We have performed 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 (δν/E 2 = −2.26(2) × 10 −10 Hz/(V/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 (∼ 10%) between ab initio and semiempirical calculations is due to the contribution of the continuum spectrum to the sum over intermediate states. PACS numbers: 32.60.+i,31.30.Gs,31.25.Eb Atomic clocks are now important for both practical applications and fundamental physics. One of the dominant uncertainties in high-precision measurements of frequencies in atomic clocks is the ac stark shift induced by blackbody radiation (see e.g. [1]). There is some disagreement on the value of this shift. Early measurements [2,4,7] and ab initio calculations [5,8] support a value which is close to −2.2 × 10 −10 Hz/(V/m) 2 while more recent measurements [10,11] and semiempirical calculations [3,9,12] claim that actual number might be about 10% smaller.In the present work we have performed fully ab initio calculations of the radiation frequency shift and have identified the source of the disagreement between different theoretical results as the contribution of the continuum spectrum states into summation over the complete set of intermediate states. The continuum spectrum was included in all the ab initio calculations and missed in the semiempirical considerations. We demonstrate that adding the contribution of the continuum spectrum to where it was missed brings all theoretical results to good agreement with each other and with early measurements.Blackbody radiation creates a temperature dependent electric field, described by the Planck radiation lawThis leads to the following expression for the average electric field radiated by a black body at temperature T:This electric field causes a temperature-dependent frequency shift of the atomic microwave clock transitions. It can be presented in the form (see, e.g.Here T 0 is usually assumed to be room temperature (T 0 = 300K). The frequency shift in a static electric field isCoefficients k and β are related bywhile ǫ is a small correction due to frequency distribution (1). In the present work we calculate the coefficient k.In the case when there is no other external electric field the radiation shift can be expressed in terms of the scalar hyperfine polarizability of the atom. This corresponds to averaging over all possible directions of the electric field. The hyperfine polarizability is the difference in the atomic polarizabilities between different hyperfine structure states of the atom. The lowest-order effect is linear in the hyperfine interaction and quadratic in the electric field. The corresponding third-order perturbation theory expressions, after angular reduction have the form δν 1 (as) = ...