Viscosity Cross Sections Research Articles

3He-3He Scattering in 3He-HeII Mixtures at Low Temperatures

The total and viscosity cross sections of 3He-3He collisions in HeII are calculated. The basic achievement of the paper is the prediction of the Ramsauer-Townsend effect in this mixture. The RT minimum appears as a result of a balance between attractive short-range and repulsive zero-range interactions. In the low- energy limit the cross sections are dominated by S-wave scattering. In this limit, these cross sections are strongly modified by many-body effects. The influence of S-scattering decreases with increasing pressure and concentration because of the overall repulsion of medium effects. The effect of the P-wave scattering appears as a resonance-like behavior (peak structure) in the total cross section. This peak structure increases with pressure and concentration. For high energies, these cross sections are independent of pressure and concentration. This indicates that the high-energy behavior is dominated by the self-energy contribution; and the medium effects can be neglected.

Scattering Properties of Spin-Polarized Liquid 3He

In this paper, the scattering properties of spin-polarized liquid 3 He ( 3 He ↑ ) are studied using the Galitskii-Migdal-Feynman (GMF) formalism. The effective cross sections—including the total, diffusion and viscosity cross sections—are cal- culated. It is found that these cross sections tend to decrease with increasing spin po- larization f . The S-wave scattering cross section is the most significant partial wave contributing to the total cross section at low energy. This contribution decreases with increasing f ; whereas the contribution of the higher angular-momentum waves, es- pecially the P-wave, increases with increasing f . The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the cross sec- tions at low temperatures. For comparison purposes, the effective cross sections in the Brueckner-Bethe-Goldstone (BBG) formalism are calculated. These remain zero up to the Fermi momentum, beyond which they are equal to those given by the GMF for- malism. We deduce that hole-hole scattering plays an essential role in the scattering properties.

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid 3He and (for the first time) to liquid 4He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid 3He, it is found that S-wave scattering dominates for wave number k<0.5 A−1. At the Fermi momentum k F, the effective partial cross section σ l (and thus the total cross section σ T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 A−1, the effective total cross section is nearly constant. On the other hand, it is found in liquid 4He that S-wave scattering dominates for k<0.3 A−1, and a peak exists in σ T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the l=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the 3He gas. It is, therefore, a purely many-body effect in liquid 3He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.

Elastic and related transport cross sections for singly charged ion–atom scattering involving H, Be and C atoms and their ions

The elastic scattering of protons on Be and C atoms and of Be+ and C+ ions on hydrogen atoms is investigated using the multichannel quantal molecular orbital close-coupling method. The elastic, momentum transfer and viscosity cross sections, relevant to particle transport modelling, are calculated in the energy range 10−4 eV–10 keV. The corresponding charge transfer and target or projectile excitation cross sections are also calculated for comparison. The influence of channel couplings on the elastic processes is analysed. The molecular structure information required for the cross-section calculations was obtained by employing the multireference single- and double-excitation configuration interaction method.

Potential elastic electron scattering by atoms in the spin-polarized approach

A model based on the local spin density approximation has been suggested to describe elastic potential electron scattering by atoms with half-filled subshells. This model is applied to the case of electron scattering by such atoms having one s1-, p3-, d5- or f7-subshell (i.e. Ag, Sb, Mn and Eu). The angular dependences of asymmetry functions and differential cross sections (DCSs) both with and without taking into account absorption effects, integral elastic, absorption, diffusion and viscosity cross sections have been calculated at the 10 eV collision energy. Similar characteristics have been calculated for the Mn atom at the 20 eV energy. DCSs are calculated both in the local (spin-unpolarized) and local spin density (spin-polarized) approximations and compared with each other. Some cross sections for Ag, Mn, Eu atoms are compared with available experimental and theoretical data.

Mean free paths and elastic and related transport cross sections for neutrals and singly charged ions of Li, Be, and B in hydrogen plasmas

The mean free paths are computed from the momentum transfer cross sections associated with collisions of protons with Li, Be, and B and for Li, Li+, Be+, and B+ colliding with atomic hydrogen, for center of mass energies between 0.0001 and 10 000 eV. The elastic and viscosity cross sections are also calculated for these collision systems. A fully quantum mechanical approach has been used up to 100 eV along with a more approximate, quasiclassical method between ∼0.1 and 10 000 eV.

Elastic and related transport cross sections for singly charged ion–atom scattering of light metals (Li, Be, B) and hydrogen

Elastic differential and integral cross sections are calculated using a fully quantum-mechanical treatment and new, highly accurate potential curves, for collisions of light metal atoms (Li, Be, B) or their singly charged ions with hydrogen ions or atoms and their isotopes, over the six-decade range of centre-of-mass collision energy 0.0001–100 eV. In addition, the momentum transfer and viscosity cross sections, relevant to transport modelling, have been computed along with results of the classical trajectory Monte Carlo (CTMC) method in an extended energy range (0.01–10000 eV). The CTMC results, though less accurate, also include the inelastic processes of charge transfer, excitation and ionization, enabling improved assessment of the accuracy achieved through comparison of the results of the cross sections obtained with two methods in the overlapping energy range. We also study a fully neutral system, Li + H, using both methods. All of the data calculated here are explicitly tabulated on the World Wide Web for convenient use in plasma modelling and we find a mass-dependent scaling of the cross sections for the hydrogen isotopes.

Momentum Transfer and Viscosity from Proton‐Hydrogen Collisions Relevant to Shocks and Other Astrophysical Environments

The momentum transfer and viscosity cross sections for proton-hydrogen collisions are computed in the velocity range of ~200-20,000 km s−1 relevant to a wide range of astrophysical environments such as supernova remnant shocks, solar wind, winds within young stellar objects or accretion disks, and interstellar protons interacting with the heliosphere. A variety of theoretical approaches are used to arrive at a best estimate of these cross sections in this velocity range that smoothly connect with very accurate results previously computed for lower velocities. Contributions to the momentum transfer and viscosity cross sections from both elastic scattering and charge transfer are included.

Differential cross sections for elastic electron scattering by ytterbium atoms in the energy range 2–2000 eV: I. Real optical potential part approximation

Elastic electron scattering by ytterbium atom was studied within the 2 eV–2 keV interaction energy range using an approximation of parameter-free real part of the optical potential (OP) with allowance for spin–orbit interaction. The analytical approximation parameters were obtained for the static potential (being the main OP term), and the electron density of the target atom was calculated within the local approximation of relativistic density functional theory. The exchange potential was taken in the free electron gas approximation. The parameter-free correlation-polarization potential was used to take into account the polarization of the atom by the incident electron. Integral, momentum transfer and viscosity cross sections as well as angular dependences of differential elastic scattering cross sections (DCSs) were calculated. The positions of nine critical DCS minima were determined, the highest-energy minimum being located at [1150.9 eV; 135.70°]. A good agreement of the angular dependence of DCS with the experimental data available for 10, 20, 40, 60 and 80 eV was obtained. The above cross sections were also compared with other theoretical data, namely with the relativistic Dirac–Fock calculations with no absorption being taken into account. The phase analysis performed using the variable phase method has shown the differences in the available theoretical calculations of DCS at 10 eV to be caused principally by the manner of the exchange interaction being taken into account.

Electron scattering by magnesium: excitation of the 3s4s 1S0, 3s3d 1D2 and 3s4p 1P1 states

Differential cross sections (DCSs) for electron impact excitation of the 3s4s 1S0, 3s3d 1D2 and 3s4p 1P1 states in magnesium at incident electron energies of 10, 20, 40, 60 eV have been measured. The energy-loss spectra within the energy range of the 3s4s 1S0, 3s3d 1D2, 3s4p 1P1 and 3s3p 1P1 states have been recorded up to 150°. The absolute DCSs were determined by using inelastic (3s4s 1S0, 3s3d 1D2, 3s4p 1P1)-to-inelastic (3s3p 1P1 resonance state) intensity ratios and DCSs for the resonance state (Filipović et al 2006b J. Phys. B: At. Mol. Opt. Phys. 39 2583). The absolute DCSs were extrapolated to 0° and 180° and then integrated to yield integral, momentum transfer and viscosity cross sections. The results have been analysed and compared with available experimental data and theoretical calculations.

Electron scattering by magnesium: excitation of the 3s3p 1P1 state

Differential cross sections (DCS) for electron-impact excitation of the 3s3p 1P1 state in magnesium at incident electron energies E0 = 10, 15, 20, 40, 60, 80 and 100 eV have been measured and corresponding calculations carried out. Scattered-electron intensities were measured over a wide range of scattering angles (10°–150°) and normalized to the DCSs at 10° experimentally obtained by Filipović et al (2006 Int. J. Mass Spectrom. 251 66). Corresponding calculations have been conducted in the relativistic distorted-wave approximation. Integrated (integral, momentum transfer and viscosity) cross sections are determined by numerical integration of our DCSs. The results are analysed and compared with previous experimental data and theoretical calculations.

Elastic and related transport cross sections for protons scattering from the noble gases He, Ne, Ar, Kr, and Xe

Using a fully quantum mechanical treatment, cross sections have been calculated over a wide range of center-of-mass collision energies (0.1–10 000eV) for the elastic scattering of protons from noble gas atoms He, Ne, Ar, Kr, and Xe. In addition, the momentum transfer and viscosity cross sections, relevant to transport modeling, have been computed along with results of the classical trajectory Monte Carlo method. The comparison of the results from two methods of calculation enables improved insight into the accuracy of the cross sections obtained within various energy ranges. Scaling relations of fusion energy research interest are given allowing the data to be applied for D+ and T+ impact. Also, owing to improvements and extensions of the methods utilized here, we describe updated elastic and transport cross sections for H++C in the Appendix. All of the data calculated here are explicitly tabulated on the worldwide web for convenient use in plasma modeling.

Electron scattering by ytterbium: II. Excitation of the 4f14(6s6p 3P1, 5d6s 1D2 and 6s7p 1P1) and 4f135d6s2 (7/2, 5/2)1 states

Differential cross sections (DCSs) for electron-impact excitation of the 4f146s6p3P1 (2.231 eV) state of ytterbium have been determined experimentally at incident electron energies, E0 = 10, 20 and 40 eV, and scattering angles (θ) from 2° to 150° (at 10 eV from 10°). Also, DCSs for the 4f145d6s 1D2 (3.432 eV) and 4f135d6s2 (7/2, 5/2)1 (3.578 eV) states at E0 = 10 and 20 eV, and the 4f146s7p 1P1 (5.029 eV) state at 20 and 40 eV have been measured. These measurements were performed at θ between 10° and 150° for the 4f145d6s 1D2 and 4f135d6s2 (7/2, 5/2)1 states, and between 2° and 150° for the 4f146s7p 1P1 state. The inelastic-to-reference inelastic (the 4f146s6p 1P1 resonance state) intensity ratios were obtained from energy-loss spectra recorded with overall energy resolution of 65 meV (FWHM) and angular resolution of 1.5°. Using these ratios and DCSs for the reference state (Predojević et al 2005 J. Phys. B: At. Mol. Opt. Phys. 38 1329) the absolute inelastic DCSs were determined. In this way the obtained DCSs were extrapolated to 0° and 180° and numerically integrated to yield integral, momentum transfer and viscosity cross sections. Our results are compared with available calculated values and experimental data.

Differential and integrated cross sections for the elastic electron scattering by calcium atom

The experimental and theoretical studies of elastic electron scattering by calcium atom have been made. The experimental investigation was carried out using a crossed electron-atom beam technique. The measurements were performed at electron-impact energies (E0) of 10, 20, 40, 60 and 100 eV and for a range of scattering angles (θ) from 10° up to 150°. The absolute differential cross sections (DCSs) have been obtained from the elastic-to-inelastic (the resonant 41P0 state) intensity ratio at θ = 10° at each E0. Calculations have been performed in the optical potential approximation for the same E0 and θ between 0° and 180°. Results for DCSs and integrated (integral, momentum transfer and viscosity) cross sections are presented and compared with those predicted by existing calculations.

Electron scattering by ytterbium: I. Excitation of the 4f146s6p 1P1 resonance state and elastic collision

Differential cross sections (DCSs) for electron-impact excitation of the 4f146s6p 1P1 resonance state of ytterbium were measured at 10, 20, 40, 60 and 80 eV incident electron energies (E0) and scattering angles (θ) between 2° and 150°. The absolute DCS scale for the 1P1 state was determined through normalization of its relative DCSs to the optical oscillator strength using the forward scattering function method. DCSs for elastic electron scattering by ytterbium were measured at the same energies for θ between 10° and 150°. Elastic-to-inelastic intensity ratios were obtained from energy-loss spectra recorded with overall energy resolution of 65 meV (FWHM) and angular resolution of 1.5°. Both inelastic and elastic DCSs were extrapolated to 0° and 180° and numerically integrated to yield integral, momentum transfer and viscosity cross sections. Our results are compared with scarce experimental and theoretical data.

Differential and integrated cross sections for the electron excitation of the 4 1Po state of calcium atom

Differential cross section (DCS) data for excitation of the 4 1Po state (2.93 eV) of Ca atoms by electrons have been obtained using a crossed electron–atom beam technique. The measurements were divided into two groups. The first one consists of measurements at 10, 20, 40, 60 and 100 eV impact electron energies from 1° to 10° scattering angle interval. The second group of measurements are those at larger scattering angles (10°–150°) at the same energies except 100 eV. Absolute values have been obtained by normalizing generalized oscillator strengths (GOS) to optical oscillator strength (OOS) in the minimum momentum transfer squared (K2) limit. Integral, momentum transfer and viscosity cross sections have been determined from DCSs. A comparison is made with existing relativistic distorted wave calculation.

Study of He flow properties to test He dimer potentials

The parameters which characterize the energy distribution of a supersonic helium beam are measured at different source parameters. The data are compared with the results of calculations based on three different He–He interatomic potentials in order to test their ability to describe the helium free jet expansion. This article follows a previous paper where calculations were performed at source temperatures between 20 and 80 K using the the Lennard-Jones and the Tang–Toennies–Yiu potential [K. T. Tang, J. P. Toennies, and C. L. Yiu, Phys. Rev. Lett. 74, 1546 (1995)] but no satisfactory agreement was found. Here, calculations are presented also for a potential curve recently proposed by Hurly and Moldover [J. J. Hurly and M. R. Moldover, J. Res. Natl. Inst. Stand. Technol. 105, 667 (2000)]. The source temperature range where calculations are performed is extended between 6 and 300 K in order to compare the predictions of the three potentials with other measurements present in literature. Possible experimental limitations to the beam performances are discussed and in particular the skimmer interference is taken into account. As the considered potentials only partially describe the experiments, a phenomenological viscosity cross section is proposed which represents in a satisfactory way the He flow properties over the whole range of source temperatures.

Elastic and transport cross sections for argon in hydrogen plasmas

Accurate elastic differential scattering cross sections have been computed through a fully quantum mechanical approach for hydrogen ions (H+, D+, or T+) colliding with argon in the center of mass energy range of 0.1 to 200 eV. With the appropriate weight functions, these differential cross sections have been integrated to yield the momentum transfer, viscosity, and integral elastic cross sections. The momentum transfer and viscosity cross sections have been extended to higher collision energies (up to 10 keV) using a classical, three-body scattering method. Results have been compared with those of a simple model and previous recommended values. Knowledge of these cross sections, tabulated and made available through the world wide web, is of use to modeling and diagnostics of gaseous electronic, fusion, and other plasma environments.

Elastic processes involving vibrationally excited molecules in cold hydrogenplasmas

We describe here a comprehensive quantum mechanical study of elastic scatteringof protons by vibrationally excited hydrogen molecules and of hydrogen atoms byvibrationally excited hydrogen molecular ions, in the range of collisionenergies from a fraction of an eV to 6 eV. The problem was solved withina treatment considering all inelastic processes between the vibrationalstates, including excitation, charge transfer and dissociation. This wasrealized by expanding the problem in vibrational bases of H2 and H2+which, in addition to all bound states, contained a large number of discretizedvibrational continuum states, and solving the resulting set of coupled channelequations. The sudden approximation was applied with regard to rotations of thetarget molecule, and particular attention has been paid to convergence of theelastic cross sections with the number of partial waves of the projectile. Importantplasma transport related moments of the elastic scattering cross section, themomentum transfer and viscosity cross sections, are also reported here andcompared with inelastic cross sections for various vibrationally excited states.

Transport cross sections relevant to cool hydrogen plasmas bounded by graphite

Atomic collision quantities relevant to transport in hydrogen plasmas bounded by graphite walls are considered. Fully quantal, ab initio calculations of the differential and integral elastic scattering cross sections for H+, D+, and T+ colliding with C at center of mass energies between 0.1 and 200 eV are described. The computed elastic cross section and its transport moments, the momentum transfer, and viscosity cross sections, are compared with those from a simple analytical model (the Massey–Mohr approximation) and with a three-body classical scattering approach in order to extend the data to higher collision energies. For energies typical of the edge plasma, the elastic scattering cross section is found to be as much as 10 times larger than that estimated from the widely used analytical approximation. The highly accurate quantal results are also tabulated and made available to the plasma science community through the world wide web.