The quantum-defect-orbital method has been reformulated in order to include both relativistic effects and the electron correlation described by a core polarization potential. All quantities appearing in this formulation may be evaluated analytically. A comparison with experimental results demonstrates, on one hand, significance of the relativity-correlation corrections and, on the other, inadequacy of the relativistic quantum-defect-orbital approach when indirect relativistic effects are important, i.e. when atoms contain closed shells of d electrons.
The corrections to the ionization energies of two-electron ions due to relativistic effects are studied by different two-component relativistic methods. In particular, the results obtained by the standard Pauli-Cowan-Griffin method and by two variants of the Douglas-Kroll-Hess method (the one based on the free-particle transformation and the one in which the transformation accounts for the nuclear potential) are compared with those calculated using the four-component Dirac-Fock method. Limits of applicability of each of these methods have been indicated. Results acceptable in the whole range of the nuclear charge (relativistic corrections accurate up to 4% for Z≤85) are given only by the Douglas-Kroll-Hess method which goes beyond the free-particle transformation. Each of the other two approaches either underestimates or overestimates the corrections due to relativistic effects.
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