Analysis of the intermediate energy R-matrix theory

Abstract

The intermediate energy R-matrix (IERM) theory, first introduced by Burke et al. (1987) has been applied to electron scattering by atomic hydrogen by Scholz et al. (1988) and Scott et al. (1989). In principle, the only approximation inherent in this approach relates to the treatment of the scattering wavefunction in the external R-matrix region. Here the couplings between the channels of interest and all other physically open channels are neglected. The author demonstrates that these couplings are small in this region of configuration space and hence that the IERM theory includes the physics which dominates intermediate energy scattering. The mechanism for the formation of pseudo-resonances in IERM calculations is also described along with the averaging procedure used to extract the physical T-matrix elements. The author shows that this procedure removes the unitarity of the S-matrix and therefore accounts for the flux lost into channels not explicitly included in the external region expansion of the scattering wavefunction. Calculations which explicitly include a large number of pseudo-channels are reported. The resulting T-matrices are found to be in agreement with the averaged results hence validating the T-matrix averaging procedure.