Frequency shift of hyperfine transitions due to blackbody radiation

We have performed calculations of the size of the frequency shift induced by a static electric field on the clock transition frequencies of the hyperfine splitting in Yb⁺, Rb, Cs, Ba⁺, and Hg⁺. The calculations are used to find the frequency shifts due to blackbody radiation which are needed for accurate frequency measurements and improvements of the limits on variation of the fine-structure constant α. Our result for Cs [δν∕E²=-2.26(2)×10^-10Hz∕(V∕m)²] is in good agreement with early measurements and ab initio calculations. We present arguments against recent claims that the actual value might be smaller. The difference (~10%) is due to the contribution of the continuum spectrum in the sum over intermediate states.