Definition of Cross Sections for the Creation, Destruction, and Transfer of Atomic Multipole Moments by Electron Scattering: Quantum Mechanical Treatment

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

“…We will follow here the treatment of Kulish and Fadeev [33], Veselova [29], Rosenberg [34][35][36] and Chandler and Gibson [28] in an attempt to modify the treatment of Csanak et al [1,2] so that it is applicable for ionic targets. The latter treatment, which was relevant for atoms, was in turn based on the wave-packet treatment of scattering by Rodberg and Thaler [49].…”

“…We assume that the wavefunctions corresponding to the |αJM ion state vectors are antisymmetric in all of the bound-electron coordinates. By constructing the 'in' asymptotic state according to equation (1), we have assumed, as in [1] and [2], that the A( k) function is strongly peaked around the value k = k in and it is normalized according to the equation…”

“…We will discuss below (see section 3) an ambiguity that arises in the case of electron-ion elastic scattering and how that ambiguity can be resolved via the use of the Gell-Mann-Goldberger (GG) ('two-potential') formula. Interestingly, Csanak et al [53] conjectured that for electron-ion scattering, the alignment creation cross section formula for elastic scattering would be the same as for inelastic scattering, a conjecture that appears to have been correct. Since the derivation of the multipole cross sections for inelastic scattering from this point on is the same as in the works of Csanak et al [2], it will only be briefly summarized here.…”

“…In the earlier works of Csanak et al [1,2], the wavepacket formalism of scattering was used to obtain a quantum mechanical definition of atomic multipole moment creation, destruction and transfer cross sections for electron scattering by atoms (or by ions in plasmas where screening effects are operational) for both elastic and inelastic scattering. These cross sections play an important role in the populationalignment collisional-radiative model (PACR) of Fujimoto and collaborators [3][4][5] intended for the modelling of cylindrically symmetric plasmas and they can also be useful for plasma kinetic models with more general distribution functions.…”

“…In this work, we will follow the wave-packet propagation approach of Csanak et al [1,2], properly modified according to Dollard [25], Kulish and Fadeev [33], Chandler and Gibson [28], Rosenberg [34][35][36] and Bencze and Chandler [40] to take into account the long-range Coulomb potential as well as exchange effects. We will define the multipole creation, destruction and transfer cross sections for electron scattering by ions and we will show how the Dollard definition of the electron-ion scattering operator can be related to some calculational schemes that have been used in the past for electron-ion scattering.…”