J Hata

The representation of higher-order relativistic corrections in the MCDF-EAL method

The MCDF-EAL method is shown to be closely related to the procedure used to solve the Bethe-Salpeter equation by Douglas and Kroll (1974) in their study of helium 3P fine structure. The authors interpret the former as a method based on a well defined effective Hamiltonian derived from QED which yields a solution within a finite set of CSF which is exact to all orders of perturbation theory. This interpretation allows one to examine the contribution of higher-order terms in the perturbation series for 23P in helium-like F VIII, 1s2p2 4P levels in the lithium isoelectronic sequence and 1s22s22p2 3P levels in the carbon isoelectronic sequence. These terms are shown to be essential if the theoretical predictions are to match the precision obtainable in current experiments. In the case of the carbon sequence, the authors identify discrepancies due to missing (non-relativistic) correlation contributions, and show how these may be taken into account in some cases.

MCDF calculations of wavelengths and radiative lifetimes in helium-like ions

The use of multi-configuration Dirac-Fock (MCDF) wavefunctions for computing wavelengths and radiative lifetimes is described and illustrated by calculations for transitions originating in the 23P0,1,2 levels of helium-like ions. Good agreement is obtained with experimental results and with other theoretical calculations. The contributions of the transverse (Breit) interaction between electrons and of the lowest-order Lamb shift and vacuum polarisation corrections significantly improve the results.

Fine structure of the 1s2s2p 4P degrees and 1s2p2 4P terms of the lithium isoelectronic sequence and wavelengths of transitions between them

Recent MCDF (-OL) calculations by Cheng et al. (1978) of the fine structure of the 1s2s2p 4P0 and 1s2p2 4P terms in lithium-like ions and of the wavelengths of transitions between them show indifferent agreement with available experimental measurements. The authors have repeated the calculations using the same set of CSF but employing the MCDF-EAL method; fine structures for C IV, N V, O VI and Mg X are now predicted to lie within experimental error limits for the most part, and wavelengths are correct to about one part in 103. Some reasons for this striking improvement are discussed.

Tests of QED in two-electron ions. II. The 23S-23P0,1,2 energies

For pt.I see ibid., vol.16, no.4, p.507-21 (1982). Examines the use of MCDF calculations to estimate relativity correlation corrections to the 1s2s 3S1-1s2p 3P0,1,2 energies of the helium isoelectronic sequence. This is shown to give small but systematic differences from previous estimates based on the Breit-Pauli method. A new method of estimating two-electron corrections to the Lamb shift is described, and the results are compared with earlier estimates and with current experimental data.

Tests of QED in two-electron ions. I. Methodology and 23P fine structure

Precision measurements of the wavelengths of 1s2s 3S1-1s2p 3PJ transitions in ions of the helium isoelectronic sequence have recently been carried out with a view to testing QED in systems containing more than one electron. A critical review of the theoretical methods for calculating these energies is given in this paper and the one that follows. The authors demonstrate that relatively simple MCDF calculations can give high precision estimates of 23P fine-structure splittings.

The 1s2s2p2 5P-1s2p3 5S transitions in the beryllium isoelectronic sequence

An MCDF-EAL calculation on the 1s2s2p2, 1s22s2p and 1s2p3 states in the beryllium isoelectronic sequence has been used to predict fine structures and transition wavelengths for atomic numbers in the range 4<Z<20. The authors report improved agreement for the 5P-5S transition wavelengths with experiment in C III, N IV and O V by comparison with previous MCDF-OL calculations.

Comments on relativistic two-body interaction in atoms

The relativistic two-body interaction in many-electron atoms is investigated in detail. The authors show that the transferred energy contribution which appears in the expression of the two-body interaction is significant at the present level of experimental accuracy. They also show that the Coulomb and Feynman gauge expressions for the relativistic two-body interactions are equivalent in the on-shell energy case for a local potential, but the same terms appear in different orders of approximation in the two gauges. In addition, a critical comparison between the MCDF-EAL and MCDF-OL methods is made from this point of view.

Tests of QED in two-electron ions. IV. A status report

For pt.III see ibid., vol.16, p.L433-6 (1983). The variety of approximations used in estimation of the wavelengths of 1s2s 3S-1s2p 3P lines studied in this series reveals the need for a status report. Two new features are discussed: the need for basis set extrapolation at the low-Z end of the isoelectronic sequence, and an estimate of two-body corrections to the electron self-energy. The recommended theoretical values lie mostly within experimental error estimates for Z<10. For higher values of Z the authors propose to change to the values given in the second paper (1983) of this series.

Comments on fine-structure intervals of the 1s22s22p5 2P state in fluorine isoelectronic sequence

The MCDF-EAL method is used to calculate fine-structure intervals of the 1s22s22p5 2P state in the fluorine isoelectronic sequence, and compared with experiment and MCDF-OL results by Kim and Huang (1982). No systematic discrepancies between the theory and experiment are found.

Inclusion of the electron anomaly in effective Hamiltonians for perturbative (Breit-Pauli) and non-perturbative approaches to fine structure

The anomalous magnetic moment of the electron makes an non-trivial contribution of fine-structure splittings which has, nonetheless, been ignored in many ab initio calculations. This paper aims to present a straightforward derivation of an effective Hamiltonian for relativistic calculations which includes the electron anomaly, both at the Dirac-Fock level and in the Breit-Pauli approximation. It thus provides the framework for comparative studies of predicted fine structure using these two methods which are the subject of separate publications.