Frequency Shift of the Cesium Clock Transition due to Blackbody Radiation

We perform ab initio calculations of the frequency shift induced by a static electric field on the cesium clock hyperfine transition. The calculations are used to find the frequency shifts due to blackbody radiation. Our result [$\delta \nu /E^2=-2.26(2)\times {10}^{-10}\mathrm{Hz}/(\mathrm{V}/\mathrm{m}{)}^2$] is in good agreement with early measurements and ab initio calculations performed in other groups. We present arguments against recent claims that the actual value of the effect might be smaller. The difference ($\sim 10\%$) between ab initio and semiempirical calculations is due to the contribution of the continuum spectrum in the sum over intermediate states.