Low-Energy e-He(2¹L) Scattering Calculations

Abstract

Cross sections for e-He(21L) scattering have been calculated in the energy range 1 ^E eV. For I > 0 partial cross sections a simple analytical method, proposed by the authors before, which is essentially an extension of Seaton's exact resonance method, has been applied. In the case 1 = 0, when a complex "angular momentum quantum number" in the rotated space appears, a matching procedure has been adopted, making use of a more realistic model potential.The results for Q(21S-21S), ^(2 1S-21P) and Q(21 P-2*P) cross sections are compared with other theoretical calculations and in the case of the elastic Q(21S-21S) cross section with the available experimental data as well.The applicability of the analytical method used in the electron-atom scattering calculations is discussed, in particular for those processes which play a dominant role in the Stark broaden ing of spectral lines from plasmas. Finally, the relevance of the present method to searching for an eventual resonant (or virtual) state near 2X S threshold has been discussed. I. IntroductionElectron-atom collision processes have been the subject of extensive experimental and theoretical studies, owing to their utmost importance in many physical systems, in particular in not too high tem perature plasmas. However, even in the case of e-H scattering, an exact analytical treatment of the complete collision phenomenon is beyond our pre sent mathematical capabilities, and a number of semianalytical, approximate methods have been de veloped (see e.g. Drukarev [1]). Employing refined numerical procedures, many of these methods are capable to provide accurate cross sections for vari ous processes (see e. g. Burke and Seaton [2]), usually at the expense of a considerable computing time consumed. On the other hand, in some applications scattering matrix elements (or the corresponding cross sections) of moderate accuracy, but in simple analytical form are needed, as is the case with the quantum theory of Stark broadening (Baranger [3]). In particular, in the expression for the halfwidth and shift of an isolated nonhydrogenic line one en counters the quantity I -Si Sr i, where $*(/> are the scattering matrix (diagonal) elements, for the elastic scattering on the initial (final) state of the transition. Since at low impact energies (these are usually met in plasmas where Reprint requests to Dr. P. Grujic, Institute of Physics, P. 0. Box 57, 11001 Belgrade, Yugoslavia. neutral species are still present) coupling with other atomic states are important (see e.g. Barnes and Peach [4]), second and higher order processes, like i -> i, i -> i" -etc., make considerable contributions to S^f) [5].One of the most powerful low-energy approxima tions for treating electron-atom (ion) scattering is the close coupling equations method. Within this approximation, the only analytically completely tractable case, to our knowledge, has been the dipole exact resonance model, due to Seaton [5], which applies to the hydrogen (degenerate) target. The principal shortcoming of the original Seaton t...