arXiv:1409.5985 · Physical Review A

Relativistic calculations of C6 and C8 coefficients for strontium dimers

S. G. Porsev, Marianna S. Safronova, Charles W. Clark

Published Nov 18, 2014• 13 citations

Abstract

The electric-dipole and quadrupole polarizabilities of the $5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ state and the ${C}_{6}$ and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the ${0}_{u}$ and ${1}_{u}$ energy levels are ${C}_{6}({0}_{u})=3771(32)$ a.u. and ${C}_{6}({1}_{u})=4001(33)$ a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate ${C}_{8}$ coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the ${}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

DOI: 10.1103/physreva.90.052715

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Relativistic coupled-cluster calculations of the polarizabilities of atomic thallium

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Blackbody-radiation shift in the Sr optical atomic clock

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High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

S. G. Porsev, Andrei Derevianko

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C 6, C 8, and C 10 of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.

Journal of Experimental and Theoretical PhysicsFeb 1, 2006125 citations

arXiv:1409.5985 · Physical Review A

Relativistic calculations of C6 and C8 coefficients for strontium dimers

S. G. Porsev, Marianna S. Safronova, Charles W. Clark

Published Nov 18, 2014• 13 citations

arXiv HTML PDF

Abstract

The electric-dipole and quadrupole polarizabilities of the

5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

state and the

{C}_{6}

and

{C}_{8}

coefficients for the

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}

and

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

dimers of strontium are calculated using a high-precision relativistic approach that combines configuration interaction and linearized coupled-cluster methods. Our recommended values of the long-range dispersion coefficients for the

{0}_{u}

and

{1}_{u}

energy levels are

{C}_{6}({0}_{u})=3771(32)

a.u. and

{C}_{6}({1}_{u})=4001(33)

a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate

{C}_{8}

coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the

{}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}

transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

DOI: 10.1103/physreva.90.052715

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Long-range interaction coefficients for ytterbium dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$ , $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ , and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$, $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$, and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.

arXiv:1307.2656Physical Review AJan 24, 201435 citations

Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers

S. G. Porsev, Marianna S. Safronova, Andrei Derevianko +1 more

We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate ${C}_{6}$ and ${C}_{8}$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the ${C}_{8}$ coefficient of heteronuclear $A+B$ dimers in terms of the ${C}_{6}$ and ${C}_{8}$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$ . We report results of calculation of the ${C}_{6}$ coefficients for the Yb-Rb ${}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and ${}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}$ dimers, and the ${C}_{8}$ coefficients for the Yb-Li ${}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and Yb-Rb ${}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate ${C}_{6}$ and ${C}_{8}$ coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the ${C}_{8}$ coefficient of heteronuclear $A+B$ dimers in terms of the ${C}_{6}$ and ${C}_{8}$ coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states $A$ and $B$. We report results of calculation of the ${C}_{6}$ coefficients for the Yb-Rb ${}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and ${}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}$ dimers, and the ${C}_{8}$ coefficients for the Yb-Li ${}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and Yb-Rb ${}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ dimers. Uncertainties are estimated for all predicted properties.

arXiv:1401.6585Physical Review AFeb 6, 201415 citations

Two-dipole and three-dipole dispersion coefficients for interaction of alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions

Neelam Shukla, Bindiya Arora, Lalita Sharma +1 more

Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole $C_6$ and three-dipole $C_9$ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The $C_6$ and $C_9$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated $C_6$ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the $C_6$ coefficients for alkaline-earth atoms with alkaline-earth ions and the $C_9$ coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg $^+$ , Ca $^+$ , Sr $^+$ , and Ba $^+$ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole $C_6$ and three-dipole $C_9$ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The $C_6$ and $C_9$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated $C_6$ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the $C_6$ coefficients for alkaline-earth atoms with alkaline-earth ions and the $C_9$ coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg$^+$, Ca$^+$, Sr$^+$, and Ba$^+$ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.

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Relativistic coupled-cluster calculations of the polarizabilities of atomic thallium

Yong-Bo Tang, Ningning Gao, Bing-Qiong Lou +1 more

Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$ , $7s$ , $7p$ , $8s$ , $8p$ , and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7{s}_{1/2}$ , $7{p}_{1/2}$ , $8{p}_{1/2}$ , and $8{p}_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6{p}_{1/2}$ -- $7s$ and $6{p}_{3/2}$ -- $7s$ transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7{s}_{1/2}$ -- $7{p}_{1/2}$ and $7{s}_{1/2}$ -- $7{p}_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6{p}_{1/2}$ -- $7{p}_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the $6p$, $7s$, $7p$, $8s$, $8p$, and $6d$ states and the dynamic dipole polarizabilities of the $6p$ and $7s$ states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the $7{s}_{1/2}$, $7{p}_{1/2}$, $8{p}_{1/2}$, and $8{p}_{3/2}$ states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the $6{p}_{1/2}$--$7s$ and $6{p}_{3/2}$--$7s$ transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the $7{s}_{1/2}$--$7{p}_{1/2}$ and $7{s}_{1/2}$--$7{p}_{3/2}$ transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the $6{p}_{1/2}$--$7{p}_{1/2}$ transition, are also evaluated and compared with available theoretical and experimental values.

Physical Review ADec 14, 201810 citations

Blackbody-radiation shift in the Sr optical atomic clock

Marianna S. Safronova, S. G. Porsev, Marianna S. Safronova +2 more

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.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.

arXiv:1210.7272Physical Review AJan 23, 2013140 citations

High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

S. G. Porsev, Andrei Derevianko

Journal of Experimental and Theoretical PhysicsFeb 1, 2006125 citations

The electric-dipole and quadrupole polarizabilities of the

5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

state and the

{C}_{6}

and

{C}_{8}

coefficients for the

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}

and

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

{0}_{u}

and

{1}_{u}

energy levels are

{C}_{6}({0}_{u})=3771(32)

a.u. and

{C}_{6}({1}_{u})=4001(33)

a.u., respectively. They are in good agreement with recent results from experimental photoassociation data. We also calculate

{C}_{8}

coefficients for Sr dimers, which are needed for precise determination of long-range interaction potential. We confirm the experimental value for the magic wavelength, where the Stark shift on the

{}^{1}{S}_{0}\text{\ensuremath{-}}{}^{3}{P}_{1}^{o}

transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the

6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

, and

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the

{C}_{6}

coefficients for the Yb-Yb

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}

and

{}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

dimers and

{C}_{8}

coefficients for the

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}

and

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

dimers.

We derive the relativistic formulas for the van der Waals coefficients of Yb--alkali-metal dimers that correlate to ground and excited separated-atom limits. We calculate

{C}_{6}

and

{C}_{8}

coefficients of particular experimental interest. We also derive a semiempirical formula that expresses the

{C}_{8}

coefficient of heteronuclear

A+B

dimers in terms of the

{C}_{6}

and

{C}_{8}

coefficients of homonuclear dimers and the static dipole and quadrupole polarizabilities of the atomic states

A

and

B

. We report results of calculation of the

{C}_{6}

coefficients for the Yb-Rb

{}^{3}{P}_{1}^{o}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and

{}^{1}{S}_{0}+5p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}^{o}

dimers, and the

{C}_{8}

coefficients for the Yb-Li

{}^{1}{S}_{0}+2s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

and Yb-Rb

{}^{1}{S}_{0}+5s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

dimers. Uncertainties are estimated for all predicted properties.

Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole

C_6

and three-dipole

C_9

dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The

C_6

and

C_9

coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated

C_6

coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the

C_6

coefficients for alkaline-earth atoms with alkaline-earth ions and the

C_9

coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg

^+

, Ca

^+

, Sr

^+

, and Ba

^+

as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.

Using the relativistic coupled-cluster method, we calculate the static dipole polarizabilities of the

6p

7s

7p

8s

8p

, and

6d

states and the dynamic dipole polarizabilities of the

6p

and

7s

states of the thallium atom. The trivalent thallium atom is computationally treated as a monovalent system, together with all linear and nonlinear terms of single- and double-cluster operators included in the correlation calculations. We observe that the dominating contributions to the static scalar polarizabilities of the

7{s}_{1/2}

7{p}_{1/2}

8{p}_{1/2}

, and

8{p}_{3/2}

states are from one or two specific transitions. The matrix elements of these specific transitions can be determined by combining the experimental values of relevant static scalar polarizabilities. A number of magic wavelengths for the

6{p}_{1/2}

7s

and

6{p}_{3/2}

7s

transitions in the range of 488--1300 nm and the longest tune-out wavelength of the ground state are determined. These magic wavelengths and tune-out wavelength may be useful for further thallium experiments. Experimental measurements of the magic wavelengths near 1245 nm would give estimates of the

7{s}_{1/2}

7{p}_{1/2}

and

7{s}_{1/2}

7{p}_{3/2}

transition matrix elements and their ratio. Furthermore, lifetimes of many excited states, as well as the Stark-induced scalar and vector dipole polarizabilities for the

6{p}_{1/2}

7{p}_{1/2}

transition, are also evaluated and compared with available theoretical and experimental values.

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.