Reducing the dimensionality of grid based methods for electron-atom scattering calculations below ionization threshold

For total energies below the ionization threshold it is possible to dramatically reduce the computational burden of the solution of the electron-atom scattering problem based on grid methods combined with the exterior complex scaling. As in the R-matrix method, the problem can be split into the inner and outer problem, where the outer problem considers only the energetically accessible asymptotic channels. The (N+1)-electron inner problem is coupled to the one-electron outer problems for every channel, resulting in a matrix that scales only linearly with size of the outer grid.