The unified method described previously for combining high-precision nonrelativistic variational calculations with relativistic and quantum electrodynamic corrections is applied to the 1s2 1S0, 1s2s 1S0, 1s2s 3S1, 1s2p 1P1, and 1s2p 3P0,1,2 staters of helium-like ions. Detailed tabulations are presented for all ions in the range 2 ≤ Z ≤ 100 and are compared with a wide range of experimental data up to 34Kr+. The results for 90U+ significantly alter the recent Lamb shift measurement of Munger and Gould from 70.4 ± 8.3 to 71.0 ± 8.3 eV, in comparison with a revised theoretical value of 74.3 ± 0.4 eV. The improved agreement is due to the inclusion of higher order two-electron corrections in the present work.

The dispersion coefficients C 6 , C 8 , and C 10 for the interactions between H, He, and Li are calculated using variational wave functions in Hylleraas basis sets with multiple exponential scale factors. With these highly correlated wave functions, significant improvements are made upon previous calculations and our results provide definitive values for these coefficients.

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High-precisipn varlatipnal eigenvalues fpr the 1& 2s S, 1+ 2p P, and 1z 3d D states pf hthium are calculated using multiple basis sets in Hylleraas coordinates. Convergence to a few parts in 10' -10" is achieved. The nonrelativistic energies for infinite nuclear mass are -7.478060323 10(31) a.u. for the ls 2s S state, -7.410156 521 8(13) a.u. for the ls 2p P state, and -7.335 523 541 10(43) a.u. for the 1s 3d D state. The corresponding specific isotope shifts due to mass polarization are also calculated with similar accuracy. The 1s 2s S -1s 2p P and 1s 2p P -1s 3d D transition energies for Li and Li, as well as the isotope shifts, are calculated and compared with experiment. The results yield an improved ionization potential for lithium of 43487.167(4) cm '. Expectation values of powers of r; and r; and the delta functions 8(r;) and 6(r;,) are evaluated.PACS number(s): 31.15.Ar, 31.50.+w

Rates are calculated for the decay of metastable 2s», ions to the ground state by the simultaneous emission of two photons. The calculation includes all relativistic and retardation effects, and all combinations of photon multipoles which make significant contributions up to Z = 100. Summations over intermediate states are performed by constructing a finite-basis-set representation of the Dirac Green's function. The estimated accuracy of the results is 10 ppm for all Z up to 100. The decay rates are about 20 (aZj'%%uo larger than an earlier calculation by Johnson owing to the inclusion of higher-order retardation effects. The general question of gauge invariance in two-photon transitions is discussed.

Variational solutions to the Dirac equation in a discrete I. ' basis set are investigated. Numerical calculations indicate that for a Coulomb potential, the basis set can be chosen in such a way that the variational eigenvalues satisfy a generalized Hylleraas-Undheim theorem. A number of relativistic sum rules are calculated to demonstrate that the variational solutions form a discrete representation of the complete Dirac spectrum including both positiveand negative-energy states. The results suggest that widely used methods for constructing I. ' representations of the nonrelativistic electron Green s function can be extended to the Dirac equation. As an example, the relativistic basis sets are used to calculate electric dipole oscillator strength sums from the ground state, and dipole polarizabilities.

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