On the convergence of close-coupling results for low-energy electron scattering from magnesium

We use three different implementations of the non-relativistic close-coupling method to investigate the convergence of theoretical predictions for electron scattering from magnesium at impact energies below 1 eV. It is found that the convergence of the close-coupling expansion is extremely slow, particularly for the L = 1 partial wave that is dominated by a shape-resonance common to many similar quasi-two-electron systems. An accurate prediction of the scattering length (we obtain −2.4 ± 0.1 a0) is also a nontrivial problem. Although the shape resonance in the L = 1 channel can be predicted in agreement with experiment already in small close-coupling expansions with three or nine coupled states (see Bartschat and Sadeghpour 2003 J. Phys. B: At. Mol. Opt. Phys. 36 L9 for details), this fortuitous agreement is due to simultaneously inaccurate descriptions of both the N-electron target and the (N + 1)-electron collision problems. We demonstrate how a more systematic though slow convergence pattern of the close-coupling expansion can be achieved by concentrating on a highly accurate target description before attempting to solve the collision problem.