Hand in hand with the advances in experiments, there is a continuing advance in atomic theory with applications to astrophysics and elementary particle physics. Although the Hamiltonian describing the detailed interactions of electrons in atoms and molecules is known, the calculation of the structure and spectroscopy of many-electron systems to high accuracy continues to be a challenging problem. Atomic and molecular theorists have developed powerful numerical methods and extensive computer codes to calculate energy levels, wavefunctions, and spectral line strengths. For instance, the precise cesium parity violation experiment described above would not have been so valuable without equally precise calculations of the cesium wavefunctions needed to evaluate the signal expected from particle theory. Likewise, the experiments searching for an atomic or molecular EDM rely on the atomic codes to predict the expected size of T-violating effects in atoms and molecules. Similar codes are now being used to select atomic transitions to use in the search for a time change in α. In astrophysics many spectral lines are observed from species that are difficult to produce in the laboratory. Atomic and molecular theory provides critically important input to the models used in the interpretation of these astronomical observations.

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