Blackbody radiation shift in the Sr optical atomic clock

We evaluated the static and dynamic polarizabilities of the $5s^2$ $^1$S$_0$ and $5s5p$ $^3{\rm P}^{\circ}_0$ states of Sr using the high-precision relativistic configuration interaction + all-order method. Our calculation explains the discrepancy between the recent experimental $5s^2$ $^1$S$_0$ - $5s5p$ $^3{\rm P}^{\circ}_0$ dc Stark shift measurement = 247.374(7) a.u. [T. Middelmann, S. Falke, C. Lisdat and U. Sterr, arXiv:1208.2848 (2012)] and the earlier theoretical result of 261(4) a.u. [S. G. Porsev and A. Derevianko, {\em Phys. Rev. A} {\bf 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; -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. For further information, see http://arxiv.org/abs/1210.7272