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Black-body radiation (BBR) shift is an important systematic correction forthe atomic frequency standards realizing the SI unit of time. Presently, thereis a controversy over the value of the BBR shift for the primary $^{133}$Csstandard. At room temperatures the values from various groups differ at $3\times 10^{-15}$ level, while the modern clocks are aiming at $10^{-16}$accuracies. We carry out high-precision relativistic many-body calculations ofthe BBR shift. For the BBR coefficient $\beta$ at $T=300K$ we obtain$\beta=-(1.708\pm0.006) \times 10^{-14}$, implying $6 \times 10^{-17}$fractional uncertainty. While in accord with the most accurate measurement, our0.35%-accurate value is in a substantial, 10%, disagreement with recentsemi-empirical calculations. We identify an oversight in those calculations.Comment: 4 page

physical review letters

High-Accuracy Calculation of the Blackbody Radiation Shift in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Cs</mml:mi><mml:mprescripts /><mml:none /><mml:mn>133</mml:mn></mml:mmultiscripts></mml:math>Primary Frequency Standard

High-Accuracy Calculation of the Blackbody Radiation Shift in theCs133Primary Frequency Standard