The calculations of the energies of the singlet doubly excited states 2p 2 1 D, 3d 2 1 G, 4f 2 1 I of helium-like systems we have done in our previous paper [Biaye et al., Eur. Phys. J. D 13, 21 (2001).] are extended to the other singlet doubly excited (nl) 2 states with n ≤ 4. The energies are calculated in the framwork of the variation method by using some special forms of Hylleraasa-type wave functions with a real Hamiltonian. The results which we have obtained are in good agreement with some experimental data and other theoretical results.

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In this paper, we calculate energies for ns 2 1 S, np 2 1 D, nd 2 1 G, nf 2 1 I, 3snp 1,3 P • , 3s3d 1,3 D and 3p3d 1,3 F • doubly excited states (DES) of the helium isoelectronic sequence using the screening constant by unit nuclear charge (SCUNC) method in the framework of a semi-empirical procedure. Calculations are performed for total energies of low-lying DES (n 5) in He-like ions with 2 Z 10. The possibility of using the SCUNC method in the investigation of high-lying DES in two-electron systems is demonstrated in the present paper in the case of ns 2 1 S levels, where accurate energy positions are tabulated up to n = 20 and compared to the spin-dependent localized Hartree-Fock density functional (SLHF) with exchange-correlation (XC) potential calculations (Zhou and Chu 2005 Phys. Rev. A 71 022513) and to the works-function (WF)-based exchange (WF XC) potential approach values (Roy and Chu 2005 Phys. Rev. A 71 022513). In addition, the present method is used in the calculation of energy resonances for ns 2 1 S, np 2 1 D and nd 2 1 G excited states (n 5) in high-Z-helium-like ions (11 Z 19), and a comparison with the double sums over the complete hydrogen spectrum calculations (Ivanov and Safronova 1993 Opt. Spektrosk. 75 506) is made. All the results obtained in the present work agree with the available literature values.

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The 2snp±1,3Po doubly excited states with n⩽6 of helium-like ions are investigated using screening constant by unit nuclear charge (SCUNC). Calculations are performed for total energies, excitation energies and total Coulomb interaction energies between the two electrons in He-isoelectronic series up to Z=10. The results obtained agree with the available theoretical and experimental literature values.