Blackbody radiation shift of theCs133hyperfine transition frequency

Abstract

We report the theoretical evaluations of the static scalar polarizability of the $^{133}\mathrm{Cs}$ ground state and of the blackbody radiation shift induced on the transition frequency between the two hyperfine levels with ${m}_{F}=0$. This shift is of fundamental importance in the evaluation of the accuracy of the primary frequency standards based on atomic fountains and is employed in the realization of the SI second in the International Atomic Time scale at the level of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$. Our computed value for the polarizability is ${\ensuremath{\alpha}}_{0}=(6.600\ifmmode\pm\else\textpm\fi{}0.016)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}39}{\mathrm{C}\phantom{\rule{0.3em}{0ex}}\mathrm{m}}^{2}∕\mathrm{V}$ in agreement at the level of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ with recent theoretical and experimental values. As regards the blackbody radiation shift we find for the relative hyperfine transition frequency $\ensuremath{\beta}=(\ensuremath{-}1.49\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at $T=300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in agreement with frequency measurements reported by our group and by Bauch and Schr\"oder [Phys. Rev. Lett. 78, 622 (1997)]. This value is lower by $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ than that obtained with measurements based on the dc Stark shift and than the value commonly accepted up to now.