ratio increased, electron density decreased and electron temperature increased. Collision cross sections of low energy electrons can explain electron parameter behaviors. By the strong electron attachment of fluorine species which were generated from CF4, low energy electrons depleted by attachment, and the overall electron temperature increased. However, as the elastic collision cross section of CF4 is not different from that of O2, the heating mechanism and physics of high energy electrons did not change.

Positronium collisions with polar molecules

We calculate elastic and positronium (Ps) break-up cross sections for collisions of Ps with the polar molecules CO, HCl, and LiF in the fixed-nuclei approximation. We incorporate electron exchange and correlation for these processes by using the free-electron-gas model developed earlier for Ps scattering by rare-gas atoms, ${\mathrm{N}}_{2}$, ${\mathrm{O}}_{2}$, and ${\mathrm{CO}}_{2}$ molecules. The present target molecules provide a range of dipole moments from the weakly polar CO to the strongly polar LiF. We find that Ps scattering is similar to electron scattering when the cross sections are plotted as a function of projectile velocity for the targets with smaller dipole moments (CO, HCl). However, we do not see such a similarity for LiF which has a large dipole moment. Below the Ps break-up threshold we observe resonance structures similar to those obtained earlier for the other molecular targets that we have studied.

Elastic Electron Scattering by Diborane(6) and Diborane(4) Molecules

We present integral, differential, and momentum transfer cross sections for elastic electron collisions with the two most stable isomers of the B2H4 molecule, hereafter referred to as isomer I (C2v symmetry) and isomer II (D2d symmetry), and with the B2H6 molecule (D2h symmetry). The isomer I of B2H4 and the B2H6 molecule are known for their electrodeficiency in the "three-center two-electron" (3c-2e) bond, a region in which a hydrogen atom occupies a bridged position between two non-hydrogen atoms. The cross sections were computed by using the Schwinger multichannel method implemented with norm-conserving pseudopotentials, and the scattering calculations were carried out in the static-exchange and static-exchange plus polarization levels of approximation for energies from 0.1 to 50 eV. We discuss the presence of shape resonances in the scattering cross sections. We also made a direct comparison among the cross sections of these three targets.

ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

ECCPA: Calculation of classical and quantum cross sections for elastic collisions of charged particles with atoms

Higher order polarizabilities and the positron forward scattering problem: Convergence between calculated and measured cross sections in the very low energy regime

We have employed a well established correlation-polarization model potential to calculate the elastic cross sections for positron collisions with O2 , N2 and CO2 from 0.01 eV to Eps. The description of the outer component of the positron-molecule potential was improved introducing higher polarizability and the hyperpolarizabilities terms. The obtained cross sections were applied in the forward correction of the measured total cross sections and much improved convergence between the calculated elastic cross sections and the corrected measurements was found.

Elastic and Inelastic Cross Sections for Low-Energy Electron Collisions with ClF Molecule Using the R-Matrix Method

The ClF molecule belongs to an interhalogen family and is important in laser physics and condensed phase molecular dynamics. The elastic and excitation scattering cross sections are obtained in a fixed nuclei approximation using the UKRmol+ codes based on R-matrix formalism. The scattering calculations were performed in the static-exchange (SE), static-exchange-plus-polarisation (SEP), and close-coupling (CC) models. Three CC models with different target states were employed, namely, the 1-state, 5-states, and 12-states. In the CC model, the target states were represented by configuration interaction (CI) wavefunctions. A good agreement of dipole and quadrupole moments of the ground state was obtained with the experimental values, which indicates a good representation of the target modelling. The study predicted the existence of a shape resonance in the SE, SEP, and 5-states CC models. This resonance vanished in the 12-states CC model. The excitation cross sections from ground to the lowest two excited states were also reported. The elastic differential and momentum transfer cross sections were obtained in the 12-states CC models. The contribution of long-range interactions to elastic scattering was included via Born closure approach. The quantities like collision frequencies and rate coefficients were also presented over a wide range of electron temperatures. The ionization cross sections were computed using the binary-encounter-Bethe (BEB) model. The results were reported in C2v point group representation.

Nonthermal Messages from Thermal Planetary Atmospheric Systems

Light atmospheric gas constituents tend to evaporate from the planetary gravitational fields. The point is that not only the uppermost atmospheric layer contributes to this gas escape, but the lower layers contribute their share as well and give the outcoming particle flow a nonthermal, non-Maxwellian character. In this article we do study the outflow of hydrogen atoms from a planetary oxygen atmosphere assumed to be one-dimensionally stratified by the action of the planet‘s gravitational field. This outflow is modified by local elastic collisions of upwards flying H-atoms with the heavy major atmospheric background constituent, as in case of the terrestrial atmosphere, the monoatomic oxygen atoms. This shock-modulation of the upwards particle flow produces nonthermal kinetic features of the particle distribution which we want to decribe. Since angle-integrated elastic collision cross sections are velocity-dependent, falling off with the velocity v like (1/v), the occuring collision-modulation of the H-atom flow does change the kinetic velocity profile of the escaping H-atoms. Deeply down in the lower atmophere the local H-atoms, like the O-atoms as well, are in thermodynamical equilibrium characterized by Maxwell Boltzmann distributions with a common temperature TH = TO. Nevertheless, at the upper exobase border of the atmosphere the resulting H-atom escape flow is shown to be a nonMaxwellian, non-equilibrium flow with non-thermal escape-relevant properties. We describe this collisional modification of the H-escape flow and can quantify the upcome of kinetic non-equilibrium features like power laws in the H-distribution function. Thus, as we demonstrate in this article, this collisional modulation effect via velocity-dependent collision cross-sections acts as a typical process to convert equilibrium distributions into non-equilibrium distribution functions. On the basis of this new kinetic theoretical approach we then calculate the effective escape flux of H- atoms to open space, demonstrate its nonthermal character, and quantify its difference with respect to the classical Jeans escape value. We find that with the classical Jeans formula one slightly overestimates the actual escape flux by an amount that varies between 30 - 80 percent, depending on the temperature of the lower atmosphere of the planet which varies with the solar 10.7-cm- radioflux.

Slowdown and Heating of Interstellar Neutral Helium by Elastic Collisions Beyond the Heliopause.

Direct sampling of interstellar neutral (ISN) atoms close to the Sun enables studies of the very local interstellar medium (VLISM) around the heliosphere. The primary population of ISN helium atoms has, until now, been assumed to reflect the pristine VLISM conditions at the heliopause. Consequently, the atoms observed at 1 au by the Interstellar Boundary Explorer (IBEX) were used to determine the VLISM temperature and velocity relative to the Sun, without accounting for elastic collisions with other species outside the heliopause. Here, we evaluate the effect of these collisions on the primary ISN helium population. We follow trajectories of helium atoms and track their collisions with slowed plasma and interstellar hydrogen atoms ahead of the heliopause. Atoms typically collide a few times in the outer heliosheath, and only ~1.5% of the atoms are not scattered at all. We use calculated differential cross sections to randomly choose scattering angles in these collisions. We estimate that the resulting primary ISN helium atoms at the heliopause are slowed down by ~0.45 km s-1 and heated by ~1100 K compared to the pristine VLISM. The resulting velocity distribution is asymmetric and shows an extended tail in the antisunward direction. Accounting for this change in the parameters derived from IBEX observations gives the Sun's relative speed of 25.85 km s-1 and temperature of 6400 K in the pristine VLISM. Finally, this paper serves as a source of the differential cross sections for elastic collisions with helium atoms.

Elastic positron-uracil scattering cross sections

We report elastic integral and differential cross sections for positron collisions with uracil (${\mathrm{C}}_{4}{\mathrm{H}}_{4}{\mathrm{N}}_{2}{\mathrm{O}}_{2}$) for impact energies up to 10 eV. The cross sections were calculated employing the Schwinger multichannel (SMC) method in the static plus polarization approximation. The Born-closure procedure was applied to account for the long-range potential due to the permanent dipole moment of uracil. The present results are compared with experimental and theoretical data available in the literature, showing an overall good agreement with previously reported results. We also applied our differential cross sections to provide a correction to the total cross-section measurements by Anderson et al. [J. Chem. Phys. 141, 034306 (2014)] in order to account for the lack of angular resolution in the apparatus used by these authors. Besides, we applied a simple model employed by Franz and Gianturco [Phys. Rev. A 88, 042711 (2013)] to estimate the temperature effects on the uracil cross section. In particular, the level of agreement of the SMC differential cross sections as compared with the experimental findings is encouraging.

Single pencil beam benchmark of a module for Monte Carlo simulation of proton transport in the PENELOPE code.

PENH is a recently coded module for simulation of proton transport in conjunction with the Monte Carlo code PENELOPE. PENELOPE applies class II simulation to all type of interactions, in particular, to elastic collisions. PENH uses calculated differential cross sections for proton elastic collisions that include electron screening effects as well as nuclear structure effects. Proton-induced nuclear reactions are simulated from information in the ENDF-6 database or from alternative nuclear databases in ENDF format. The purpose of this work is to benchmark this module by simulating absorbed dose distributions from a single finite spot size proton pencil beam in water. Monte Carlo simulations with PENH are compared with simulation results from TOPAS Monte Carlo (v3.1p2) and RayStation Monte Carlo (v6). Different beam models are examined in terms of mean energy and energy spread to match the measured profiles. The phase-space file is derived from experimental measurements. Simulated absorbed dose distributions are compared to experimental data obtained with the ionization chamber array MatriXX 2D detector (IBA Dosimetry) in a water tank. The experiments were conducted with a clinical IBA pencil beam scanning dedicated nozzle. In all simulations a Fermi-Eyges phase-space representation of a single finite spot size proton pencil beam is used. In general, there is a good agreement between simulated results and experimental data up to a distance of 3cm from the central axis. In the core region (region where the dose is more than 10% of the maximum dose) PENH shows, overall, the smallest deviations from experimental data, with the largest radial rms (root mean square) smaller than 0.2. The results achieved by TOPAS and RayStation in that region are very close to those of PENH. For the halo region, that is the area of the dose distribution outside the core region reaching down to 0.01% of the maximum intensity, the largest rms achieved by TOPAS is always smaller than 0.5, yielding better results than the rest of the codes. The physics modeling of the PENELOPE/PENH code yields results consistent with measurements in the dose range relevant for proton therapy. The discrepancies between PENH appearing at distances larger than 3cm from the central-beam axis are accountable to the lack of neutron simulation in this code. In contradistinction, TOPAS has a better agreement with experimental data at large distances from the central-beam axis because of the simulation of neutrons.

Simulation of ion flux of actinides and uranium fission products in the plasma separator with a potential well

This work is devoted to the development of a plasma mass separation method with a potential well for spent nuclear fuel reprocessing. The configuration of the separation chamber with an axial magnetic field up to 0.25 T and a radial electric field up to 3 kV/m is considered. Using numerical simulation, we study the ion flux motion with the same mass composition as the spent nuclear fuel injected along magnetic field lines. The effect of fields and initial injection parameters on the spatial separation of actinides from uranium fission products is investigated. The simulation of the ion flux motion is also performed taking into account elastic collisions of ions with background gas atoms. Elastic collision cross sections for U+, Pu+, Cs+, and Sr+ ions in helium and argon are obtained theoretically. We show that in argon, the separation is possible up to a pressure of the order of 1 mTorr, while in helium, it is possible to separate elements by mass groups in the collisional regime at pressures up to about 10 mTorr.

Electron and Positron Scattering by the Formamide Molecule.

We report calculated elastic integral, differential, and momentum transfer cross sections for electron and positron collisions with the formamide (HCONH2) molecule, for impact energies up to 10 eV. We have used the Schwinger multichannel method in the static-exchange and static-exchange plus polarization approximation for collisions of electrons and the static plus polarization approximation for collisions of positrons. The Born-closure procedure was applied to account for the long-range potential due to the permanent dipole moment of formamide. We obtained the well-characterized π* shape resonance located at around 2.38 eV, which belongs to the A″ symmetry of the Cs point group. Our integral and differential cross sections for collisions of electrons were compared with the data available in the literature and showed a good qualitative agreement. To the best of our knowledge, no experimental and theoretical data are currently available for positron-formamide collision, so our present cross sections were compared with the cross sections of formic acid, which is also polar and is isoeletronic to formamide.

Nuclear effects in proton transport and dose calculations

Interactions of protons with nuclei are modeled in a form that is suitable for Monte Carlo simulation of proton transport. The differential cross section (DCS) for elastic collisions of protons with neutral atoms is expressed as the product of the Rutherford DCS, which describes scattering by a bare point nucleus, and two correction factors that account for the screening of the nuclear charge by the atomic electrons and for the effect of the structure of the nucleus. The screening correction is obtained by considering the scattering of the projectile by an atom with a point nucleus and the atomic electron cloud described by a parameterization of the Dirac-Hartree-Fock-Slater self-consistent electron density. The DCS for scattering by this point nucleus atom is calculated by means of the eikonal approximation. The nuclear correction to the DCS for elastic collisions is calculated by conventional partial-wave analysis with a global optical-model potential that describes the interaction with the bare nucleus. Inelastic interactions of the projectile with target nuclei are described by using information from data files in ENDF-6 format, which provide cross sections, multiplicities, and angle-energy distributions of all reaction products: light ejectiles (neutrons, protons, …), gammas, as well as recoiling heavy residuals. These interaction models and data have been used in the Monte Carlo transport code penh, an extension of the electron-gamma code penelope, which originally accounted for electromagnetic interactions only. The combined code system penh/penelope performs simulations of coupled electron-photon-proton transport. A few examples of simulation results are presented to reveal the influence of nuclear interactions on proton transport processes and on the calculation of dose distributions from proton beams.

Electron scattering from allene and 1,2-butadiene

The Schwinger multichannel method is employed to calculate elastic cross sections for electron collisions with allene (C3H4) and 1,2-butadiene (C4H6) molecules. Integral elastic and differential cross sections were obtained for both molecules in the static-exchange and static-exchange-polarization approximations, for energies from 0.1 eV to 10 eV. Both molecules have a π* shape resonance centered at 2.4 eV in the integral cross section, and a Ramsauer-Townsend minimum was found at around 0.34 eV in the allene cross section. The present differential elastic cross sections are compared between the two molecules and with the experimental and theoretical data available. Some of the features in the cross sections are analyzed and discussed in the context of the methylation effect, since the 1,2-butadiene molecule can be viewed as the methylated allene molecule. Electronic structure calculations are also performed in order to help in the interpretations of our results.