The one-electron Fues potential model is used to describe the like ion interaction for the isoelectronic sequence up to Z = 26. Ab initio data of the first few excited energy levels are used to determine accurate potential functional parameters depending on all the quantum numbers of a given state. A 1/Z expansion of the parameters is given in order to cover the He sequence. Accurate bound energies and well defined wavefunctions of single excited states are given. Continuum wavefunctions and elastic scattering electron - hydrogen-like ion phase shifts are derived.