An exactly soluble base problem for atomic systems is presented which appro
ximates the atomic Hamiltonian as a sum of identical one-electron operators
. The eigenfunctions of the one-electron operator consist of a radial funct
ion multiplied by a spherical harmonic. Energies for many-electron atoms ar
e found by summing the one-electron energy eigenvalues according to the Pau
li principle. These energies are rigorous lower bounds to the exact energie
s.