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

Abstract

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 Fujimoto’s 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.

Corrigendum: The creation, destruction, and transfer of multipole moments in electron- and proton-impact ionization of atoms and ions (2013J. Phys. B:At. Mol. Opt. Phys. 46 245202)

“…This is a follow-up to the first corrigendum which was reported in [2] to correct errors of a similar nature in another previously reported work [3]. The source of all those errors resides in the treatment of charged-particle scattering and the subtle manipulations made to obtain some of the equations in both [1,3]. All equation numbers cited here correspond to those of [1] unless specified otherwise.We found that equation ( 8), along with equations ( 10) and ( 15) which lead to the formula given by equation ( 17), are erroneous.…”

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The present corrigendum is dedicated to correcting unfortunate errors made in certain equations of our paper [1]. We should first stress the point that those errors have no serious consequences on the main results of the paper and most derived equations remain valid.

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The creation, destruction, and transfer of multipole moments in electron–ion three-body recombination using the Gell-Mann–Goldberger–Watson method

“…, 0 0, , 5 ¹ ¢ Following now the procedure of Joachain [11] and Csanak et al [17], we take the derivative of the left-hand side of equation (5) with respect to t and the t ¢  -¥ limit to obtain for the rate coefficient the formula…”

“…In our previous work [1], hereafter referred to as I, the wavepacket formalism of scattering has been used for the quantum mechanical definition of multipole moment creation, destruction and transfer rate coefficients for three-body electron-ion recombination. The same formalism has been used earlier for the treatment of the multipole moment cross section problem for electron-atom and electron-ion scattering [2][3][4] and for electron-and proton-impact ionization of atoms and ions [5]. Such cross sections play an important role in the population-alignment collisional-radiative model (PACR) of Fujimoto and collaborators [6][7][8] intended for the modeling of plasmas with cylindrically symmetric electron velocity distributions.…”

Kinetic equations for cylindrically symmetric plasmas including atomic coherence and Coulomb potential effects

“…In earlier works, Csanak et al discussed the creation, destruction and transfer of multipole moments in electron scattering by ions [28], by electron-impact ionization of ions [29], and in electron-ion three-body recombination [30]. Thus with the kinetic equations developed here for highly charged ions, the theoretical foundation of the complete PACR calculational scheme for such systems has been formally realized.…”