Electronic excitation of atoms and molecules using the linear-algebraic method

The linear-algebraic method for electron-molecule scattering is generalized to treat inelastic collisions involving a set of primary coupled channels. The coupling between these channels is expanded in separable form using a set of Cartesian Gaussian functions. As a consequence of the separable expansion, we need only to solve a set of uncoupled, homogeneous and inhomogeneous equations in each channel to obtain the basis in which the final solution is expanded. The separable form of the coupling allows the physical solution to be obtained with use of the matrix elements of the interaction and the overlap integrals between the solutions and the basis used for the separable expansion. The method is applied to inelastic scattering from H, He, ${\mathrm{H}}_2$ ${\mathrm{}}^{+}$, and ${\mathrm{H}}_2$. Comparison with exact solutions of the close-coupling equations indicates that the method is quite accurate, provided that the basis set used in the separable expansion is flexible enough to span the interaction region.