Abstract
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 Schrödinger 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.
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