Z-expansion calculations of energy levels and transition probabilities in many-electron atoms

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This paper reviews recent calculations of energy levels and transition probabilities in many-electron atoms, based on expansions in inverse powers of the nuclear charge. Emphasis is given to simple approximation methods that apply to a wide class of atomic states. It is shown that the variational screening approximation often yields an accurate estimate of energy contributions of order Z−1 and that the relativistic contributions to the energy levels of light and moderately light atoms are comparable to or greater than the nonrelativistic contributions of order Z−1 when the degree of ionization exceeds 3 or 4. A new method is described for normalizing Coulomb wave functions that figure in the approximate evaluation of electric-dipole transition integrals. It employs variational screening parameters and makes use of double perturbation theory.