Blackbody radiation shifts and theoretical contributions to atomic clock research

A review of the theoretical calculations of the blackbody radiation (BBR) shifts in various systems of interest to the atomic clock research in presented. The calculations for monovalent systems, such as Ca⁺, Sr⁺, and Rb are carried out using the 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. New method for accurate calculations of BBR shifts for divalent systems such as Sr is discussed. The new approach combines the relativistic all-order method and the configuration interaction method. The evaluation of the uncertainty of the BBR shift values is discussed in detail.