Multipolar theory of black-body radiation shift of atomic energy levels and its implications for optical lattice clocks

A black-body radiation (BBR) shifts of (nsnp ^3P_0) - (ns^2 ^1S_0) clock transition in divalent atoms Mg, Ca, Sr, and Yb are evaluated. A theory of multipolar BBR shifts is developed and its implications are discussed. At room temperatures, the resulting uncertainties in the BBR shifts are relatively large and substantially affect the projected 10^{-18} fractional accuracy of the optical-lattice-based clocks.