Relativistic calculation of atomic structures

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Abstract
The current state of the art in relativistic calculation of atomic structures is surveyed. The theory is modelled on the practice in non-relativistic calculations, using many-particle wave functions built from Dirac central field spinors. The Hamiltonian includes quantum electrodynamic effects in the form of the Breit approximation for the interaction energy of two electrons. Within the limits for which this is valid, it is possible to construct matrices for one- and two-particle operators and hence to perform atomic structure calculations which automatically include the major relativistic effects. The theory can be greatly simplified by using Racah's tensor operators. Major applications have utilized the Hartree or Hartree-Fock methods, and the relevant equations are formulated in detail. Numerical Hartree-Fock solutions for the average of the ground configuration have now been obtained for most elements with atomic number less than 103, and some solutions have also been obtained for ions. The same methods have been used to investigate the likely configurations of superheavy elements with atomic numbers as high as 168. A few calculations have also been done using a relativistic analogue of Roothaan's method. Methods of solution and numerical results are described for both types of calculation. No attempt has been made to describe the perturbation techniques due to Layzer and Bahcall, since an adequate review of recent work in this area has been given by Doyle. A brief description is also given of some problems in which it has been necessary to take relativistic effects into account including, in particular, elastic scattering of low and medium energy electrons from heavy elements, the calculation of x-ray scattering factors, and the probability of electron shake-off following sudden perturbations.

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