Blackbody-radiation shift in the Sr optical atomic clock

We evaluated the static and dynamic polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1$%$ uncertainty; $\ensuremath{-}$0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7$%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.