RelativisticB-splineR-matrix method for electron collisions with atoms and ions: Application to low-energy electron scattering from Cs

Abstract

The $B$-spline $R$-matrix method with nonorthogonal orbital sets is extended to a fully relativistic version based on the solution of the many-electron Dirac equation. The $B$-spline basis is used to generate both the target description and the $R$-matrix basis functions in the inner region. Using $B$-splines of different orders for the large and small components prevents the appearance of pseudostates in the spectrum of the Dirac equation. Using term-dependent and thus nonorthogonal sets of one-electron functions enables us to generate accurate and flexible representations of the target states and the scattering function. Our method is based upon the all-electron Dirac-Coulomb Hamiltonian and thus may be employed for any complex atom or ion, without the use of phenomenological core potentials. As a first test of the method, we consider elastic electron scattering from Cs atoms in their ground state. Close agreement with experiment is obtained for the total and the angle differential cross sections at various energies between 1 eV to 7 eV, as well as for several spin asymmetry parameters. The results represent a substantial improvement over those obtained in previous Breit-Pauli and Dirac $R$-matrix calculations.