G. Csanak

Differential cross sections for electron impact excitation of Xe: I. Excitation of the five lowest levels; experiment and theory

Experimental and theoretical differential cross sections (DCSs) for electron impact excitation of the five lowest levels of xenon are reported. The experimental data were obtained at impact energies of 10, 15, 20 and 30 eV for scattering angles in the range of to . The scattering intensities for excitation of various levels with respect to that of the combined two lowest levels (representing the corresponding DCS ratios) were measured with conventional electrostatic electron energy-loss spectrometers. Absolute DCSs for excitation of the combined two lowest levels were derived from DCS ratios for excitation of the combined two lowest levels and elastic scattering and utilizing the elastic DCSs of Register et al. These DCS ratios were obtained from scattering intensity ratios measured with conventional electrostatic electron energy-loss spectrometers after correction for instrumental effects by utilizing electron time-of-flight measurements for determining the proper value of this ratio at scattering angle for each impact energy. The unitarized first-order many-body theory and the unitarized distorted-wave approximation were applied to obtain the theoretical differential cross sections for impact energies of 10, 15, 20, 30, 50 and 80 eV. The present experimental and theoretical results are compared with each other and with other available experimental and theoretical DCSs.

The creation, destruction and transfer of multipole moments in electron scattering by ions

Expanding on previous works that involved the scattering of electrons by atoms, we use the wave-packet propagation scheme of Dollard to define multipole moment creation, destruction and transfer cross sections for elastic and inelastic scattering of electrons by ions. We find that our cross section formulae for inelastic scattering agree with those obtained by Fujimoto and coworkers, who used semi-classical collision theory and the impact approximation, but differ from the expressions obtained by them for elastic scattering cross sections. This latter result is due to the fact that Dollard?s theory takes into account the concept that, in the case of electron?ion scattering, the incident and scattered electrons are asymptotically not free. In addition, we apply the Gell-Mann?Goldberger (?two-potential?) formula in order to provide an unambiguous definition of elastic cross sections, as well as to provide a convenient way of obtaining practical expressions associated with well-established methods, such as the Coulomb?Born and distorted-wave approximations. The present theoretical framework will be the basis for numerical calculations considering specific examples in a future work.

Cross sections for the excitation of 3s,3p,3d,4p, and 4s manifolds in e-Ne collisions

Theoretical differential and integral cross sections are reported for inelastic scattering of electrons by neon atoms for incident electron energies in the range of 20-100 eV. Transitions from the ground state to forty states associated with the 3s, 3p, 3d, 4s, and 4p manifolds were considered. The methods employed were the distorted wave approximation and first-order many-body theory, where the distorting potential includes the static-exchange potential. A comparison of our results with experimental data and other theoretical results are shown and discussed.

Corrigendum: The creation, destruction and transfer of multipole moments in electron scattering by ions (2012 J. Phys. B: At. Mol. Opt. Phys. 45 105202)

We found that the second line of equation (15) and equations (17), (18), (20), and (25) leading to the formula given by equation (27) are erroneous. Analogously, the second line of equation (57), as well as equations (58) and (63), which lead to equation (65), are erroneous. Nevertheless the formulae given by equations (27) and (65) are correct (except for a typographical error in equation (65)). Consequently, all inferences made from equations (27) and (65) are also correct. The reason for the error in the above equations is the unusual form of the intertwining relation for charged-particle scattering and the decisive role it plays in obtaining the above equations. The unusual form of the intertwining relation for multichannel charged-particle scattering was obtained by Dollard [26] (equation (408) on p 80), which is to be compared to the form of the same relation for scattering with shortrange interaction potentials. (See e.g. in [50] pp 39–40, or in [26], equation (316) on p 64.) Consequently, for chargedparticle systems the mentioned erroneous equations cannot be obtained, while they are valid for particles interacting via short-ranged potentials 5 .

Creation, destruction, and transfer of atomic multipole moments by electron scattering: Liouville-space formulation

In previous works, expressions for the atomic multipole moment cross sections were derived from a traditional collision approach. In the present work, we have derived the fundamental formula (see equation (35)) from which all of the atomic multipole moment cross sections can be obtained by using Liouville-space methods introduced by Fano (1963 Phys. Rev. 131 259). This simple, elegant formula is an expression for the multipole cross sections in terms of the Liouville-space transition operator (sometimes referred to as the tetradic transition matrix or the transition superoperator). The transition superoperator, in turn, can be expressed in terms of the traditional quantum mechanical transition operators via a formula which is sometimes referred to as ?Fano?s convolution formula?. Upon application of this formula to our Liouville-space expression for the multipole cross sections, the resulting cross section formulae are identical to those obtained in previous works. Establishing this connection with the Liouville-space formalism allows us to apply powerful group theoretical techniques in order to obtain expressions of practical interest. As a specific example, we consider the transition rate for the final-state multipole moment which can be obtained via the use of a ?connecting factor? from the initial values of the multipole moments. The ?connecting factor?, in turn, is expressed in this work as a Liouville-space matrix element of the tetradic transition matrix. Based on this expression and the symmetry properties of the electron?atom collisional system, certain symmetry relations are obtained for the ?connecting factors?. Since these factors are proportional to the multipole cross sections, corresponding relations are also obtained for those cross sections, which results in a reduction in the number of values that needs to be calculated for plasma modelling applications. An additional corollary of practical importance is that, in the case of cylindrically symmetric plasmas, the same symmetry relations also hold for the multipole rate coefficients. We provide an explicit derivation of this new, important result.

The creation, destruction, and transfer of multipole moments in electron- and proton-impact ionization of atoms and ions

Expanding on previous works that involved elastic and inelastic scattering of electrons by atoms and ions, we use the wave-packet propagation scheme of Dollard to define multipole moment creation, destruction and transfer cross sections for electron- and proton-impact ionization of atoms and ions. The electron-impact cross sections can then be used by defining appropriate rate coefficients for use in Fujimotos population-alignment collisional-radiative model for cylindrically symmetric plasmas. Our result for the alignment creation cross section is in agreement with those formulae that were obtained earlier intuitively or by semi-classical collisional methods. The multipole cross sections obtained here can be used also for modelling the relaxation behaviour of laser-excited plasmas under cylindrical symmetry conditions. We have also derived the electron- and proton-impact ionization multipole cross sections in terms of Liouville-space quantities, which then enabled us by using group theoretical methods to obtain the azimuthal-angle dependence of the multipole cross sections and symmetry properties that are results of reflection across a plane over the collisional axis.

The derivation of kinetic equations for anisotropic plasmas from the impact approximation

We derive the generalized population-alignment collisional-radiative model and the magnetic sublevel to magnetic sublevel (MSTMS) rate equation scheme from Fanos quantum impact approximation under certain hypotheses. This derivation employs a fully quantum mechanical treatment, as opposed to the semi-classical or intuitive approaches that have been used and applied in previous works. We have also given a quantum mechanical derivation for the formula, obtained semi-classically by Omont, Fujimoto and Kazantsev and co-workers, which expresses the rate coefficient for a cylindrically symmetric plasma in terms of those associated with a unidirectional, monoenergetic plasma. A practical prescription has also been provided for obtaining the MSTMS rate coefficients in terms of fundamental quantities that are readily calculated with available computer codes.

Various applications of atomic physics and kinetics codes to plasma modeling

A collection of computer codes developed at Los Alamos have been applied to a variety of plasma modeling problems. The CATS, RATS, ACE, and GIPPER codes are used to calculate a consistent set of atomic physics data for a given problem. The calculated data include atomic energy levels, oscillator strengths, electron impact excitation and ionization cross sections, photoionization cross sections, and autoionization rates. The FINE and LINES codes access these data sets directly to perform plasma modeling calculations. Preliminary results of some of the current applications are presented, including, the calculation of holmium opacity, the modeling of plasma flat panel display devices, the analysis of some new results from the LANL TRIDENT laser and prediction of the radiative properties of the plasma wakefield light source for extreme ultraviolet lithography (EUVL). For the latter project, the simultaneous solution of atomic kinetics for the level populations and the Boltzmann equation for the electron energ...

Comments on the interpretation of electron-photon coincidence experiments

An important consequence of the spin-orbit coupling effect is discussed for the interpretation of electron-photon coincidence experiments. If spin-orbit coupling is included into the scattering process new parameters have to be introduced. Previous experiments on neon, argon, krypton and mercury have to be reinterpreted in terms of these parameters.

Ne IX line G-ratio in a non-Maxwellian and anisotropic plasma

We have theoretically studied how the presence of a small proportion of energetic beam electrons mixed to a bulk of Maxwellian electrons in a hot plasma affects the temperature-dependent intensity ratio G = (x + y + z)/w of the helium-like triplet intercombination (x, y) and forbidden (z) lines to the singlet resonance line (w). By modelling the electron distribution function as a combination of a Maxwellian isotropic component and a monoenergetic beam component, detailed calculations of the G ratio of the Ne8 + lines have been performed for temperatures Te of the Maxwellian component and kinetic energies e0 of the beam component in the ranges 106?107 K and 1.5?25 keV, respectively. A magnetic sublevel-to-magnetic sublevel collisional-radiative model has been used for determining the populations of the upper magnetic sublevels of the four lines at an electron density below 1013 cm?3. Excitations from the ground 1s2?1S0 and metastable 1s2s?3S1 magnetic sublevels to the 1snl (n = 2?4) magnetic sublevels as well as the inner-shell ionization of the lithium-like ion in its ground level were taken into account. All basic atomic data, including the radiative transition probabilities and the collisional excitation and ionization cross sections, were computed using the flexible atomic code. It is found that the contribution of a 5% fraction of the beam component can reduce the G ratio by a factor of 30 at Te = 106 K and of 2.4 at Te = 3 ? 106 K. Our calculations also indicate that the effect of directionality of the beam component on G is negligible for e0 above ?10 keV and that for a given Te, G is practically insensitive to variations in e0 above ?7 keV.