Finite basis sets for the Dirac equation constructed fromBsplines

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Abstract
A procedure is given for constructing basis sets for the radial Dirac equation from B splines. The resulting basis sets, which include negative-energy states in a natural way, permit the accurate evaluation of the multiple sums over intermediate states occurring in relativistic many-body calculations. Illustrations are given for the Coulomb-field Dirac equation and tests of the resulting basis sets are described. As an application, relativistic corrections to the second-order correlation energy in helium are calculated. Another application is given to determine the spectrum of thallium (where finite–nuclear-size effects are important) in a model potential. Construction of B-spline basis sets for the Dirac-Hartree-Fock equations is described and the resulting basis sets are applied to study the cesium spectrum.

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