Black-body radiation shifts and theoretical contributions to atomic clock research

A review of theoretical calculations of black-body radiation (BBR) shifts in various systems of interest to atomic clock research is presented. Calculations for monovalent systems, such as Ca⁺, Sr⁺, and Rb are carried out using a relativistic all-order single-double method, where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. A recently developed method for accurate calculations of BBR shifts in divalent atoms such as Sr is discussed. This approach combines the relativistic all-order method and the configuration interaction method. The evaluation of uncertainties in theoretical values of BBR shifts is discussed in detail.