Viscosity Cross Sections Research Articles

Scattering of e∓ from H2O

SynopsisTheoretical differential, elastic, total, momentum transfer, viscosity cross sections and spin-polarization for the elastic scattering of e∓ by H2 O molecule in the energy range 10 eV-10 keV have been calculated. These calculations have been carried out within the framework the Dirac partial wave analysis. We have employed a complex optical potential and additivity rule (AR) to compute the cross sections. Present results reasonably agree with available experimental data and other theoretical findings.

Scattering of e± from N2 in the energy range 1 eV–10 keV

The differential, integrated elastic, inelastic, total, momentum transfer, viscosity, and ionisation cross sections for electron and positron scattering from the homonuclear diatomic nitrogen molecule over an incident energy range of 1 eV–10 keV are calculated using the additivity rule. Dirac partial wave analysis is employed to calculate the cross sections of the constituent atoms of molecules, using a complex optical model potential (OPM). Comparison of our results of the additivity rule with the available experimental data and other theoretical predictions is presented. Our findings produce reasonable results in intermediate and high energies.

Scattering of e∓ from ytterbium atoms

The differential, total, momentum transfer and viscosity cross sections for the elastic scattering of electrons and positrons by ytterbium atoms have been calculated. We have also calculated the total inelastic and ionization cross sections. In addition, the Sherman function S(θ) and the inelastic mean free paths have been determined for the scattering of both projectiles. The critical minima in the elastic differential cross sections (DCS) were determined from the analysis of the DCS and S(θ). These investigations have been carried out within the framework of two different theoretical approaches at the impact energies 1 eV–0.5 GeV for both projectiles. In the atomic domain the solution involves a complex projectile-atom optical potential while in the nuclear domain only the nuclear potential has been employed. Both approaches employ the Dirac partial wave analysis. Our results are in reasonable agreement with available experimental data and other theoretical findings. To the best of our knowledge, for positron scattering, there are no experimental data available in the literature.

Elastic scattering of electrons by Sr atom: a study of critical minima and spin polarization

Within the framework of the complex optical potential, the critical minima (CM) in the differential cross sections and the spin polarization in the elastic scattering of electrons by the Sr atom are studied in the energy range Ei = 1–1000 eV using the Dirac and Schrödinger partial wave methods. The two methods are, respectively, termed as the optical potential method of Dirac (OPMD) and optical potential method of Schrödinger (OPMS). The differential cross sections (DCSs), total cross sections (TCSs), momentum transfer cross sections (MTCSs), integral elastic cross sections (IECSs), viscosity cross sections (VCSs) and inelastic cross sections (INCSs) for e–Sr scattering are also calculated for the same energy range. In OPMD, the complex optical potential is composed of the static, exchange, polarization and absorption potentials. The OPMS potential, on the other hand, comprises the static, local exchange, polarization, spin-orbit, and absorption components. The number of CM points has been found to be respectively 7 and 5 with OPMD and OPMS methods in the DCSs of e–Sr scattering. The number of maximum spin polarization points observed is 13 and 10 for the OPMD and OPMS respectively. The energy dependence of TCS, MTCS, IECS, VCS, and INCS, studied in this work, show a non-monotonous pattern for energies beyond about 50 eV. So far as we are concerned, this is the first work for the study of CM in the DCSs of the e–Sr scattering as there are neither experimental nor theoretical studies published in the literature for the same.

E± Ar scattering in the energy range 1 eV ≤ Ei ≤ 0.5 GeV

A theoretical investigation on differential, integral, momentum transfer, viscosity cross sections and spin polarization for elastically scattered electrons and positrons from Ar atoms in the energy range 1 eV ≤ Ei ≤ 0.5 GeV is presented. In addition, we have studied the critical minima in the elastic differential cross sections, and the absorption, total and ionization cross sections. Two different theoretical approaches, depending upon the incident energy, are employed for solving the relativistic Dirac equation with the partial-wave decomposition. The solution of the relativistic equation involves the use of either complex optical-model potentials or only nuclear potentials at higher energies. A comparison of the present results with the available experimental data and other theoretical findings produces a reasonable agreement throughout the investigated energy range.

Total and Viscosity Cross Sections for Krypton Gas at Boiling Point

We have calculated total and viscosity cross sections for krypton gas at boiling point by using a Galitskii-Migdal-Feynman (GMF) formalism which is essentially an independent-pair model ‘dressed’ by a many-body medium. The interaction potential in our work is theHartree-Fock dispersion (HFD-B) potential.

A study of the critical minima and spin polarization in the elastic electron scattering by the lead atom

A complex optical potential, in the framework of Dirac partial wave analysis, is employed to study the minima in the differential cross sections (DCSs) and the spin polarization due to the elastic scattering of electron by Pb atom. In addition, integral, momentum-transfer, absorption, viscosity and total cross sections are also reported for the energy region 6 eV ≤ Ei ≤10 keV. This complex optical potential comprises the static, exchange, polarization and absorption components. We obtain, in total, 12 critical minima (CM) positions, where DCS attains its smallest values and 22 points with of the maximum values of spin polarization (MSP). CM and MSP are found to be correlated in terms of Ei and scattering angles where the spin-flip amplitude overrides the magnitude of their direct counterpart. As per as we know, there is neither any experimental nor any theoretical study on CM of e-Pb scattering available in the literature. A detailed comparison shows a good agreement between our predicted results with the available experimental and other theoretical findings.

Scattering Properties of Ground-State 23Na Vapor Using Generalized Scattering Theory

The scattering properties of ground-state 23Na vapor are investigated within the framework of the Galitskii–Migdal–Feynman formalism. Viewed as a generalized scattering theory, this formalism is used to calculate the medium phase shifts. The scattering properties of the system—the total, viscosity, spin-exchange, and average cross sections—are then computed using these phase shifts according to standard recipes. The total cross section is found to exhibit the Ramsauer–Townsend effect as well as resonance peaks. These peaks are caused by the large difference between the potentials for electronic spin-singlet and spin-triplet states. They represent quasi-bound states in the system. The results obtained for the complex spin-exchange cross sections are particularly highlighted because of their importance in the spectroscopy of the Na2 dimer. So are the results for the scattering lengths pertaining to both singlet and triplet states. Wherever possible, comparison is made with other published results.

Transport Properties of Spin-Polarized Atomic Hydrogen Using Generalized Scattering Theory

Our results for the scattering and thermophysical properties of spin-polarized atomic hydrogen \((\hbox {H}{\downarrow })\) have been presented in the temperature range 0.01–10 K using the Galitskii–Migdal–Feynman formalism. These results include the quantum second virial coefficient, the average total and viscosity cross sections, the viscosity, the diffusion coefficient, and the thermal conductivity. The calculations have been undertaken using three triplet-state potentials: Morse-type, Silvera and Born–Oppenheimer potentials. The Morse potential is less attractive and very simple, but less accurate to describe spin-polarized atomic hydrogen. That explains the differences between it and the other two potentials, which are clearly better. From the results of the average total cross sections, it is concluded the \(\hbox {H}{\downarrow }\) remains a gas even at low temperature. The viscosity, the thermal conductivity, and the diffusion coefficients of \(\hbox {H}{\downarrow }\) increase in all cases with increasing temperature.

BEAMDB and MolD – databases for atomic and molecular collisional and radiative processes: Belgrade nodes of VAMDC

We present two atomic and molecular (A&M) databases, MolD and BEAMDB, hosted by the SerVO – the Serbian virtual observatory ( http://servo.aob.rs ). These databases and web applications have been implemented in accordance to the standards developed by Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu ). The MolD database contains photo-dissociation cross-sections for individual rovibrational states of the diatomic molecular ions and rate coefficients for the atom-Rydberg atom chemi-ionisation and inverse electron-ion-atom chemi-recombination processes. The Belgrade electron/atom(molecule) database (BEAMDB) provides collisional data for electron interactions with atoms and molecules. Differential cross sections (DCS) are presented for both elastic and inelastic (excitation) cross sections in tabulated data tables. These DCS data are integrated over a full range of scattering angles in order to achieve integral, momentum transfer and viscosity cross sections as functions of impact electron energy. Beside these tables, energy loss spectra are presented in the graphical form.

Electron impact excitation of the 6p27s 4P1/2 state of bismuth from the ground state

We have measured differential cross sections for electron impact excitation of the 6p27s 4P1/2 state of bismuth. The excitation is performed from the ground state at incident electron energies of 10, 20, 40, 60, 80 and 100 eV. Scattered-electron intensities are obtained in the angular range from 2° to 150°. The forward scattering function method is utilized for normalization. Integrated (integral, momentum transfer and viscosity) cross sections are determined by numerical integration of DCSs. The results are analyzed and compared with available experimental data.

Collision Cross Sections for O + Ar(+) Collisions in the Energy Range 0.03-500 eV.

The interatomic potentials of the a(2)Π and b(2)Π states of the OAr(+) molecule are calculated using the relativistic complete-active space Hartree-Fock method followed by a multireference configuration interaction calculation with an aug-cc-pwCVNZ-DK basis sets where N is 4 and 5. The calculations were followed by an extrapolation to the complete basis set limit. An avoided crossing between the two potential energy curves is found at an internuclear separation of 5.75 bohr (3.04 Å). As the transition probability between the curves is negligible in the relative collision energy range 0.03-500 eV of interest here, collisions on the lower adiabatic a(2)Π potential may be treated without reference to the upper state. For low energies and orbital angular momentum quantum numbers, the one-dimensional radial Schrödinger equation is solved numerically using a Numerov algorithm method to determine the phase shift. The semiclassical JWKB approximation was employed for relative energies greater than 5 eV and orbital angular quantum numbers higher than 500. Differential, integral, transport (diffusion), and viscosity cross sections for elastic collisions of oxygen atoms with argon ions are calculated for the first time for the range of relative collision energies studied. The calculated cross sections are expected to be of utility in the fields of nanotechnology and arc welding. The combination of an Ar(+)((2)P) ion and a O((3)P) atom gives rise to a total of 12 different molecular electronic states that are all coupled by spin-orbit interactions. Potential energy curves for all 12 states are computed at the complete active space self-consistent field (CASSCF) level and scattering calculations performed. The results are compared with those obtained using just the lowest potential energy curve.

Viscosity cross sections for the heavy noble gases

We have calculated viscosity cross sections for argon, krypton and xenon from zero to 1 keV using the phase shifts from our previous publication [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] which presented total elastic and momentum transfer cross sections for these gases. As previously, we present simple analytic fits to our results to aid in modelling plasmas containing these atoms. By using the current results and those in reference [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] the first two ‘partial cross sections’ used in the general moment method of solving the Boltzmann equation can be obtained. The agreement of our viscosity cross sections with experimentally derived results indicates the overall reliability of our calculations.

Electron-impact cross sections ofSiH2using theR-matrix method at low energy

The electron-impact collision cross sections are calculated for a ${\text{SiH}}_{2}$ molecule using the $R$-matrix approach in the low-energy range. The elastic and electron-excited inelastic cross sections are calculated in the correlated and uncorrelated approximations. All electronic states arising due to single-electron transitions from Hartree-Fock configurations up to threshold are considered in the target wave-function expansion. Partial waves up to $l=4$ are used to represent continuum electron orbitals. The Born corrected converged cross sections are obtained for the radical with a nonzero dipole moment by considering the contributions of higher partial waves $(l>4)$. The effect of a small dipole moment on cross sections is analyzed. Besides determining the cross sections, the role of active space in the target and scattering problem, including the resonances is discussed. This work reports elastic, inelastic, and differential cross sections and few-electron-collision energy-transfer parameters. In particular, we show the viscosity cross sections and rate coefficients for elastic and electron-excited processes.

Singlet extension of the MSSM as a solution to the small cosmological scale anomalies

In this work we show that the general singlet extension of the MSSM can naturally provide a self-interacting singlino dark matter to solve the small cosmological scale anomalies (a large Sommerfeld enhancement factor can also be obtained). However, we find that the NMSSM (the singlet extension of the MSSM with Z3 symmetry) cannot achieve this due to the restricted parameter space. In our analysis we introduce the concept of symmetric and antisymmetric viscosity cross sections to deal with the non-relativistic Majorana-fermion dark matter scattering.

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.

Scattering properties of ground-state spin-polarized atomic hydrogen

In this paper, the scattering properties of ground-state spin-polarized atomic hydrogen (H↓) are studied at 0K using the Lippmann–Schwinger formalism. The total, diffusion and viscosity cross sections, as well as the S-wave scattering length, are calculated. The S-wave scattering cross section is found to be the most significant partial wave contributing to the total cross section at low energy. The contribution of the higher angular momentum waves, especially the D-wave (ℓ=2), to the scattering increases with increasing relative momentum k. Our calculations are performed for three triplet-state potentials: Morse-type, Silvera and Born–Oppenheimer potentials. It is also noted that as k→0, the results of the Morse potential are larger than those of the Silvera and Born–Oppenheimer potentials. This is because of the exponential tail of the Morse potential which falls off more rapidly than the r−6 behavior of the Silvera and Born–Oppenheimer potentials. Also, the Morse potential is relatively shallower than the other two potentials. For high k, the Morse cross sections approach the corresponding Silvera cross sections. This is because these triplet-state potentials have almost the same short-range part. The total cross sections reflect the quantum oscillations arising from the diffraction caused by the repulsive short-range part of the potential. Our results are consistent with those obtained by other methods.

Measurements of differential cross sections for elastic electron scattering and electronic excitation of silver and lead atoms

This paper presents absolute differential cross sections (DCSs) and integrated cross sections (ICSs) for both elastic and inelastic electron scattering by lead and silver atoms in the energy range from 10 to 100 eV. The DCSs were measured as a function of scattering angle. Scattering angles are from 1° to 150° for the excitations of the unresolved 4d105p 2P1/2, 3/2 silver line and 6p7s 3P0,1 lead line, while for the elastic scattering they span from 10° to 150°. The measurements utilize crossed beam technique with effusive atomic beam being perpendicularly crossed by electron beam. Monoenergetic electron beam is obtained by means of hemispherical selector and it is focused by cylindrical electrostatic lenses while effusive atomic beam is formed by heating of Knudsen type oven. Absolute values for the resonance states are obtained by normalization of relative differential cross sections to the optical oscillator strengths, while the absolute values for the elastic scattering are obtained from the intensity ratios at particular scattering angles. Obtained absolute DCSs were extrapolated to 0° and 180° and numerically integrated to yield integral, momentum transfer and viscosity cross sections. The experimental results have been compared with the corresponding calculations.

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

A Lennard-Jones (LJ) binary interaction model for dilute gases is obtained by representing the exact scattering angle as a polynomial expansion in non-dimensional collision variables. Rigorous theoretical verification of the model is performed by comparison with exact values of diffusion and viscosity cross sections and related collision integrals. The collision quantities given by the polynomial approximation model agree within 3.5% with those of the exact LJ scattering. The proposed model is compared in detail with the generalized soft sphere (GSS) model which is the closest in terms of fidelity among existing direct simulation Monte Carlo collision models. The GSS model's performance for the collision integral used in the first approximate of viscosity coefficient is comparable to the proposed model for most reduced temperatures. However, other collision integrals deviate significantly, even at moderate reduced temperatures. The high fidelity of the proposed model at low reduced temperatures enables non-equilibrium simulations of gases with deep LJ potential well such as metallic vapors. The model is based on the scattering angle as opposed to viscosity or diffusion coefficients and provides a direct link to molecular dynamics simulations.

Analysis of Chemistry Models for DSMC Simulations of the Atmosphere of Io

Hypervelocity chemical reactions between SO2 and O are studied using the molecular dynamic/quasi-classicaltrajectory method for conditions relevant to the modeling of the rarefied atmosphere of Io, a moon of Jupiter. The implementation of both molecular dynamic/quasi-classical-trajectory and total-collisional-energy chemistry reactionmodelsindirectsimulationMonteCarloisstudiedinazero-dimensionaltime-dependentanalysisandatwodimensionalaxisymmetricdirectsimulationMonteCarlosimulationtomodelasimpleplanetary flowcondition.The molecular dynamic/quasi-classical-trajectory simulations were found to result in lower reaction rate constants and reactionprobabilitiesthanthetotal-collisional-energymodel,andthevibrationalfavoringfeatureoftheSO2 � O ! SO � 2O reaction was revealed. The total collision cross section using the more general viscosity cross section was also obtained through the molecular dynamic/quasi-classical-trajectory simulations and was found to have a significantlydifferentenergydependencecomparedwiththeoriginalvariablehardspherecrosssection.Forthetwodimensional direct simulation Monte Carlo simulations it was found that the structure of the flow as well as the chemically formed sulfur oxide were different for the molecular dynamic/quasi-classical-trajectory and the totalcollisional-energy reaction probabilities and total cross sections. In addition, the reaction region was found to be highly nonequilibrium, which suggests that molecular dynamic/quasi-classical trajectory is a more suitable chemistry model for the simulation of Io’s atmosphere.