Integral Elastic Scattering Cross Sections Research Articles

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.

Resonances in the integral elastic scattering cross section of ozone below 20 eV

Elastic scattering of electrons by ozone is considered. Calculations are made at the static exchange level of approximation using the polyatomic R-matrix method. Several shape resonances are found below 20 eV scattering energy. Integral elastic scattering cross sections are evaluated and these are found to be in good agreement with the few widely spaced energy points available from experiment, which did not indicate the presence of a resonance.

Total cross section measurements for electron scattering on CH 4 from 4 to 300 eV

Total cross sections have been measured for electron scattering on CH 4 in the 4–300 eV energy range utilizing a linear attenuation technique. The present results are compared with existing experimental data of other groups in this energy range. Generally, a good agreement with other experimental data is found except with those of Barbarito, Basta and Caliechio and Sueoka and Mori. The total electron scattering cross sections below 10 eV are inconsistent with available integral elastic scattering cross sections. It is suggested that the elastic data are in error and should be remeasured.

R-matrix calculations of low-energy electron scattering by oxygen molecules.

The R-matrix method has been used to study the scattering of electrons by oxygen molecules for impact energies in the range from threshold to 15 eV. Electronic excitation cross sections for transitions to the ${\mathit{a}}^{1}$${\mathrm{\ensuremath{\Delta}}}_{\mathit{g}}$, ${\mathit{b}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$, and ``6 eV'' states of oxygen are presented. Important contributions from a $^{2}\mathrm{\ensuremath{\Pi}}_{\mathit{u}}$ resonance, in addition to the well-known $^{2}\mathrm{\ensuremath{\Pi}}_{\mathit{g}}$ resonance, are found to significantly modify previous theoretical predictions. Integral elastic-scattering cross sections are also obtained for the first time for a complicated open-shell system using an ab initio method.

Total cross sections for high-energy electron scattering by H2 (1 Sigma g+), N2 (1 Sigma g+), and O2 (3 Sigma g-).

Total inelastic cross sections are calculated for collisions of ground-state ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$ with fast electrons according to the revised Bethe theory given by Inokuti et al. The asymptotic forms of the total elastic-scattering cross sections in the first Born approximation due to Inokuti and McDowell and including an electron exchange correction are also evaluated for these molecules. For ${\mathrm{H}}_{2}$, various accurate configuration-interaction wave functions are used to compute the total inelastic and the integral elastic-scattering cross sections. Good agreement between theory and experiment is found for the total cross sections (inelastic and elastic) for high incident energies as well as incident energies near 1 keV. The cross sections are also given for ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}$. Since there are no experimental reports for the integral elastic cross section for ${\mathrm{N}}_{2}$ or ${\mathrm{O}}_{2}$ at very high incident energies, the comparison is made only for the experimental data at incident energies near 1 keV. It is found that the theoretical results overestimate the experimental data by about 30% for ${\mathrm{N}}_{2}$. However, the Bethe total inelastic cross sections are in good agreement with experiments. Since the Born-Bethe approximation may not be valid at lower incident energies, more accurate experimental data at very high incident energies are required for valid comparison with the theoretical results reported here.

Complex optical potential model for electron–molecule scattering, elastic scattering, and rotational excitation of H2 at 10–100 eV

We report nonempirical calculations for differential and integral elastic scattering cross sections, absorption cross sections (accounting for electronic inelasticity), and total scattering cross sections for electron–H2 scattering at 10–100 eV. The calculations are based on a complex, energy-dependent effective potential consisting of four terms: A static potential calculated from ab initio extended-basis-set Hartree–Fock (EBSHF) wave functions, a polarization potential calculated from an ab initio EBSHF adiabatic polarization potential modified by the local-kinetic-energy semiclassical polarization model to account for nonadiabatic effects, an exchange potential calculated from the EBSHF static electron density and static potential by the semiclassical exchange approximation, and an imaginary absorption potential calculated from the EBSHF static electron density and static potential by the quasifree scattering model with Pauli blocking. We obtain good agreement with all available experimental data at impact energies 10, 40, and 100 eV. Additional calculations with simplified potentials show that nonadiabatic effects on the real polarization potential and the inclusion of an imaginary absorption potential are both essential to the success of the theory except for the large-angle scattering at the highest energy, where the calculated absorption effect is too strong.

Integral elastic-scattering of Kr+ and Xe+ ions in collision with He atoms

Integral elastic-scattering cross sections in collision with He atoms were measured for Kr+ and Xe+ ions with kinetic energies in the range 0.5–3.0 keV formed under various source conditions. Variation of source gas compositions and methods of ion formation had no effect on the cross sections. A possible explanation of the results is that the population distributions of the ions (2P3/2 and 2P1/2) produced in the ion source are quite similar.

Repulsive potentials derived from the integral elastic scattering of Ar+ and Ne+ ions in collision with He atoms

Integral elastic scattering cross sections have been measured for Ar+ and Ne+ with kinetic energies in the range 0.4–3.0 keV scattered by stationary He atoms through effective laboratory angles greater than 5×10−3 rad. The effective repulsive potentials in the range 0.7–7 eV have been derived from the cross sections. The potential values are compared with the statistically weighted mean of the potentials of the quasimolecular states X 2Σ and A 2Π obtained in configuration interaction calculation by Olson and Liu for Ar+–He and by Blint for Ne+–He. Agreement between the experimental and the theoretical values is satisfactory.

Electron scattering from Li at 5.4, 10, 20 and 60 eV impact energies

Differential and integral cross sections for elastic scattering and for the excitation of the 2p2P, 3p2P, 4p2P and 3s2S states of lithium have been determined and elastic momentum transfer cross sections have been obtained at 5.4, 10 and 60 eV electron impact energies. The cross sections were normalized to the absolute scale by using the total cross section measurements of Kasdan et al. (1971). The integral elastic scattering cross sections have been compared to calculations utilizing the Glauber and Born approximations and the 2p2P integral cross section results have been compared with optical excitation function measurements and with close-coupling calculations.

Experimental determination of repulsive potentials between alkali ions (Li+, K+, and Cs+) and hydrogen molecules (H2 and D2)

Integral elastic scattering cross sections of alkali ions (Li+, K+, and Cs+) in collision with room temperature hydrogen molecules (H2 and D2) were measured in the ion energy range 500–4000 eV. Some difference in the cross sections due to the replacement of the target gases were found in K+- and Cs+-hydrogen systems. Most of the difference can be explained by the difference of the target masses. The repulsive potentials deduced from the cross sections in a usual manner are represented by the following formulas independently of the isotopes: Li+: V(R) = 345 exp(−4.31 R), 0.88 < R < 1.43; K+: V(R) = 810 exp(−3.52 R), 1.33 < R < 1.98; and Cs+: V(R) = 1110 exp(− 3.26 R), 1.55 < R < 2.25; where V(R) is in units of electron volts and R in angstroms.

Experimental Determination of the Repulsive Potentials between Li+ Ions and Rate-Gas Atoms

Integral elastic scattering cross sections of Li + ions scattered through effective laboratory angles greater than 5×10 -3 rad in collision with Ne, Ar, and Kr atoms at room temperatures were measured in the ion energy range of 500–4000 eV. The repulsive potentials derived from the cross sections are represented by the following analytical formulas:

Elastic Scattering of Li+ Ions in Helium

Repulsive potentials between a Li+ ion and a He atom have been derived from the experimental values of integral elastic scattering cross sections of the ions in the energy range of 500–4000 eV. The potentials are well represented by the following analytical expression: V(r)=428 exp(−5.11r), 0.78≤ r≤ 1.21, where V(r) is in units of eV and r in angstroms.

Experimental Determination of the Repulsive Potentials between K+ Ions and Rare-Gas Atoms

Integral elastic scattering cross sections have been measured by the attenuation method for potassium ions with an energy selected in the range of 500–4000 eV scattered by room-temperature He, Ne, Ar, and Kr atoms through effective laboratory angles greater than 5×10−3 rad. The repulsive potentials have been derived from the measured values of the cross sections with allowance for the density distribution across the beam in the collision chamber. The potentials are well represented by the following expressions: He: V(r) = 1110 exp(−4.15r) for 1.23 < r < 1.77,Ne: V(r) = 4910 exp(−4.40r) for 1.55 < r < 2.04,Ar: V(r) = 2920 exp(−3.46r) for 1.79 < r < 2.43, and Kr: V(r) = 6420 exp(−3.69r) for 1.92 < r < 1.53, where V(r) is in electron volts and r in angstroms.