Transport Cross Sections Research Articles

The Role of Color-Magnetic Monopoles in a Gluonic Plasma

The role of color-magnetic monopoles in a pure gauge plasma at high temperature T > 2 T c is considered. In this temperature regime, monopoles can be considered heavy, rare objects embedded into matter consisting mostly of the usual “electric” quasiparticles, quarks and gluons. The gluon-monopole scattering is found to hardly influence thermodynamic quantities, yet it produces a large transport cross section, significantly exceeding that for pQCD gluon-gluon scattering up to quite high T. This mechanism keeps viscosity small enough for hydrodynamics to work at LHC.

Interpretation of thermoelectric power behaviour of Zinc nanowire composites: Phonon-scattering mechanism

We develop a theoretical model for quantitative analysis of temperature-dependent thermoelectric power ( S) of Zn nanowires. In doing so, we first use the Mott expression to compute the electron diffusive thermoelectric power ( S c diff. ) using Fermi energy as electron-free parameter, S c diff. shows linear temperature dependence. Further, the S c diff. contribution is subtracted from the experimental data and the difference ( S experimental – S c dif ) is characterized as phonon drag thermoelectric power ( S ph drag ) which is obtained within the relaxation time approximation where the thermoelectric power is limited by the scattering of phonons with impurities, grain boundaries, charge careers and phonons in the nanowires. The S ph drag shows anomalous temperature-dependent behaviour, which is an artifact of various operating scattering mechanisms. The observed anomalies are well accounted in terms of interaction among the phonons–impurity, phonon-grain boundaries, phonon–electron and the umklapp scattering. It is also shown that for phonons the scattering and transport cross-sections are proportional to ω 4 in the Rayleigh regime where ω is the frequency of the phonons. Numerical analysis of thermoelectric power from the present model shows similar results as those revealed from experiments.

Thermodynamics and transport properties of thermal plasmas: the role of electronic excitation

The role of electronic excited states in affecting the thermodynamic and transport properties of thermal plasma is investigated in the temperature range [300–100 000 K] and in the pressure range [1–103 atm] for hydrogen and [10−2–103 atm] for nitrogen. Thermodynamic functions have been calculated modelling in different ways the electronic levels of atomic species (ground-state, Debye–Hückel and confined-atom approximations). Frozen and reactive specific heats as well as isentropic coefficients are strongly affected by the electronic excitation whereas compensation effects smooth its influence on the total specific heat, i.e. the sum of frozen and reactive contributions. Higher-order approximations of the Chapman–Enskog method have been used to evaluate transport coefficients, including electronically excited states as separate species. The importance of a state-to-state approach to calculate transport coefficients is presented taking into account the strong dependence of transport cross sections on the principal quantum number. Results for hydrogen, nitrogen and air plasmas are widely discussed.

Incorporation of the Goudsmit–Saunderson electron transport theory in the Geant4 Monte Carlo code

The present work describes the implementation of the multiple scattering formalism for charged particle transport based on the Goudsmit–Saunderson angular distribution and satisfying the Lewis spatial displacement theories. Furthermore, the most realistic total cross sections and transport cross sections for single elastic scattering of electrons and positrons by neutral atoms were carried out using the ELSEPA code. The extended model has been incorporated in the Geant4 Monte Carlo code system (currently used in many fields of application for transport of particles and covering a large range of energies from 0.1 keV to 100 TeV). Additionally, techniques are developed that allow the distributions to be scaled to account for energy loss. This new representation allows on-the-fly sampling of Goudsmit–Saunderson angular distributions in a screened Rutherford approximation suitable for Class II condensed history Monte Carlo codes. The reliability of the model is demonstrated through a comparison of simulation results with experimental data. Good agreement is found for electrons with kinetic energies down to a few keV.

Role of monopoles in a gluon plasma

We study the role of magnetic monopoles at high enough temperature $T>2{T}_{c}$, when they can be considered heavy, rare objects embedded into matter consisting mostly of the usual ``electric'' quasiparticles, quarks, and gluons. We review available lattice results on monopoles at finite temperatures. Then we proceed to classical and quantum charge-monopole scattering, solving the problem of gluon-monopole scattering for the first time. The explicit calculations are performed in the framework of the Georgi-Glashow model; the results that we obtain are nevertheless quite general. Connections to QCD are carefully discussed. We find that, while the gluon-monopole scattering hardly influences thermodynamic quantities, it does produce a large transport cross section, significantly exceeding that for pQCD gluon-gluon scattering up to quite high $T$. Thus, in spite of their relatively small density at high $T$, monopoles are extremely important for quark-gluon plasma transport properties, keeping viscosity small enough for hydrodynamics to work at the LHC.

High temperature Mars atmosphere. Part I: transport cross sections

In the perspective of higher approximations of the Chapman-Enskog theory for transport property calculations, existing transport cross sections databases for interactions involving Earth atmosphere species have been updated and extended to Mars atmosphere components, proposing a phenomenological approach for the derivation of the relevant elastic collision integrals in neutral-neutral and neutral-ion interactions. Inelastic collision integrals terms, due to resonant charge exchange channels, have been considered and the asymptotic approach extended to the estimation of charge transfer cross section of multiple resonant processes.

Scattering of electrons in graphene by clusters of impurities

It is shown that formation of clusters of charged impurities on graphene can suppress their contribution to the resistivity by a factor of the order of the number of impurities per cluster. The dependence of conductivity on carrier concentration remains linear. In the regime where the cluster size is large in comparison to the Fermi wavelength, the scattering cross section shows sharp resonances as a function of incident angle and electron wave vector. In this regime, due to the dominant contribution of scattering by small angles, the transport cross section can be much smaller than the total one, which may be checked experimentally by comparison of the Dingle temperature to the electron mean-free path.

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.

Experimental and theoretical study of the energy loss of Be and B ions in Zn

Energy-loss measurements and theoretical calculations for Be and B ions in Zn are presented. The experimental ion energies range from 40 keV/u to 1 MeV/u, which includes the energy-loss maximum and covers a lack of experimental data for these systems from intermediate to high energies. The measurements were performed using the Rutherford backscattering technique. The ab initio calculations are based on the extended Friedel sum rule--transport cross-section method for the valence electrons and the Shellwise local plasma approximation for the bound electrons. A comparison of these calculations to the present experimental data for Be and B and previous values for H, He, and Li ions on the same target is included. This confirms the applicability of the employed theoretical framework also for ions of intermediate atomic number.

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.

Study on electron scattering in solid targets using accurate transport cross-sections

The Vicanek and Urbassek theory [M. Vicanek, H.M. Urbassek, Phys. Rev. B 44 (1991) 7234] combined with a Monte Carlo simulation are used to investigate the transport of 0.5–4 keV electrons in solid targets. The cross-sections used to describe the electron transport have been calculated via a new improved version of the approximate analytical expression given by Jablonski [A. Jablonski, Phys. Rev. B 58 (1998) 16470]. Some applications are presented here for the calculation of electron backscattering coefficient in semi-infinite Al and Cu targets. The obtained results accord with success with the experiment and clearly represent an improvement with respect to previous theoretical calculations.

Reflection of keV light ions from solids at oblique and grazing incidence

The particle reflection coefficient of light keV ions backscattered from heavy targets has been determined by two different analytical approaches: by the single collision model in the case of nearly perpendicular incidence and by the small-angle multiple scattering theory in the case of glancing angles of incidence. The obtained analytical formulae are approximately universal functions of the scaled transport cross-section describing the reflection of all light ions from heavy targets. Going from perpendicular to grazing incidence, the transition from pure single to pure multiple scattering type of reflection is observed. For larger values of the scaling parameter the results of these theories cover the whole region of ion incident angles and the present estimates of the particle reflection coefficient are in good agreement with the results obtained from the empirical formula of Tabata et al.

Improved expression for calculating electron transport cross sections

We report a simplified correction for the electron transport cross sections (TCSs) for a number of selected atomic targets ranging from H to U and electron energies between 50 and 4000 eV. The correction has been made to the approximate analytical expression of transport cross sections derived by Jablonski [A. Jablonski, Phys. Rev. B 58 (1998) 16470] where an argued parameter is introduced. The latter is obtained from a polynomial fit. The energy dependence of the percentage deviation between TCSs from the corrected expression and those obtained from other sources is presented. The TCSs calculated in the present work showed better agreement with accurate values of TCSs than those reported in earlier publications. This may facilitate the evaluation of parameters needed for quantitative Auger-electron spectroscopy and X-ray photoelectron spectroscopy.

Cutoff criteria of electronic partition functions and transport properties of atomic hydrogen thermal plasmas

Transport coefficients of equilibrium hydrogen plasma have been calculated by using different cutoffs of electronic partition functions and different sets of transport cross sections of electronically excited states. The selection of both the cutoff criterion and transport cross sections deeply affects the transport coefficients of the H, H+, e plasma mixture in the temperature range of 10 000–50 000 K and in the pressure interval of 1–1000 atm.

Measurement of the lifetime of rubidium atoms in a dark magneto-optical trap

The lifetimes of rubidium atoms in a dark magneto-optical trap are measured at different populations of the 'bright' and 'dark' hyperfine states of captured atoms. It is found that the lifetime of atoms in the trap decreases if they spend more time in the bright state. A simple explanation of this effect is proposed which is based on the increase in the transport cross section for collisions of thermal rubidium atoms surrounding the trap with cold rubidium atoms upon their electronic excitation.

SU‐GG‐J‐82: Elastic Scattering of Electrons in Gold: An Event‐By‐Event Simulation Algorithm Based On the NIST Cross‐Section Data

Purpose: An increasing number of studies report on new approaches to detection and therapy of cancer based on the use of gold nanoparticles. Interaction of these nanoparticles with ionizing radiation, used either for diagnostic or therapeutic purposes, distorts the radiation field, especially on a microscopic scale. Monte Carlo calculation of dose distributions on such a scale, and microdosimetric analysis require event‐by‐event algorithms. The purpose of this study was to develop an event‐by‐event algorithm for simulation of electron elastic scattering in gold that is based on accurate cross sections from the NIST data base, Version 3.1. Method and Materials: Angular dependencies of the NIST singly differential cross sections were fitted with a linear combination of the Wentzel cross section and Legendre polynomials of up to the 11th order. An algorithm was developed for sampling a scattering angle from the distribution represented by this linear combination. The algorithm is based on a rejection scheme. An angle is sampled from a simple distribution that has three components represented by Wentzel, isotropic, and backscatter (peak at π) terms. The sampled angle is rejected with a probability depending on the ratio of this simple distribution and the desired one. For some applications the three component distribution can be a sufficiently accurate representation of the NIST cross sections. Results: Fitting parameters have been determined for electron energies in the range from 50 eV to 1 keV. Total cross sections calculated with these parameters agreed with the NIST data within 2×10−4 % and transport cross sections agreed within 0.5%. The algorithm has been implemented in a computer code and tested. The probability of accepting an angle in the rejection scheme was in the range of 0.25 to 0.54 depending on electron energy. Conclusion: An algorithm has been developed for accurate simulation of electron elastic scattering in gold.

The effect of nanoparticles on the thermal conductivity of crystalline thin films at low temperatures

This study is concerned with the prediction of the effective thermal conductivity of nanocomposite thin films consisting of nanoparticles randomly distributed in a solid matrix. Crystalline sodium chloride with embedded monodisperse silver nanoparticles is investigated as a case study for thin films where phonons are the main heat carriers. To the best of our knowledge, the equation for phonon radiative transfer is solved for the first time, with an exact scattering transport cross section of the nanoparticles as a function of frequency which was obtained from the literature. The one-dimensional equation for phonon radiative transfer based on the isotropic scaling approximation is solved on a spectral basis using the discrete ordinates method to predict the temperature profile and the heat flux across the nanocomposite thin films. The thermal conductivity is retrieved at temperatures where the effects of Umklapp and normal processes can be neglected and scattering by the particles on phonon transport dominates. The method of solution and closure laws were validated with experimental data of thermal conductivity for bulk samples at 2.53, 5.94, and 10.56 K. The effects of the film thickness (1 μm to 2.5 cm), nanoparticle diameter (5 to 100 nm) and volume fraction (0.0001 to 0.2) on the thermal conductivity of the nanocomposite thin film are investigated. The results indicate that the thermal conductivity decreases with decreasing particle radius as well as with increasing particle concentration. Finally, a dimensional analysis revealed a power-law relationship between the dimensionless thermal conductivity and a dimensionless length of the order of the acoustic thickness of the medium. These results can be used to design nanocomposite thin films for various low-temperature thermal applications by choosing optimal nanoparticle radius and volume fraction, and film thickness.

High-frequency limit of the transport cross section in scattering by an obstacle with impedance boundary conditions

The scalar scattering of a plane wave by a strictly convex obstacle with impedance boundary conditions is considered. A uniform bound of the total cross section for all values of the frequency is presented. The high-frequency limit of the transport cross section is calculated and presented as a classical functional of the variational calculus.

Stopping of slow ions

This chapter addresses the stopping and straggling of ions at velocities up to the Thomas-Fermi speed vTF = Z1 2/3v0, with the main focus on velocities up to the Bohr speed v0.This topic is characterized by many unsolved problems both on the experimental and the theoretical side. Experimental findings play a more dominant role in this chapter than in other parts of this monograph. The newly found reciprocity principle is explored in the evaluation of data. Much existing theory is based directly or indirectly on electron-gas theory, especially Fermi-gas theory. The Lindhard-Scharff formula and Firsov’s theory are discussed along with various extensions. The transport cross section approach is explored in conjunction with partial waves, Born approximation as well as linear and nonlinear dielectric theory. Stopping cross sections are known to show pronounced oscillations as a function of the atomic number Z1 of the projectile, and presumably also of Z2, where evidence is weaker.

Theoretical and experimental study of energy loss of Li ions in Zn

We have performed a combined theoretical and experimental study of the energy loss of Li ions in Zn, on a wide range of energies, together with comparative studies for H and He ions on the same target. By using Zn films and the Rutherford backscattering technique, we were able to determine the stopping power for Li ions in the (0.3 to 5) MeV energy interval. The experimental results cover an energy range which includes the maximum of the stopping power. The values obtained agree well with previous measurements performed in a limited energy interval and with the semiempirical code SRIM 2006. On the other hand, we have performed ab initio theoretical calculations based on the extended Friedel sum rule--transport cross section formulation for the valence electrons and the shellwise local plasma approximation for the inner shells. This theoretical description reproduces reasonably well the experimental results on the whole studied energy range. The same occurs with previous measurements performed with H and He on the same target. The importance of the screened potential on the stopping power due to the valence electrons is stressed in the present description.