Hulthén Transform Functions for the Excited States of Two-Electron Atoms

Abstract

Hulthén functions are used to approximate the 2p and 3d orbitals of the lowest 1P, 3P, 1D, and 3D states of helium and to approximate the 2p orbitals of the lowest 3P states of the two-electron ions of Li, Be, and B. The orbital approximations and energies of the singlet states obtained using Hulthén 1p and 2d functions are identical to those obtained by Chong from minimal basis Slater 2p and 3d functions. The Hulthén 1p functions differ significantly from the Slater 2p functions only for the 3P states. The energies obtained for the 3P states are lower than those obtained from the minimal basis Slater functions. Using the new results for the 1P and 3P states of He, a term separation of 0.0087 a.u. is obtained. This value is in close agreement with the Hartree—Fock value of 0.0088 a.u.