Example: elastic electron scattering calculated by R-matrix method

Elastic scattering are one of the most important elementary processes in gases. It can be described as

AB + e^- -> AB + e^-

Cross section of elastic scattering is responsible for main plasma characteristics, i.e., for example, spectral line width or collective process as diffusion, thermal conductivity, viscosity and mobility.

Elastic scattering can be investigated by different more or less exact and laborious methods. It is possible to mark two methods among it: effective radius method for s-phase as very visual and obvious and R-matrix method as rather exact and scientifically grounded. S-phase effective radius method answers low electron energy. At the high energy it can be combined with another one, for example, transport cross section at the high energy can be calculated with the use of polarizability.

Elastic electron scattering by Al

The ground state of Al has the configuration 3s²3p¹. For R-matrix calculation software product “RMATRX1” by Berrington Keith A. at al. (1995 Computer Physics Communications 92 290) is used. To calculate basis wave function HF-86 (Froese Fischer C. // 1987 Computer Physics Communications 43 355) is used within the bounds of Hartree-Fock method. Spin of the aluminum atom is ½ because it has only one electron on its outer orbital. It means that using the method of effective radius we have to know both triplet and singlet scattering length (L_t  and L_s).. Both Ls and Lt can be calculated also with the use of R-matrix.

Result of R-matrix calculation of elastic scattering cross section is on the left figure. As we can see, R-matrix method are in rather good agreement with the other results (Fabrikant, Wells). The full solution for effective radius method obtained by joining the regions of high and low energy is on the right figure.