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

Abstract

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.

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

“…This approach shows that he assumed that V is a short-range potential. (Thus his treatment and ours here too does not include electron-ion scattering discussed in [3].) If we now assume that E d = E c (i.e.…”

“…In previous works by Csanak et al [1][2][3], cross section formulae have been derived for the creation, destruction, and transfer of atomic multipole moments (and of ions in plasmas where there are screening effects) and of ionic multipole moments by elastic and inelastic electron scattering under non-relativistic 4 Guest scientist. [1,3] and relativistic [2] conditions, respectively.…”

“…In previous works by Csanak et al [1][2][3], cross section formulae have been derived for the creation, destruction, and transfer of atomic multipole moments (and of ions in plasmas where there are screening effects) and of ionic multipole moments by elastic and inelastic electron scattering under non-relativistic 4 Guest scientist. [1,3] and relativistic [2] conditions, respectively. In [1,3] the wave-packet propagation method of Rodberg and Thaler [4] was used, while in [2] the Gell-Mann-Goldberger (GG) [5] method was utilized based on Joachain's [6] implementation of it for cross section calculations.…”

“…[1,3] and relativistic [2] conditions, respectively. In [1,3] the wave-packet propagation method of Rodberg and Thaler [4] was used, while in [2] the Gell-Mann-Goldberger (GG) [5] method was utilized based on Joachain's [6] implementation of it for cross section calculations. Thus, both treatments used conventional wave function methods to accomplish their goals.…”

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

“…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.…”