Complex-coordinate calculations with complex basis sets

Two proposals have recently been made for improving the convergence of complex-coordinate calculations of electron-atom scattering resonances. The first is that complex (Siegert-type) functions be added to the usual basis of real functions, and the second is that bound-state basis functions not be rotated to the complex plane. In this paper we present calculations which test these suggestions for the lowest e-He⁺ resonance, comparing the results with previous studies. The stabilization length criterion is employed to assess the convergence and stability of the variational energies. We conclude that neither of these suggestions satisfactorily removes the difficulties associated with complex-coordinate calculations of resonance lifetimes.