Features of the Theory of Resonant Electron Scattering on Atoms

Kinetic equations whose solution requires the cross sections of elastic and inelastic electron scattering on atoms and molecules are used to solve numerous problems in plasma physics. To construct cross sections, modern calculations of the characteristics of resonant electron scattering are required, which are based on the use of methods operating with a complex Hamiltonian. The complex absorbing potential (CAP) method is used for a similar class of problems, but is characterized by unstable estimates of the resonance parameters. In this study, for a single-channel problem with an explicit parameterization of the scattering matrix, we analyze the features of the CAP method. It is shown that, depending on the choice of the initial conditions, there are two types of CAP-trajectories with real limits as the complex scaling factor tends to zero. The trajectories of the first type are characterized by the presence of the optimal point, and the trajectories of the second type are characterized by the presence of a closed section in the vicinity of the resonance. It is also shown that for finite values of the scaling factor, the CAP trajectory does not pass through resonance. These conclusions are qualitatively confirmed by the results of the independent application of the CAP method to the calculations of model and many-electron systems.