Early four-component calculations of hfs constants in atoms

1 Early four-component calculations of hfs constants in atoms 

Breit was one of the first to realize the importance of relativity for the magnetic hyperfine constant in heavy elements [4]. He already used Dirac s formalism in 1931 and obtained relativistic energy corrections numerically but without having accurate many-particle methods at hand. 

A combined approach starting from an unrestricted Hartree-Fock (UHF) scheme in L5-coupling in combination with radial four-component calculations was performed by Desclaux and co-workers [78]. These authors investigated the hyperfine structure of Ga and Br allowing diflFerent radial parts for all the spin orbitals. These functions were then jj recoupled corresponding to the electronic configurations 

The analysis of the results obtained showed the relevance of the inner shell polarization which was accounted for by the UHF calculations. Since a fully numerical four-component code including exchange was not at hand at that time the authors also had to analyze the impact of Slater s exchange approximation especially its transferability from the nonrelativistic to the relativistic realm. Shortly after these investigations Desclaux and Bessis presented fully numerical four-component calculations now substituting Slater s approximation by an explicit treatment of exchange and reported results for A and B values of Sc, Cu, Ga and Br [79]. 

Another approach to relativistic hyperfine values was the calculation of relativistic correction factors (RCF) performed by Rosen and Lindgren for group 1 [80] and group 13 elements [81]. These factors were determined as the relativistic and nonrelativistic ratio for (r ) expectation values. 

---