Relativistic Atomic Structure Calculations I: Basic Theory and the Finite Basis Set Approximation

Atomic electronic structure calculations have been used to test theories of the physical laws since the advent of quantum mechanics in the 1920’s. Much of the current activity in atomic structure theory involves the development of accurate and efficient computational techniques in order to model astrophysical phenomena or spectroscopic experiments of great complexity, so that atomic physics seems distant from the well—publicised areas of fundamental research into high—energy physics. It is not, however, true to suggest that the atom is no longer of service in our attempts to understand the forces in Nature. The relative simplicity of the atom has allowed the incorporation of new fundamental developments into computational models which test our understanding of the physical laws in complex systems. These models include the small effects which have been observed experimentally which arise in the theories of quantum electrodynamics (QED) and the non—conservation of parity (PNC).