Momentum Transfer Cross Section For Electrons Research Articles

Electron swarm and transport coefficients for the binary mixtures of SF6 with Ar and Xe

A pulsed Townsend technique was used to measure the electron drift velocity, the longitudinal diffusion, and the effective ionization coefficients, and the limiting field strength for the binary mixtures of SF6 with Ar and Xe. This paper covered a wide range of the density-reduced electric field strength E/N between 50 and 700 Td (1 Townsend (Td) = 10−17 V cm2). The content of SF6 in the gas mixtures was varied over the range 1–90%. For the SF6–Ar mixture, the electron drift velocities were found to be higher than those for pure SF6, and conversely for the SF6–Xe mixture. The above can be explained in terms of the larger momentum transfer cross-section for electrons in Xe than in Ar. The limiting field strength for the SF6–Xe mixture was found to be higher than that for the SF6–Ar one, but still lower than that for the SF6–N2 mixture.

Angle-differential and momentum-transfer cross sections fore−+Rb,Cs, and Fr collisions at low energies:3Foshape resonances inRb−,Cs−,andFr−ions

Based on the relativistic Dirac R-matrix method, we calculate angle-dependent and momentum-transfer cross sections for electron scattering by Rb, Cs, and Fr atoms at impact energies below 3 eV. Our results for momentum transfer for ${e}^{\ensuremath{-}}+\mathrm{Rb}$ and Cs collisions are compared with available data from swarm experiments. We find clear evidence for a ${\mathrm{Cs}}^{\ensuremath{-}}{(}^{3}{F}^{o})$ shape resonance at 1.528 eV, in excellent agreement with angle-dependent electron-scattering measurements. We analyze and compare the ${}^{3}{F}^{o}$ shape resonance in ${e}^{\ensuremath{-}}+\mathrm{Rb},$ Cs, and Fr elastic collisions.

Ab initio calculation for low-energy elastic scattering of electrons from sulfur atoms

The multiconfiguration Hartree-Fock method for continuum wave functions has been used to perform calculations of elastic scattering of electrons from the open-shell sulfur atom at low energies. The electron correlation and polarization of the sulfur atom by the scattered electron, which are very important in this calculation, have been taken into account very accurately {ital ab initio} through the configuration-interaction procedure by optimizing both bound and continuum orbitals simultaneously at each kinetic energy of the scattered electron. The scattering lengths, phase shifts, and differential, total and momentum-transfer cross sections for electrons elastically scattered from sulfur atoms are calculated for the impact-energy range from 0 to 27.2 eV. The wave functions computed exactly at zero energy are used to compute the scattering length. The present results are compared with other available theoretical results. {copyright} {ital 1997} {ital The American Physical Society}

Cross sections of e--O scattering at intermediate and high energies (Ei=8.7-1000 eV).

Various total cross sections and elastic differential as well as momentum-transfer cross sections for electron scattering by oxygen atoms are calculated for incident energies ${\mathit{E}}_{\mathit{i}}$=8.7--1000 eV. A partial-wave analysis of the local, complex, energy-dependent optical potential yields reliable total cross sections. Discrepancies between theories and experiment exist at low energies, but a reasonable energy-variation picture of various ${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{-}}}$O cross sections emerges. The present total inelastic cross sections are similar to but higher than the recommended total ionization cross sections.

Pseudopotential calculations of elastic scattering of low-energy electrons (< 20 eV) from neon atoms

Pseudopotential calculations of phase shifts, differential, total, and momentum-transfer cross sections for electrons elastically scattered from neon atoms are reported in the impact energy range 0–20 eV. The results are found to be in very good agreement with existing experimental and other theoretical data.

Accurate ab initio calculation on the low-energy elastic scattering of electrons from helium.

The multiconfiguration Hartree-Fock method developed by Saha [Phys. Rev. A 39, 5048 (1989)] to study scattering of electrons from atoms has been applied to the low-energy elastic scattering of electrons from helium atoms. The short-range electron correlation and the long-range dynamical polarization of the target by the scattering electron, which are very important in these calculations, have been taken into account in an accurate ab initio manner through the configuration-interaction procedure. Detailed results for phase shifts, elastic differential, integral-elastic, and momentum-transfer cross sections for electrons elastically scattered from helium are reported for the low and intermediate energies ranging from 0.58 to 50 eV. The present results are compared with accurate experimental measurements and theoretical calculations. It is found that the present multiconfiguration self-consistent-field method produces high-quality results that show excellent agreement with experimental measurements and compare well with other accurate theoretical calculations.

Low-energy elastic scattering of electrons from neon atoms.

The multiconfiguration Hartree-Fock method of Saha, Pindzola, and Compton (Phys. Rev. A 38, 128 (1988)) applied to photoionization of atoms has been extended in order to consider elastic scattering of electrons from neon atoms. The dynamical polarization and the electron-correlation effects, which are very important in this case, have been taken into account more accurately in the ab initio method through the configuration-interaction procedure. Phase shifts, and differential, integral, and momentum-transfer cross sections for electrons elastically scattered from neon atoms are reported for the impact-energy range from 0.136 to 70 eV. The calculated results are compared with experimental and other theoretical results. It is found that the present multiconfigurational self-consistent-field method yields high-quality results which show excellent agreement with experiment and compare well with other theoretical results.

The influence of the electron transport cross sectional shape on electron energy distribution functions in DC and microwave plasmas

A numerical solution of a system of equations describing DC and microwave diffusion-controlled discharge plasmas has been carried out. It is shown that a knowledge of the energy dependence of the electron momentum transfer cross section makes it possible to predict a priori the dissimilarities in the electron distribution functions in the two types of discharge: differences in electron mean energies in the case of equal power consumptions in inert gas plasmas; information on differences in electron distribution function 'tails' in the case of equal electron mean energies in inert gas plasmas and in the case of equal power consumptions in molecular plasmas.

Quantum limit cyclotron resonance in p-GaAs

Electron scattering by neutral acceptors has been studied through far infrared (λ=172 μm) cyclotron resonance on p-GaAs at 4.2 K. It is found that (1) The inverse relaxation time is considerably smaller in the quantum limit than that predicted by D.C. transport theory in the absence of a magnetic field. (2) The same increase linearly with neutral acceptor concentration. (3) The electron momentum transfer cross section by neutral acceptor is by more than an order of magnitude smaller than that by neutral donor even in the quantum limit.

Electron transport in low density alkane gases: Effects of chain length and flexibility

The Ramsauer–Townsend (RT) minimum in the electron momentum transfer cross section (σm) occurs at the same energy (ξRT=0.12±0.01 eV) in all n-alkanes from C2H6 to n-C10H22. The lack of dependence on chain length indicates that the electron being scattered interacts with a chain segment that contains only two or three carbon atoms. The value of ξRT increases with increasing sphericity of the molecules, being 0.17 eV for i-butane, 0.22 eV neo-pentane, and 0.25 eV for methane. At high fields the electron drift velocity attains a ‘‘saturation’’ value (vsat) in the C1 to C5 hydrocarbons: 100 km/s in CH4, 54 km/s in C2H6, 51 km/s in C3H8, 49 km/s in n-C4H10, and 43 km/s in n-C5H12. Increasing the molecular sphericity increases vsat: 55 km/s in i-C4H10 and 57 km/s in neo-C5H12, to be compared with the values 49 and 43 in the n-isomers, and 100 km/s in CH4. The value of σm averaged over the thermal velocity distribution, σav, is an order of magnitude smaller than that expected from the simple polarization interaction, and is similar in magnitude to the physical cross section of the molecule. The scattering cross sections of the deuterated methanes CHxD4−x, x=0–3, are the same as those of CH4, in the low density gases.

Electron and cation transport in fluid dimethyl ether: effects of density and temperature

The effect of molecular electric dipole moment D on charge transport in fluids was examined by measurement of electron and ion mobilities in dimethyl ether (D = 1.3 D) and comparing them with the behavior in hydrocarbons. The fluid density was varied continuously from that of the normal vapor to that of the normal liquid, passing through the critical region. The density normalized mobility nμe of electrons in dimethyl ether vapor at low densities is 30-fold smaller than that in propane, although for the cations nμ+ in the ether is only 1.4-fold smaller than that in the alkane. The permanent dipole moment of the ether dominates the scattering of low energy electrons but not that of cations. The electron momentum transfer cross section is roughly 33% larger than that predicted by the Altshuler point dipole model, and has a minimum at ~0.12 eV. The energy gained from the electric field is removed mainly through inelastic collisions, even in the thermal energy range.Molecular clustering decreases both electron and ion mobilities, but the effect on the former is much larger due to the greater change in reduced mass. The extent of electron quasilocalization in the dense vapor of dimethyl ether is four times greater than that in nonpolar hydrocarbons. Electrons form relatively stable localized states in the liquid at n/ne > 2.0. Ion mobility undergoes a transition from "density control" to "viscosity control" with increasing density in the low density liquid. Viscosity control is operative at n/ne > 2.4.

Elastic scattering and vibrational excitation of CO2by 4, 10, 20 and 50 eV electrons

Elastic and vibrationally inelastic differential, integral and momentum-transfer cross sections for electrons scattered by CO2 molecules are reported at 4, 10, 20 and 50 eV impact energies. The elastic cross sections are placed on an absolute scale by means of a relative flow technique. The inelastic cross sections are normalised to the elastic ones by using the inelastic to elastic intensity ratios. Data are reported for up to ten features in the 0.0 to 0.4 eV energy-loss region.

Absolute elastic differential electron scattering cross sections for He: A proposed calibration standard from 5 to 200 eV

Absolute differential, integral, and momentum-transfer cross sections for electrons elastically scattered from helium are reported for the impact energy range of 5 to 200 eV. Angular distributions for elastically scattered electrons are measured in a crossed-beam geometry using a collimated, differentially pumped atomic-beam source which requires no effective-path-length correction. Below the first inelastic threshold the angular distributions were placed on an absolute scale by use of a phase-shift analysis. Above this threshold, the angular distributions from 10 to 140 deg were fitted using the phase-shift technique, and the resulting integral cross sections were normalized to a semiempirically derived integral elastic cross section. Depending on the impact energy, the data are estimated to be accurate to within 5 to 9%.

Low-Energy Electron Scattering from Strongly Polar Molecules. I. Glauber Approximation

The Glauber approximation has been used to obtain the differential, total, and momentum-transfer cross sections for electron scattering from strongly polar molecules; numerical calculations have been carried out for e+CsCl scattering. The big difference between the Born cross section and the recently published experimental data has been dissolved.

Momentum transfer cross sections and the Z1oscillations in stopping power

Heavy ions moving at low velocity along channelling directions in crystals are considered to lose energy by transferring momentum to target electrons which scatter elastically from them. In a model system of an atom moving through an electron gas, the stopping power is shown to be proportional to the electron momentum transfer cross section. The variation of this cross section throughout the periodic table corresponds closely to the observed variation of stopping power for channelled ions.

Momentum-Transfer Cross Sections and Conductivity Ratios for Low-Energy Electrons in He, Ne, Kr, and Xe

Conductivity ratios have been measured in weakly ionized afterglows of repetitively pulsed, electrodeless, rf discharges in helium, neon, krypton, and xenon using a microwave resonant cavity (2.7 GHz). Maxwellian electron-energy distributions were obtained at temperatures from 300\ifmmode^\circ\else\textdegree\fi{}K to 10 000\ifmmode^\circ\else\textdegree\fi{}K, as measured with a gated microwave radiometer (4 GHz), Momentum-transfer cross sections for electrons of energy up to 2 eV in neon, krypton, and xenon were determined from the measured conductivity ratios by an iterative procedure. The results in helium support the momentum-transfer cross section determined from the electron-beam experiments of Golden and Bandel. Those for neon indicate a scattering length of $+0.20{a}_{0}$. The momentum-transfer cross sections for krypton and xenon agree best with, but are generally lower than, those of Frost and Phelps and indicate a deeper (approximately 2.5 times) Ramsauer minimum. An experimental check of the theoretical electron-ion collision frequency for high-frequency, low-temperature conditions has been made.

Momentum-Transfer Cross Sections for Slow Electrons in He, Ar, Kr, and Xe from Transport Coefficients

Momentum-transfer cross sections for electrons in He, Ar, Kr, and Xe are obtained from a comparison of theoretical and experimental values of the drift velocities and of the ratio of the diffusion coefficient to the mobility coefficient for electrons in these gases. The theoretical transport coefficients are obtained by calculating accurate electron-energy distribution functions for energies below excitation using an assumed energy-dependent momentum-transfer cross section. The resulting theoretical values are compared with the available experimental data and adjustments made in the assumed cross sections until good agreement is obtained. The final momentum cross sections for helium is 5.0\ifmmode\pm\else\textpm\fi{}0.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ for an electron energy of 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ eV and rises to 6.6\ifmmode\pm\else\textpm\fi{}0.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ for energies near 1 eV. The cross sections obtained for Ar, Kr, and Xe decrease from 6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$, 2.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$, and ${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$, respectively, at 0.01 eV to minimum values of 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 0.3 eV for Ar, 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 0.65 eV for Kr, and 1.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ at 0.6 eV for Xe. The agreement of the very-low-energy results with the effective-range theory of electron scattering is good.