  Smooth model potentials with parameters selected to reproduce the spectrum of
one-electron atoms are used to approximate the singular Coulomb potential. Even
when the potentials do not mimic the Coulomb singularity, much of the spectrum
is reproduced within the chemical accuracy. For the Hydrogen atom, the smooth
approximations to the Coulomb potential are more accurate for higher angular
momentum states. The transferability of the model potentials from an attractive
interaction (Hydrogen atom) to a repulsive one (Harmonium and the uniform
electron gas) is discussed.
