Concerning the atomic one-electron model hamiltonians of which Slater-type orbitals are eigenfunctions

The well-known nodeless Slater-type orbitals are exact eigenfunctions of the atomic one-electron model hamiltonian with model potential Vsub(M) = (-α/r) + [n(n-1)-l(l+1)]/2r2, and eigenvalue Esub(M) = -(α/n)2/2. This potential is discussed, with examples, for two possible choices of the parameters α and n, for a given Esub(M). If n is chosen as the usual integral quantum number, α is larger than the net core charge Zsub(c), and the potential does not have the correct asymptotic behaviour, remaining too attractive well outside the core. If α = Zsub(c) is chosen, the potential is equivalent to the potential recently discussed by Simons. n is no longer an integer, and the potential is too repulsive in regions well outside the core. Comments on these and related potentials, and their uses, are presented. (Auth.)