Transport Cross Sections Research Articles

A semiempirical model for low energy electron–atom transport cross sections: The case of noble gases

A semiempirical approach to describe low energy electron–atom transport cross sections of easy implementation and reproduction is presented. The heart of the model is an energy independent two-parameter potential that was adjusted to reproduce the accurate total cross sections for He, Ne, Ar and Kr, measured with a threshold photoelectron source technique from meV up to 20 eV. Once the potential was conceived, the model was validated by comparing the values obtained for the calculated scattering lengths and phase shifts with the respective quantities previously reported in the literature. We close the article by presenting the momentum transfer and viscosity cross sections. Good agreement is found when compared to the similar data obtained from swarm experiments, from phase shifts according to differential cross section measurements and to the cross sections reported by sophisticated ab initio relativistic many-body calculations. Tables for the phase shifts and cross sections are provided for direct use and applications.

Deeper-band electron contributions to stopping power of silicon for low-energy ions.

This study provides accurate results for the electronic stopping cross sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross section, and induced-density approach. Recent experimental findings [Ntemou et al., Phys. Rev. B 107, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and the observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the deeper silicon bands for ion velocities approaching zero (v → 0). This indicates that mechanisms such as "elevator" and "promotion," which can dynamically excite deeper-band electrons, are active, enabling a localized free-electron gas to emulate ion energy loss, as pointed out by Lim et al. [Phys. Rev. Lett. 116, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross sections at very low velocities are considered to be a signature of the contributions of deeper-band electrons.

Influence of the ion core on relaxation processes in dense plasmas

AbstractThe effect of an ionic core on the temperature relaxation in dense hot plasma of beryllium is studied using the pseudpotential model by Gericke et al [Phys. Rev. E 2010, 81, 065401(R)]. Employing the screened version of the ion pseudpotential [by Ramazanov et al, Phys. Plasmas 2021, 28 (9), 092702], we computed the quantum transport cross section for the electron‐ion collisions in dense beryllium plasma, where screening is taking into account using the density response function in the long‐wavelength regime. The results for the transport cross section are used to compute a generalised Coulomb logarithm and electron‐ion collision frequency. Utilizing the latter, we show the effect of the ionic core on the temperature relaxation. To understand the role of the ionic core, we compare the results with the data computed considering ions as point‐like charges.

Transport cross sections and collision integrals for N(4S)–O(3P) and N(4S)–O(1D) interactions in high-temperature air plasmas

Collisions between nitrogen (N) and oxygen (O) play a crucial role in determining transport coefficients in high-temperature atmospheres of Earth and planetary. In this study, the momentum transfer, viscosity, third-moment, and fourth-moment transport cross sections for the N(4S)–O(3P) and N(4S)–O(1D) interactions are reported in the collision energy range of 10−6–10 Hartree based on the classical and semiclassical methods. The new and accurate potential energy curves for N–O interactions, which are used to provide the input for calculations of the cross sections, are calculated based on the state-of-the-art ab initio method. The classical and semiclassical collision integrals are provided at 300–50 000 K, and the results support the calculation of transport coefficients in a third-order approximation. In particular, the collision data for the N(4S)–O(1D) interaction based on ab initio points are reported for the first time. The calculated transport cross sections and collision integrals are helpful for studies of modeling the high-temperature air plasmas.

MASAP: A package for atomic scattering amplitude in solids

We present the MsSpec Atomic Scattering Amplitude Package (MASAP), composed of a computation program and a graphical interface to generate atomic scattering amplitude (ASA) of an atom, either isolated or embedded in an environment, at any chosen energy of the impinging electron up to ≈15 KeV. The ASA is calculated using an effective, complex optical potential which provides damping effects in the scattering process in a fully relativistic framework. Optionally, scalar relativistic and non-relativistic approximations are also available to assess their applicability to a given problem. In order to describe electron propagation in solids we suggest to replace ASA's based on Plane Waves (PW) scattering with effective ASA's based on curved Spherical Waves (SW) using truncated-overlapped potentials of the Muffin-Tin (MT) type constructed according to the Mattheiss prescription. The graphical user interface generates not only ASA data files providing atomic Differential Cross Sections (DCS) but also files of related quantities such as total Cross Section (CS), both elastic and inelastic, atomic tl-matrices and phase shifts. We found in general that the imaginary part of the optical potential enhances the calculated elastic DCSs in the forward direction compared to the same potential without the imaginary part, a feature related to the optical theorem, but gives rise to a lower intensity at all other directions as expected due to the damping effect of the complex part of the potential. We show calculated differential and transport Cross Sections for aluminum and gold atoms both in isolation and in crystals with the Face-Centered-Cubic (FCC) structure. Program summaryProgram Title: MASAPCPC Library link to program files:https://doi.org/10.17632/gtxp3mn5hs.1Licensing provisions: Apache 2.0Programming language: FORTRAN 77, Python3External routines:•SciPy (https://www.scipy.org)•Atomic Simulation Environment (https://wiki.fysik.dtu.dk/ase/)•h5py (https://www.h5py.org)•wxPython (https://www.wxpython.org)Nature of problem: Calculation of atomic scattering amplitudes of scattered electrons by an embedded atom in a solid including damping and relativistic effects. Comparison between ASA's in an isolated atomic system and a solid. Introduction of an effective ASA for electrons propagating in a solid derived from Multiple Scattering Theory.Solution method: Potential scattering theory. Muffin-tin approximation. Superposition of atomic electron densities obtained by self-consistent Dirac-Fock atomic calculations. Hedin-Lundqvist potential as an optical potential. Fully relativistic theory, with scalar-relativistic and non-relativistic approximations for comparison.Additional comments including restrictions and unusual features: Even though the program can perform calculations at impinging electron energies up to ≈15 Kev, DCS calculations are recommended in the range 50 : ≈1500 eV both in the case of isolated atoms and atoms embedded in solids, since this interval is more suitable for studying the details of the atomic potentials in their environment.In the case of solids, at energies lower than ≈50 eV, the details of the electronic structure might be important, whereas in the case of isolated atoms this range might suffer from the neglect of the polarization potential and coupling to available inelastic channels. In this respect an option to add an empirical form of a polarization potential to investigate its effects is available to the interested user.

Transport cross sections and collision integrals for C+(2P)–H(2S), C(3P)–H+(1S), C(1D)–H+(1S), and C+(4P)–H(2S) interactions

Transport collision integrals of interacting atoms or ions play a crucial role in modeling transport properties of high-temperature gases and plasmas. Here, we obtained the potential energy curves (PECs) of CH+ using the internally contracted multireference configuration interaction method with the Davidson correction (icMRCI+Q) method. The PECs were then used to investigate the transport cross sections and transport collision integrals for the C+(2P)–H(2S), C(3P)–H+(1S), C(1D)–H+(1S), and C+(4P)–H(2S) interactions using the classical mechanical approach and a quantum mechanical treatment of the scattering with Wentzel–Kramers–Brillouin approximations of the scattering phase shifts. The transport cross sections were obtained in the collision energy of 10−6–1 hartree, which were used to compute transport collision integrals for C–H+ and C+–H systems over the temperature range of 500–40 000 K. The C(1D)–H+(1S) and C+(4P)–H(2S) interactions are considered for the first time. Our transport collision integrals can provide data references for computing transport properties of high-temperature plasmas involving C and H atoms/ions.

Linear Source Approximation in MPACT for Efficient and Robust Multiphysics Whole-Core Simulations

This work seeks to improve upon an existing formulation of the Method of Characteristics (MOC) with a Linear Source Approximation (LSA) for problems that use nonconstant cross sections like multiphysics feedback and the two-dimensional/one-dimensional (2D/1D) formulation. The previous LSA formulation for lattice physics calculations uses precomputed coefficients that are dependent on the multigroup total or transport cross sections, and the method can be demonstrated to lack robustness when there are negative sources. In this paper, the method is reformulated to eliminate the cross-section dependence of the precomputed coefficients without adding additional operations, and a more robust formulation is also developed to prevent the calculation of negative sources. Thus, the method has increased efficiency and robustness in multiphysics and 2D/1D simulations. The new method is implemented in the MPACT code and tested on several light water reactor problems. The numerical results show that with the new Linear Source formulation, the number of mesh elements can be significantly reduced while maintaining accuracy, resulting in reduced run time and memory usage. Furthermore, our results demonstrate improved efficiency for cases with depletion, thermal-hydraulic feedback, and in three-dimensional (2D/1D) calculations without any robustness issues.

Benchmarking of Stainless Steel Cube Neutron Leakage in Research Center Rez

Integral experiments covering neutron leakage from geometrically simple assemblies with a 252Cf source inside are very valuable tools usable in the validation of transport cross-section data since geometric uncertainties play a much smaller role in simple geometric assemblies than in complex assemblies as for example reactor pressure vessel geometry. Since 252Cf spontaneous fission is a standard neutron source, the uncertainties connected with the source neutron spectrum can be even neglected. The paper refers to validation efforts of neutron leakage from an ~50 × 50 × 50-cm stainless steel block in the Research Center Rez. Both the neutron leakage flux at a distance of 1 m from the center of the cubical assembly using stilbene spectrometry and activation rates at different positions of the assembly were evaluated. In addition to experiments, main sources of uncertainty were identified and evaluated. The results of the stilbene measurements are consistent with the activation measurement results.

Elastic and electron capture processes in slow He+–He collision

Aims. The elastic and electron-capture processes of He+ ions with ground helium atoms are very important for studies in astrophysics. It is essential to have reliable state-selective charge transfer, elastic, and transport cross-sections, along with the corresponding reaction rate coefficient data, especially for low collision energies. Methods. We investigated the elastic and non-radiative electron-capture processes in He+(1s)–He(1s2) collisions are investigated employing the full quantum-mechanical molecular orbital close-coupling method. The adopted ab initio adiabatic potentials and coupling matrix elements were obtained by a multi-reference single- and double-excitation configuration interaction approach. Results. We computed the elastic, charge-transfer, and transport cross-sections in the energy range of 0.01–2500eVamu−1 and the reaction rate coefficient in the temperature range of 10–109 K. Good agreement was achieved when compared to the available experimental and theoretical results. Shape resonance, Regge, and Glory oscillations were also found in the elastic and charge transfer cross-sections in the energy region considered here.

Scattering of electron and positron by HCN: a theoretical investigation

A theoretical investigation of differential, integrated elastic, inelastic, transport (momentum transfer & viscosity), grand total (elastic+inelastic) and total ionisation cross-sections along with the Sherman functions for the scattering of electron and positron by hydrogen cyanide (HCN) in the energy range 1 e V − 1 MeV are presented in this report. We perform calculations using the single scattering independent atom model (IAM) and IAM with screening correction (IAMS). The scattering observables are calculated using a complex optical model potential in the framework of the Dirac partial wave analysis (DPWA). The inclusion of screening correction to the IAM appreciably improves the cross-sections, especially at low-impact energies. Our calculated results are compared with the available experimental and theoretical works found in the literature. Our present computational data agree well with prior results.

Hibridon: A program suite for time-independent non-reactive quantum scattering calculations

Hibridon is a program package to solve the close-coupled equations which occur in the time independent quantum treatment of inelastic atomic and molecular collisions. Gas-phase scattering, photodissociation, collisions of atoms and/or molecules with flat surfaces, and bound states of weakly-bound complexes can be treated. From calculation of the S matrix, integral and differential cross sections, stereodynamic (alignment and steric asymmetry) cross sections, as well as more specialized quantities, such as transport and tensor cross sections, and cross sections between hyperfine levels, and photodissociation amplitudes can be obtained. The program is capable of treating closed-shell systems where the nuclear motion takes place on a single Born-Oppenheimer potential as well as open-shell systems for which the nuclear motion can evolve on several coupled electronic (Born-Oppenheimer) potentials. Program summaryProgram Title: HibridonCPC Library link to program files:https://doi.org/10.17632/sk9zcvz8vs.1Developer's repository link:https://doi.org/10.5281/zenodo.7551616Licensing provisions: GPLv3Programming language: Fortran 90External routines/libraries: LAPACK, BLASNature of problem: Solution of the time-independent Schrödinger equation for the inelastic scattering of atoms and molecules, for the photodissociation of molecules, and for the ro-vibrational motion of weakly bound molecular complexes.Solution method: The scattering wavefunction is expanded in a set of internal states of the system, constructed as direct products of the internal states of one (or both) fragments and angular functions which describe the rotation of one collision partner about the other. The Schrödinger equation for the nuclear motion is solved by determining the expansion coefficients as a function of the interparticle separation starting from the short-range classically forbidden region outwards to the asymptotic region. The S matrix is given by the asymptotic behavior of the wavefunction. Integral and differential cross sections, as well as other scattering and photodissociation quantities are calculated from the S matrix.

A new efficient approach for the calculation of cross-sections with application to Yukawa potential

Large-scale and systematic calculations of scattering amplitudes and cross-sections for charged particle collisions are of fundamental importance for understanding the physical properties of materials in different research fields. However, the elaborated theoretical methods for cross-sections are generally restricted to a finite range of impact energies. Here, we present an efficient approach for the calculation of the scattering amplitude and cross-sections ranging from low to high collision energies based on the variable phase method, where the Wentzel–Kramers–Brillouin and Born approximations for scattering phase shifts (SPSs) are incorporated into the numerical algorithm to alleviate the computational cost. For this purpose, quantitative criteria for the validity of these approximations are established based on the properties of the turning points of the potentials. For different scattering potentials, the corresponding planes can be established as a guideline to select the optimal combination for calculating the scattering amplitude and cross-section. The demand for quantum treatment of phase shifts is reduced by one to two orders of magnitude, which strongly benefits the computation of cross-sections for high-energy scattering. It has been found that the quantum treatment for SPSs is necessary near the quantum states involving quantum tunneling and resonance. To testify the validity of the approach, the SPSs and also transport cross-sections are calculated for Yukawa potentials, and good agreements are obtained in comparison with other available high-precision calculations. The proposed numerical approach can be straightforwardly generalized to other scattering potentials and permits one to efficiently calculate the scattering cross-sections for a large energy range.

The elastic scattering cross sections of the N[formula omitted]-H and N-H[formula omitted] collisions for the transport theory

The transport cross sections and integrated cross sections are calculated for interactions of hydrogen and nitrogen atoms and ions (in the ground and excited states) for use in plasma science and hypersonic flows theory. The data for the transport cross sections are given in the energy range typically needed (or broader) for those applications: 10−6-37 hartree (around 2.7⋅10−5eV-1 keV). The reported cross sections are calculated from the high quality ab initio potential energy curves with additional extrapolation for highly repulsive region. The methods and energy range are discussed in the context of LXCat and IAEA (ALADDIN and CollisionDB) databases. The uncertainty of data is also estimated.

A Theoretical Study of Scattering of e± by Tl Atom

This article incorporates details of our calculations of the observable quantities for the scattering of electrons and positrons from a post transition metal Thallium (Tl), in the energy range of 1 eV ≤ Ei ≤ 1 MeV, using the relativistic Dirac partial wave (phase-shift) analysis employing a complex optical-potential. Absolute differential, integrated elastic and inelastic, transport, total ionization, and total cross sections and a thorough study of the critical minima in the elastic differential cross sections along with the associated angular positions of the maximum polarization points in the Sherman function are provided to study the collision dynamics. The optical potential model incorporates the interactions of the incident electron and/or positron with both the nucleus and the bound electrons of the target atom. In-depth analyses of the spin asymmetry, which are sensitive to phases related interference effect, brought on by the various ingredients of the lepton-atom interaction, are also presented. The performance of the current approach to explain the observations, with the exception of the extremely low energy domain, is shown by a comparison of the previous experimental and theoretical results on this target atom.

Trajectory dependence of electronic energy-loss straggling at keV ion energies

Accurate knowledge of ion energy deposition in materials is imperative for a wealth of scientific and technological applications. Here, the authors measure the energy-loss straggling, i.e., the energy distribution variance of transmitted ions, for $k\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}V$ ions of H, He, B, and Si in Si membranes. Straggling exhibits a significant trajectory dependence for all ions. Studying the velocity dependence of electronic energy-loss straggling and calculating transport cross sections, the authors obtain strong evidence for contributions of electron-promotion events to ion energy loss at low velocities.

Экспериментальное изучение дрейфового движения молекул SF-=SUB=-6-=/SUB=- под действием излучения CO-=SUB=-2-=/SUB=--лазера

Experiments were continued to study the physical nature of the drift motion of SF6 molecules under the action of radiation from a repetitively pulsed CO2-laser. To explain the physical nature of the effect, such phenomena as a change in the transport cross-section during laser excitation of molecules, the phenomenon of optical tweezers, thermal diffusion are considered. However, the most reasonable physical explanation of the nature of this effect is the fractionation of a gas mixture as a result of gas dynamic diffusion at the front of a cyclically expanding gas (a variant of barodiffusion).

Experimental study of the drift motion of SF-=SUB=-6-=/SUB=- molecules under the action of CO-=SUB=-2-=/SUB=--laser radiation

Experiments were continued to study the physical nature of the drift motion of SF6 molecules under the action of radiation from a repetitively pulsed CO2-laser. To explain the physical nature of the effect, such phenomena as a change in the transport cross-section during laser excitation of molecules, the phenomenon of optical tweezers, thermal diffusion are considered. However, the most reasonable physical explanation of the nature of this effect is the fractionation of a gas mixture as a result of gas dynamic diffusion at the front of a cyclically expanding gas (a variant of barodiffusion). Keywords: fractionation of gas mixture, thermal diffusion, optical tweezers, barodiffusion.

Bremsstrahlung on noble gases at low energies

A detailed analysis of the bremsstrahlung spectrum at nonrelativistic electron scattering on argon and xenon is carried out. It is shown that the approximate formulas widely used for the description of bremsstrahlung spectra lead to predictions that significantly differ from the exact results. In the limit when the photon frequency tends to zero, a rigorous proof of the relationship between the spectrum of the bremsstrahlung with a transport cross section of electron scattering on an atom is given. This proof does not require any assumptions about the dependence of the scattering phases on energy. For electron energies lower than the luminescence threshold, it is shown that the predictions for a number of radiated photons obtained by the exact formula are in good agreement with the available experimental data.

Analytical Formulas for Approximating Cross Sections of Electron Collisions with Hydrogen, Noble Gases, Alkali and Other Atoms

This paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electrons with noble gases, alkali and other atoms. For the selected sets of experimental and theoretical data, optimal analytical formulas are found, and approximation coefficients are calculated. The obtained semi-empirical formulas reproduce the values of the transport (diffusion), excitation and ionization cross sections for noble gases. Much attention is paid to the ionization cross sections of metal atoms, which are often present as an impurity in gas-discharge plasma. The approximation formulas reproduce the values of the ionization cross sections for hydrogen, metal and other elements in a wide range of energies with accurate orders of errors of the available theoretical and experimental data. For some elements with a two-hump plot of the dependence of the ionization cross section on the collision energy, it is proposed to use a two-term formula that takes into account ionization from both external and internal shells.

Coulomb logarithm and the Dreicer field in a dense semiclassical plasma

AbstractWe obtained an expression for the Coulomb logarithm for a dense semiclassical plasma based on momentum transport cross sections using an effective interaction potential. It was shown that for densities and temperatures corresponding to the dense semiclassical plasma our results are in good agreement with MD simulations. We applied the Coulomb logarithm for the calculation of the Dreicer field. The case of dense non‐thermal Lorentzian semiclassical plasma was considered, too.