Excited levels 1sn, n-1 of the two-electron atom

Closed formulas for the Coulomb and exchange integrals in the excited states 1snl, l=n-1, of the two-electron atom are applied to the computation of the ionization energy of the singlet and tripet 1s2p states from He I up to O VII and to singlet and triplet 1s3d and 1s4f states of He I and Li II. Two methods are compared: (a) the use of first-order perturbation theory considering the mutual electrrostatic repulsion e2/r12 as a small perturbation and (b) imposing as solution of the Schroedinger equation a symmetrized product of a Z and a screened Z-1 hydrogenic wave functions. Computed and experimental values of the ionization energy and of the singlet-triplet interval are compared and the evolution of agreement with increasing Z and n is discussed