Relativistic fine structure effects

For heavier atoms the pure fine-structure effect is expected to break down due to relativistic effects. In the very heavy open-shell target atom thallium (Z=81) the ground-state atoms populate only one of the fine-structure levels, and the effect may be important at low energies. In an R-matrix calculation using magnetic potentials derived from the Dirac equation, Goerss, Nordbeck and Bartschat (1991) showed that... 

Our considerations lead to yet another result the calculation of the Stark effect and the quantising of Je can have a meaning only if the influence of the relativity theory, or of a departure of the atomic field of force from a Coulomb field, is small in comparison with that of the electric field. Further, our former calculation of the relativistic fine structure is valid only if the influence of the electric fields, which are always present, is small compared with the relativity perturbation.1... 

Besides making implicit use of these really puzzling properties of the relativistic Kepler problem, the second major impact of Sommerfeld s article lies in several notions introduced which lie at the foundation of relativistic quantum chemistry and have since been instrumental in the field the notion of scalar (kinemat-ical) relativistic effects versus fine-structure effects, the introduction of the fine-structure constant, a = jhc, and the expansion of the relativistic expressions in powers of the square of this constant. The idea that relativistic effects decisively influence the structure of the outer electrons of the atoms is at the root of relativistic quantum chemistry. 

The other relativistic effect entirely neglected so far is the spin-orbit coupling. For systems in nondegenerate states, the only first-order contribution to TAE comes from the fine structures in the corresponding atoms. Their effects can trivially be obtained from the observed electronic spectra, and hence the computational cost of this correction is fundamentally zero. 

Energy levels of heavy and super-heavy (Z>100) elements are calculated by the relativistic coupled cluster method. The method starts from the four-component solutions of the Dirac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. Simultaneous inclusion of relativistic terms in the Hamiltonian (to order o , where a is the fine-structure constant) and correlation effects (all products smd powers of single and double virtual excitations) is achieved. The Fock-space coupled-cluster method yields directly transition energies (ionization potentials, excitation energies, electron affinities). Results are in good agreement (usually better than 0.1 eV) with known experimental values. Properties of superheavy atoms which are not known experimentally can be predicted. Examples include the nature of the ground states of elements 104 md 111. Molecular applications are also presented. 

DCB is correct to second order in the fine-structure constant a, and is expected to be highly accurate for all neutral and weakly-ionized atoms [8]. Higher quantum electrodynamic (QED) terms are required for strongly-ionized species these are outside the scope of this chapter. A comprehensive discussion of higher QED effects and other aspects of relativistic atomic physics may be found in the proceedings of the 1988 Santa Barbara program [9]. 

We see that due to the smallness of the fine structure constant a a one-electron atom is a loosely bound nonrelativistic system and all relativistic effects may be treated as perturbations. There are three characteristic scales... 

As we shall see later on, for a large variety of atoms and ions the relativistic effects can be accounted for fairly precisely in the framework of the so-called Hartree-Fock-Pauli (HFP) approximation, as corrections of the order a2 (a = e1 /he is the fine structure constant and c stands for the velocity of light). Then, energy operator H will have the form... 

One-particle operators Hi and H3 cause relativistic corrections to the total energy. Two-particle operators H2, H3 and H s define more precisely the energy of each term, whereas H4 and H" describe their splitting (fine structure), i.e. they cause a qualitatively new effect. These operators are also often called describing magnetic interactions. 

The results of a spin-polarization measurement of xenon photoelectrons with 5p5 2P3/2 and 5p5 2P1/2 final ionic states are shown in Fig. 5.21 together with the results of theoretical predictions. Firstly, there is good agreement between the experimental data (points with error bars) and the theoretical results (solid and dashed curves, obtained in the relativistic and non-relativistic random-phase approximations, respectively). This implies that relativistic effects are small and electron-electron interactions are well accounted for. (In this context note that the fine-structure splitting in the final ionic states has also to be considered in... 

But no fine structure - yet - until in 1915 Bohr considered the effect of relativistic variation of mass with velocity in elliptical orbits under the inverse square law of binding, and pointed out that the consequential precessional motion of the ellipses would introduce new periodicities into the motion of the electron, whose consequences would be satellite lines in the spectra. The details of the dynamics were worked out independently by SOMMERFELD [38] and WILSON [39] in 1915/16 based on a generalisation of Bohr s quantization, namely, the quantization of action the values of the phase integrals Jf = fpj.d, - of classical mechanics should be constrained to assume only integral multiples of h. 

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