  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, alpha. Our result for Cs (delta nu E^2=-2.26 times
10^{-10}Hz/(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 (approx 10%) is due to the contribution of the
continuum spectrum in the sum over intermediate states.
