Electron-atom Cross Sections Research Articles

Role of electronic excitation on thermodynamic and transport properties of argon and argon-hydrogen plasmas

Thermodynamic and electron transport properties of the argon and argon-hydrogen plasmas have been calculated under the local thermodynamic equilibrium conditions in temperature range of 10 000-40 000 K over the wide range of pressures. Electronic excitation affects strongly these properties especially at high pressures. The inclusion of electronically excited states (EES) in relevant partition function influences the internal contribution to frozen and total specific heat for argon and argon-hydrogen plasma and it has been observed that although the total specific heat of argon plasma is less than that of hydrogen plasma, yet its internal contribution is more. Compensation between different contributions to total specific heat (by including and neglecting EES) occurring in hydrogen plasmas at low pressures has not been observed in argon and argon-hydrogen plasmas. As electron transport properties strongly depend upon the degree of ionization, therefore larger relative errors are found for these properties with and without EES, and in contrast to hydrogen plasma there exist a dominance of electron-atom cross section at low temperatures and EES dominance at intermediate temperatures.

Total cross sections for electron scattering by oxides of iron

Total (elastic + inelastic) cross sections for electron impact on FeO, Fe 2O 3 and Fe 3O 4 have been calculated in the energy range 20–5000 eV by employing the additivity rule which expresses the total cross section of a molecule as an incoherent sum over the total cross sections of the constituent atoms of the molecule. The electron-atom cross sections have been obtained by a complex optical potential method through partial-wave analysis. The total cross sections for all the oxides of iron exhibit a maximum around 30 eV. The inelastic cross sections are upper bounds to the corresponding ionisation cross sections. Bethe parameters for inelastic cross sections are given.

Momentum-transfer dispersion relations for electron-atom cross sections.

We derive momentum-transfer dispersion relations by showing that at fixed impact energy the electron-atom differential cross sections are analytic functions of the momentum transfer squared ${\mathit{K}}^{2}$ in a complex plane cut from -\ensuremath{\infty} to 0, along the real axis. It is therefore natural to introduce sets of interpolating rational functions of ${\mathit{K}}^{2}$ to fit experimental data. The most suitable are the Pad\'e approximations. We find that the zeros and the poles of these approximations split into two families. One family is made of poles and zeros that sit on the cut, yielding a good simulation of it. The other family takes care of the noise in the data: poles and zeros appearing in pairs very near each other. We can therefore first filter the noise by eliminating those pairs. Among the remaining poles, one pole is extremely near ${\mathit{K}}^{2}$=0 for the inelastic differential cross sections. We apply this technique to recompute both elastic and inelastic cross sections for Xe, Kr, and Ar atoms, at impact energies of 100, 400, and 500 eV. In this way, we get the optical oscillator strength for two optically connected states. Our results are compared with other experimental as well as theoretical results.

A purely classical approach in the Born theory of the exchange scattering of electrons by atoms

A purely classical method of calculation of electron-atom cross sections is suggested. The state of the bound electron is described by the microcanonical distribution function. The probability of some transition is assumed to be determined by the measure of intersection of two manifolds in the phase space of the target-the microcanonical ensemble, corresponding to the initial state, and a similar ensemble, corresponding to the final state, the latter being shifted by a given vector q, representing the momentum transferred to the atom by the colliding electron.

A uniform WKB analysis of the coupling of electron attachment and thermalization in gases

The presence of small amounts of strongly electronegative gases such as SF6 and CCl4 can greatly perturb from equilibrium the electron energy distribution function in a variety of electron devices. The effect of the addition of these electron attaching gases on the relaxation behaviour of a nonequilibrium electron distribution is studied with a linear Fokker-Planck equation. The time dependence of the electron mobility as well as other transport properties can be expressed as a sum of exponential terms with each term characterized by an eigenvalue of the Fokker-Planck operator. This eigenvalue problem can be transformed to a Schrodinger equation with a potential function parametrized by the electron-atom cross sections, the electric field strength and the gas temperature. In the present paper, the eigenvalues and eigenfunctions are calculated with a WKB semiclassical approximation and compared with exact results.

A uniform WKB approach to electron thermalization in gases

The relaxation of a nonequilibrium distribution of electrons in gases is governed by a linear Fokker-Planck equation. The time variation of the electron transport properties can be expressed as a sum of exponential terms with each term characterized by an eigenvalue of the Fokker-Planck operator. This eigenvalue problem can be transformed to a Schrödinger equation with a potential function parametrized by the electron-atom cross section and the gas temperature. In the present paper, the eigenvalues and eigenfunctions are calculated with a WKB semiclassical approximation and compared with exact results. The application of the WKB approximation provides a useful interpretation of the results and permits the use of initial delta function distributions at much higher initial energies than previously possible. The specific applications in this paper are for the relaxation of electrons in helium and neon.

A triangular property of the associated Legendre functions

The property of the associated Legendre functions with non-negative integer indices, Pmn(z), described by the formula: Pmn (cos β)=(−1)m(a/c)n ∑n−mk=0 (n+mk) (−b/a)n−k ×Pmn−k(cos γ), where a,b,c are the sides of an assigned triangle and α,β,γ the respective opposite angles, is introduced. A useful application of this series in simplifying the calculation of collisional electron–atom cross sections higher than the dipole is mentioned. A proof of the stated identity by use of the Gegenbauer polynomials and of their generating function is given.

A new program to calculate differential and total cross sections for electron-atom or ion scattering using the momentum transfer formalism

A new program to calculate differential and total cross sections for electron-atom or ion scattering using the momentum transfer formalism

A new program to calculate differential and total cross sections for electron-atom or ion scattering using the momentum transfer formalism

A new program to calculate differential and total cross sections for electron-atom or ion scattering using the momentum transfer formalism

Laser-assisted inverse bremsstrahlung in a weakly ionised plasma

Effective electron-ion and electron-atom cross sections and energy changes in a slightly ionised gas when a laser field is present are derived. The numerical analysis is restricted to: (i) weak laser fields; (ii) mean electron kinetic energy greater than the laser photon energy; and (iii) an average electron-atom collision frequency much smaller than the frequency of the assisting field. The electron-ion cross section exhibits a sharp decreasing behaviour as a function of the laser intensity, and significant changes against the laser frequency. The electron-atom cross section shows a more smooth behaviour against the laser intensity and frequency. The energy changes are very rapidly decreasing functions of the laser frequency and are, generally, non-linear rising functions of the intensity.

Electron-atom momentum-transfer cross sections for caesium from the measured electron thermal conductivity

A method is proposed to determine the dependence of the electron-atom cross section on the energy from measured values of the thermal-conductivity coefficient in a plasma. Preliminary results on Cs are reported.

Laser-induced free-free electronic transitions near a resonance

A theory of electron-atom scattering in the presence of moderately intense laser fields is applied to resonant electron-atom scattering. The radiation field is treated in the lowest perturbative order and the electron-atom interaction is approximated in terms of the N-state close-coupling model. A resonance in the elastic electron-atom cross section in the absence of the laser field at the energy ER leads to two resonances in the free-free absorption cross section when the laser field is present. These two resonances are due to resonant scattering of the electron by the target atom before or after a photon is absorbed. If the field-free electron-atom resonance occurs in the lth partial wave, and if the photon polarization vector is taken parallel to the initial electron momentum, the angular distributions corresponding to these two resonances are proportional to cos2 theta Pl2(cos theta ) or to Pl2(cos theta ). Furthermore two versions of soft-photon approximations are tested numerically on a two-state close-coupling model. For a CO2 laser these soft-photon expressions agree within an error of only 2% with the results of the exact calculations. Application of this soft-photon approach to the Ar+e-+h(cross) omega CO(2) experiment of Andrick and Langhans (1975) yields a free-free transition rate of 150 s-1. These results agree to within 2% with the numerical calculation of Geltman (1972), who employed more realistic model potentials.

Influence of electron-atom cross section uncertainties on shock wave structure

The exact value of the electron-atom collisional ionization cross section for argon is not accurately known. The purpose of the present research is to determine numerically the effect of varying the magnitude of the electron-atom cross section on nonequilibrium shock-wave structure. Mach 18 shock waves propagating into an argon-like gas at 1 cm-Hg and 300°K have been analyzed. Thermal, ionizational, and excitational non-equilibrium are considered in the relaxation region behind the shock wave. Electrons in the relaxation region are formed by a two-step collisional process, wherein the atom is first excited and then it is ionized. The precursor is formed by ground and excited state continuum radiation and line radiation which is emitted, but not reabsorbed, in the region behind the shock wave. When the electron-atom ionization cross section is varied from 1·86 × 10 −4 to 1·86 × 10 −2 cm 2/ erg, the results show that (1) it influences the coupling between the precursor and relaxation region through the radiative source functions, (2) it does not influence the distance necessary to attain equilibrium behind the shock wave, (3) it inversely influences the magnitude of the precursor ionization, and excitation, and (4) it inversely influences both the free electron and excited state population in the relaxation layer.

Transport properties of two-temperature partially ionized argon

Calculations are presented for the transport properties of a two-temperature argon plasma based on the Chapman-Enskog and perturbed-Lorentzian solutions of the Boltzmann equations. The convergence problems known to exist in the Chapman-Enskog solution for the properties of a one-temperature argon plasma also occur here; this difficulty is removed by using the perturbed Lorentzian solution at low and moderate degrees of ionization. Also, it is found that the lowest order perturbed Lorentzian and Chapman-Enskog approximate solutions provide upper and lower bounds to the actual solution at low and moderate degrees of ionization. Finally, owing to the Ramsauer minimum in the electron-atom cross section, the electrical conductivity of the two-temperature argon plasma is found to decrease with increasing electron temperature (at fixed heavy particle temperature and electron density) at low degrees of ionization, and increase with increasing electron temperature at higher degrees of ionization.

Multiple solutions of hartree-fock equations

In the calculation of electron-atom cross sections it is often quite useful to obtain wave functions for the scattered particles which are orthogonal to the wave functions of the electrons bound in the atom. This constraint, although it may neglect certain couplings, provides a considerable simplification in obtaining certain transition matrix elements. A straightforward technique for enforcing this orthogonality condition is to include Lagrange multipliers in the differential equation. It has been found that depending on the values of the Lagrange multipliers there may be zero, one, or two solutions. However, the solution which yields orthogonality is unique. Non-iterative schemes for solutions are discussed and applied to electronhydrogen atom scattering.

Low-Energy Electron Momentum Transfer Collisions in Cesium Plasmas

An effective momentum transfer collision frequency for electrons in cesium plasmas has been determined from measurements of the electrical conductivity and plasma properties in a cesium arc column. The effective collison frequency was found to depend on electron temperature in the 2500 to 4500°K range and to be significantly dependent on degree of ionization for values of this parameter greater than about 3 × 10−4, indicating a contribution from electron-ion collisions. Numerical evaluations of the velocity integral for the electrical conductivity, modified to include electron-ion as well as electron-atom momentum transfer collisions, have been carried out using many trial functions for the electron-cesium atom momentum transfer cross section. The electron-atom cross section which has given the best fit between the calculated and measured conductivity exhibits a Ramsauer-like minimum in the 0.25-to 0.55-eV range of electron energy.

Mechanism of gas breakdown by lasers

When intense laser pulses are focused down to yield radiation intensities of about 6 × 1011 w cm-2, it is observed that air at atmospheric pressure breaks down with spark emission. It is proposed that the breakdown results from cascade or avalanche ionization, the initial electron being produced by an unspecified multi-photon transition. A free electron absorbs energy from the radiation field by making a free-free transition in the field of an atom (the system of electron plus atom constituting a negative ion). This process (bremsstrahlung absorption) is the quantum-mechanical description of the classical process considered to explain microwave breakdown-absorption of energy ΔW at electron-atom collisions due to a change of phase of the oscillatory electron velocity relative to the oscillatory electric field. It is wrong to regard bremsstrahlung absorption as a separate process from microwave breakdown process. Also the classical theory does not fail when ΔW < hv, because the absorption of a photon cannot be measured in a time less than the reciprocal of the transition probability for the free-free absorption, and during this time many electron-atom collisions may occur. For the case of atomic hydrogen gas the cross section for free-free absorption in the negative ion is known, and on the grounds that the classical rate of absorption of energy should equal the quantum mechanical rate of absorption, an equivalent electron-atom cross section of 7.4 × 10-16 cm2 is derived. After an ionization a secondary electron gains sufficient energy in the above radiation field to cause further ionization in a time of 0.73 × 10-10 sec, with losses being neglected. After about 43 generations of secondary electrons (for which a time of 3 × 10-9 sec is required) the gas in the focal volume (4 × 10-6 cm3) is fully ionized. Only when the gas is 100% ionized will the plasma strongly absorb the laser pulse by free-free transitions in the neutral atom system. Finally, the neglect of losses due to diffusion and recombination is discussed, and it is shown that the atom or positive ion gas will come to thermal equilibrium with the electron gas only after the cascade ionization is complete. A final peak gas temperature of the order of 107 °K should be reached.

Ionization Rates behind Shock Waves in Argon

The ionization rate behind shock waves in argon has been recalculated allowing for excitation and ionization by atom-atom collisions. Good agreement is obtained between these calculations and the experimental results of others for very pure argon. For pure argon, the initial rate of ionization is controlled by the rate of excitation from the ground state by means of atom-atom collisions. The atom-atom cross sections are several percent of the corresponding electron-atom cross sections. When the degree of ionization builds up to some value greater than 10−4, electron-atom collisions dominate, and then the ionization rate is controlled by the rate of energy transfer between ions and electrons by means of elastic collisions. The effect of impurities is considered and a relatively crude theory is proposed to explain the experimental observations. It is shown that one must be careful to distinguish between ionization times and luminosity delay times.