The Correlation Energies of Excited States of the Helium Sequence

The method of superposition of configurations is used to determine the contributions from radial and angular correlation to the second-order term in the expansion of the energies of excited states of the two-electron systems in inverse powers of the nuclear charge. Comparison with the similar calculation carried out by Sharma and Coulson in 1962 using an expansion in terms of Hylleraas coordinates shows that the superiority of the method of incomplete separation of variables over the method of superposition of configurations is not so pronounced as for the ground state. The contributions to the second-order energy of the 1s2s 1 S, 1s2s 3 S, 1s2p 1 P and 1s2p 3 P states from correlation are found to be - 0.0180, - 0.0041, - 0.0068 and - 0.0069 rydberg respectively, compared with the Hartree-Fock contributions - 0.2068, - 0.0906, - 0.2931 and - 0.1358 rydberg respectively. Third-order terms are also calculated.