The Dirac equation in the algebraic approximation

The construction of variational approximations to the solutions of the Dirac equation is discussed. The importance of imposing the physical boundary conditions for both the point- and finite-nuclear models on the set of trial functions is emphasised. The low-frequency Breit interaction is shown to cause no variational failure when included in the iterative solutions of the Dirac-Hartree-Fock equations. The practical advantages of calculations which variationally include the Breit interaction over conventional treatments which employ only the Coulomb interaction are discussed. Manybody perturbation theory calculations of the radial correlation energy of helium- and beryllium-like systems are reported