We have derived non-Coulomb phase shifts from measured differential cross s
ections for electron scattering by the ions Na+, Cs+, N3+, Ar8+, and Xe6+ a
t energies below the inelastic threshold. Values of the scaled squared devi
ation between the observed and fitted differential cross sections, chi(2),
for the best-fit phase shifts were typically in the range 3-6 per degree of
freedom. Generally good agreement with experiment is obtained, except for
wide-angle scattering by Ar8+ and Xe6+. Current measurements do not define
phase shifts to better than approximate to 0.1 rad even in the most favoura
ble circumstances and uncertainties can be much larger.