Electron-impact excitation of Li to high principal quantum numbers

The time-dependent close-coupling method is used to calculate electron-impact excitation cross sections for the $\mathrm{Li}\mathrm{}\left(2s\right)\mathrm{}\to \mathrm{Li}\left(n\mathcal{l}\right)$ and $\mathrm{Li}\mathrm{}\left(2p\right)\mathrm{}\to \mathrm{Li}\left(n\mathcal{l}\right)$ transitions at incident energies just above the ionization threshold. The implementation of the time-dependent close-coupling method on a nonuniform lattice allows the study of continuum-coupling effects in excitations to high principal quantum number, i.e., $n<~10.$ Good agreement is found with R-matrix with pseudostates calculations, which also include continuum-coupling effects, for excitations to low principal quantum number, i.e., $n<~4.$ Poor agreement is found with standard distorted-wave calculations for excitations to all principal quantum numbers, with differences still at the 50% level for $n=10.\mathrm{}$ We are able to give guidance as to the accuracy expected in the $n^3$ extrapolation of nonperturbative close-coupling calculations of low n cross sections and rate coefficients.