Elastic Collision Cross Sections Research Articles

Absolute Generalized Oscillator Strengths for Four Electronic Transitions in Carbon Monoxide

Generalized oscillator strengths have been measured for the υ′ = 2 level of the fourth positive bands of carbon monoxide by comparing inelastically and elastically scattered electrons at 300-, 400-, and 500-eV kinetic energy and using the elastic collision cross sections measured by Bromberg [J. Chem. Phys. 52, 1243 (1970)]. Extrapolation to zero momentum change gives f0 = 0.0429. From relative intensity measurements, the limiting oscillator strengths of the levels from υ′ = 0–12 have also been determined. From zero angle spectra, the limiting oscillator strengths for transitions to the B 1Σ+, C 1Σ+, and E 1Π states have been determined. The values are 0.0153 ± 0.0014, 0.163 ± 0.015, and 0.094 ± 0.009, respectively; υ′ = 0 in each case. Relative intensities in the fourth positive bands have also been determined (and redetermined) at various angles and kinetic energies. Possible variation in relative intensities with scattering angle is discussed. A possible reason is given for the large discrepancy (a factor of 2) between the oscillator strength obtained for the entire fourth positive bands from electron impact and from lifetime measurements by other investigators.

Electron energy distribution in a Townsend discharge in hydrogen

A solution of the Boltzmann equation has been used to select a set of elastic and inelastic collision cross sections for hydrogen which are consistent with the measured values of electron drift velocity and ionization coefficients in both electric and crossed electric and magnetic fields. The calculated distribution of electron energies obtained from the same set of cross sections is found to be in good agreement with the distribution recently measured directly at E/p=60 V cm-1 torr-1 by Kenny and Craggs. The same set of cross sections predict values of the mean electron energy which are in reasonable agreement with the data of Kenny and Craggs but which differ substantially from values estimated by applying the calculated distribution to measured values of the ratio of diffusion coefficient to mobility. Possible reasons for this discrepancy are suggested.

Energy Dependence of the Elastic Total Collision Cross Section of Identical Molecules: 4He

The velocity dependence of the total collision cross section for velocity-selected molecular beams of 4He scattered by 4He at 2°K has been measured. Undulations due to the quantum statistics have been resolved between 650 and 1200 m sec−1. Results are compared with exact and approximate calculations and the sensitivity of this effect to potential parameters is discussed. Finally we show the possibility to extract from the data the absolute value of the total collision cross section independently from scattering centers density measurements.

Differential collision cross sections of argon and neon

The elastic differential collision cross sections of argon with itself and neon with itself have been measured using the modulated molecular beam technique with mass spectrometric detection.

The influence of asymmetrical angular scattering on the mean number of electron-helium-gas-atom elastic collisions

The mean number of elastic collisions c involving helium gas atoms and an electron diffusing between two infinite perfectly absorbing planar electrodes has been calculated, using Monte Carlo techniques, taking into account the asymmetrical angular elastic scattering distribution in helium. The influence of this distribution on the c values is compared with an earlier prediction by Maier-Leibnitz, based on the work of Didlaukis; the present results do not support Maier-Leibnitz's proposal that, in the Harries-Hertz formula, the square of the total elastic collision cross section should be replaced by the product of the total cross section and the momentum transfer cross section. It is suggested that, at higher gas pressures where the Harries-Hertz formula is applicable, the square of the latter cross section is more appropriate.

CHEMICAL REACTIONS IN ELECTRICAL DISCHARGES: II. THE STRUCTURE OF THE POSITIVE COLUMN IN D-C. GLOW DISCHARGES THROUGH FAST-FLOWING GASES

After a brief summary of recent advances in the structure of the positive column of a d-c. glow discharge, general expressions are derived for rates of reaction and excitation produced by electron impact. These rate equations are expressed in terms of the easily measured electrical parameters of the discharge. Such expressions will be used in future studies of chemical reactions occurring in the positive column; a qualitative comparison to experiment is given, where possible.A general expression for the axial electric field in the positive column is obtained by equating the energy gained by the electrons in this field to that lost by collisions. The main assumption made is that axial electron concentration be constant along the column.In the second part of the paper, calculations are done which indicate that ion and electron concentration gradients exist in the positive column adjacent to the anode. It is pointed out that such a phenomenon will be pronounced only under special conditions of low transverse and high axial field, and will be enhanced with fast-flowing gases.A sample calculation is presented using the expression for the rate of electronic excitation of a species by electron impact, assuming a Maxwell–Boltzmann energy distribution for the electrons and constant elastic and inelastic collision cross sections.

Nonlinear Microwave Conductivity of a Slightly Ionized Gas for Arbitrary Collision Cross Sections

A tractable expression for the current density in a slightly ionized gas under the influence of an electromagnetic field is obtained for arbitrary velocity dependence of the electron---heavy-particle cross section for elastic collisions. The discussion is restricted to the case of a weak field in the high-frequency approximation (frequency of the field much greater than the average collision frequency) in an isotropic plasma. For the special cases of a constant mean free path and a mean free path inversely proportional to the square root of electron temperature, the current density obtained here agrees with results previously derived by Epstein. The effect of the nonlinearity is to increase the current density in phase with the applied field if the collision frequency increases with velocity, as with hard spheres; the nonlinearity decreases the in-phase component of the current density if the collision frequency decreases with velocity, as with screened Coulomb collisions. The case of constant collision frequency results in a linear current density. Simple applications to cross modulation by pulsed microwaves and frequency mixing are discussed.

Asymmetry-effects in molecule-molecule collisions

Abstract The effect of angular dependent terms in the intermolecular potential of colliding molecules is investigated in a first order distorted wave calculation. The final expression for the total elastic collision cross section is obtained in the approximation of Massey and Mohr.

Theoretical performance comparison of working fluids in a nonequilibrium mhd generator

Results of preliminary calculations are presented, based upon the theory of magnetically induced ionization, which indicate the relative performances of various systems under consideration for use in such nonequilibrium MHD power generators. All the alkali metal vapors and various seeded gas systems are considered. The flow is one-dimensional steady state with constant Mach number. The electrodes within the generator are assumed to be perfectly segmented. Because of much smaller elastic electron collision cross sections in hydrogen, helium, argon, and mercury, as compared to that of the alkali metals, the magnetic fields necessary to create the same power density are generally much lower in the former group as compared to equivalent systems in the latter group. A comparison of the alkali metal systems shows that the decrease in the ionization potential of the heavier elements is greatly overshadowed by the increase in atomic weight and especially by the increase in electron-neutral cross section. However, considering vapor pressure and dimer formation, potassium appears to be the best choice among the alkali metals as an MHD working fluid. Nonequilibrium potassium MHD generators, using only the phenomena of magnetically induced ionization, will probably require magnetic fields near 100 kgauss to produce power densities near 1 kw/cm.

Asymmetry effects in atom-molecule collisions I

For rotating molecules, scattered by particles of radial symmetry, the total elastic collision cross section is investigated. It is assumed, that the scattering takes place in a region, where a weak magnetic field is applied. Asymmetric terms in the intermolecular potential are taken into account as a small perturbation. The final result can be used to analyze experimental data obtained in scattering experiments with polarized molecular beams.

Asymmetry effects in atom-molecule collisions II

The total elastic collision cross section depends on the quantum numbers j and m j , if molecules with rotational angular momentum h ̵ √j(j+1) collide with atoms of radial symmetry. m j is the component of j measured in the direction of the relative velocity of the colliding particles. In an article quoted as I in the following we have described this dependency for cases where the intermolecular potential is of the form V = V 0(r)++ P 2( r ̂ · r ̂ ')·V 2(r) . r̂·r̂' is the cosine of the angle between the relative velocity and the molecular axis. In this article we shall specify the intermolecular potential as V = -C/r 6 - P 2( r ̂ · r ̂ ') ·C'/r 6 . The conditions will be assumed to hold, which justify the use of the Massey and Mohr approximation. The cases j = 1 and j ≫ 1 will be discussed.

Elastic and Inelastic Collision Cross Sections in Hydrogen and Deuterium from Transport Coefficients

By means of a numerical solution of the Boltzmann equation, elastic and inelastic collision cross sections have been derived for electrons in ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ subjected to a dc electric field. The cross sections for momentum transfer, rotational excitation, vibrational excitation, electronic excitation, and ionization are investigated by comparing experimental and theoretical values of transport coefficient. The same momentum transfer cross section previously obtained for ${\mathrm{H}}_{2}$ by Frost and Phelps has been found to be valid for ${\mathrm{D}}_{2}$. Good agreement is secured between experiment and theory by multiplying the theoretical rotational cross sections of Gerjuoy and Stein by approximately 1.5, provided the polarization factor of Dalgarno and Moffett is used. The final cross section for vibrational excitation of ${\mathrm{H}}_{2}$ has a threshold at 0.52 eV and a peak of 7.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 4.5 eV, whereas that of ${\mathrm{D}}_{2}$ has a threshold at 0.36 eV and a peak of 6.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 4.7 eV. The derived electronic excitation cross sections are the same for both ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. The ionization cross section was taken from the experimental results of Tate and Smith. Calculated transport coefficients for electrons subjected to crossed electric and magnetic fields, and high-frequency ac electric fields are in agreement with recent experimental and theoretical results.

Production of Low-Energy Cosmic Rays by Collisions of High-Energy Cosmic Rays with Interstellar Gas.

The production rate of protons of energy less than 1 BeV in interstellar space is calculated from empirical cross sections for proton-proton elastic and inelastic collisions in the kinetic energy range 1 to 30 BeV. Representing the cosmic ray intensity by a simple fit to the observed spectrum in the absence of solar activity the production spectrum is found to decrease steadily from zero energy to a value one- tenth as great at 500 MeV. The integrated production rate of 0-500 MeV protons is 10-26 cm-3 sec-1 from elastic collisions, and the contribution from inelastic collisions is estimated to be of lower order. The production spectrum is combined with the slowing lifetimes of protons in the interstellar gas (Meskys and Milford, Bull. Am. Phys. Soc. 8, 305, 1963) to give the density of these 0-500 MeV protons as 10-li cm-3 with an intensity of 10-i cm-2 sec-1. Recently Hayakawa, Nishimura, and Takayanagi (Publ. Astron. Soc. Japan 13, 184, 1961) have suggested that low-energy cosmic rays contribute appreciably to the heating of interstellar gas clouds, with an assumed low-energy cosmic ray intensity of order 100 cm-2 sec-1. From the above calculations it may be seen that high-energy collisions can not supply any significant fraction of such a hypothesized high intensity. Future measurements of low-energy interstellar cosmic rays will indicate what fraction of these can be attributed to the collision mechanism discussed above, and what fraction must be due to other mechanisms, such as stellar injection and interstellar magnetic field acceleration.

Thermalization of Positrons in Argon

The thermalization time required for positrons in argon is estimated by separating the energy range of positrons into the three regions (i) E > 0.01 MeV, (ii) 0.01 MeV > E > Eexc and (iii) E < Eexc (Eexc is the first excited level of the argon atom). The elastic collision cross sections determined by Marder et al. are re-evaluated. The thermalization time in region (iii) is not negligible compared with the free annihilation lifetime and most of the free positrons will be annihilated before being thermalized.

Resonance in Elastic Scattering of Electrons by Helium Atoms

In agreement with Schulz, resonance has been observed in the elastic collision cross section for electrons in helium. This occurs at approximately 0.5 eV below the 23S excitation threshold and leads to a temporary decrease of 6% in the value of the cross section. A compound He- ion state may be involved.

Use of Cataphoresis to Determine Discharge Parameters

The balance between diffusion and ion migration in dc discharges in certain mixtures of metal vapors and rare gases produces a very sharp line of demarcation between the region containing only the rare gas and the region containing both the rare gas and metal vapor. Although the formation of such a sharp boundary depends in a complex way upon the elastic and inelastic cross sections for electron-atom collisions, it can be used in a simple way for the determination of certain discharge parameters. If a cold spot with a well-defined location is provided near the cathode end of the positive column, the distance from the cold spot to the line of demarcation and the potential drop across the tube are, at a given current and rare gas pressure, accurately reproducible functions of the cold-spot temperature. If these functions are determined, and if the neutral-atom diffusion coefficient and positive ion mobility are known for the metal vapor in the rare gas, a simple theory yields values for electron concentration, electron mobility, and the ratio of electron to ion current as a function of pressure of the metal vapor. Detailed application has been made to a hot-cathode neon-mercury discharge over a range of mercury pressure from 2.5 to 25μ and for a neon pressure of 3 Torr. For a 500-mA discharge n− is about 3.5×1011 cm−3, μ− ranges from 1.4 to 2.5×106 cm2/V sec, and μ−/μ+, from 800 to 1800.

Low-Energy Collision Cross Sections of H— and OH— Ions in Oxygen

Elastic and inelastic collision cross sections have been measured for collisions of H— and OH— ions in oxygen gas in the energy range 4–350 eV. An improved collision chamber was used for the measurements. The majority of the inelastic collisions in the case of OH— are apparently due to electron detachment, but in the case of H—, charge exchange or an ion—molecule reaction or both predominate, particularly at the low energies. In the range 4–26 eV the interaction potential derived from the elastic scattering of OH— in O2 is V (eV) = —18.4/r5.34(r in Å). The large amount of inelastic scattering observed for H— in O2 precluded an accurate determination of the interaction potential in this case. The electrons produced in electron-detachment collisions of negative ions are shown to have energies considerably in excess of thermal energy.

Electron Drift Velocity in Liquid Argon and Argon–Nitrogen Mixtures

THE very large negative ion mobility observed by Malkin and Schultz1 and by Williams2 in liquid argon (about 10 cm2/V.sec) has been interpreted as indicating the existence of free electrons in this liquid. Estimates of the elastic collision cross-section by these authors on a basis of classical kinetic theory appeared to indicate that the liquid could not be considered as a compressed gas, but a comparative study of electron drift velocity data for mixtures of gaseous argon and small concentrations of molecular impurities showed that these earlier interpretations may be in error3.

Measurement by Cyclotron Resonance of Molecular Cross Sections for Elastic Collisions with 295°K Electrons

Cyclotron resonance absorption is used to obtain molecular scattering cross sections for electrons at 295°K. The electrons were present in active nitrogen obtained by passing N2 through a microwave discharge, and various gases were introduced into the active nitrogen downstream from the discharge. Very weak rf fields, with electric components parallel to the dc magnetic field, were used in order not to ``heat up'' the electrons. The observed width of the cyclotron resonance line is proportional to the molecular-electronic cross section since electron—electron collisions are not significant in these experiments. But suitable averages over electron velocities must be carried out to account for the observed line shapes and to relate the line widths to the cross sections. The spectral lines are sometimes quite asymmetric and this asymmetry can then be used as a rather sensitive measure of electron concentration. Dipolar gases were observed to have large cross sections which exhibited approximately a 32 power dependence on the dipole moment; theoretical calculations based on a partial wave treatment of dipole scatterers agreed well with experiments. The cross section for N2 is 4.96 Å2; for CO2 302 Å2; and for the dipolar gases N2O, NH3, SO2, HCF3, H2O, HCN, and CH3NO2, the cross sections are 56, 1560, 1840, 1760, 2360, 5280, and 6020 Å2, respectively. The dipolar cross sections are inversely proportional to the energy of the electrons, and both theoretical and experimental values of the cross sections refer to energies of 3k(295°)/2. The large cross section for CO2 probably arises from its large quadrupole moment.

Electron Photodetachment from Ions and Elastic Collision Cross Sections for O, C, Cl, and F

Photodetachment cross sections for ${\mathrm{O}}^{\ensuremath{-}}$, ${\mathrm{C}}^{\ensuremath{-}}$, ${\mathrm{Cl}}^{\ensuremath{-}}$, and ${\mathrm{F}}^{\ensuremath{-}}$ have been computed in the energy range from threshold to 50 ev by the Klein-Brueckner method. Elastic cross sections for electron scattering from O, C, Cl, and F in the energy range 0-15 ev have also been computed. The method of calculation is described and the results compared with earlier theoretical and experimental work.