Relativistic calculations of $C_6$ and $C_8$ coefficients for strontium dimers

Abstract

The electric dipole and quadrupole polarizabilities of the $5s5p{}^3{P}_1^o$ state and the $C_6$ and $C_8$ coefficients for the ${}^1{S}_0+{}^1{S}_0$ and ${}^1{S}_0+{}^3{P}_1^o$ 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 ${}^1{S}_0$-${}^3{P}_1^o$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.

arXiv comment10 pages

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• Transition strength measurements to guide magic wavelength selection in optically trapped molecules
• Finite field calculations of static polarizabilities and hyperpolarizabilities of In${}^{+}$ and Sr
• Magic wavelengths of the Sr ($5s^2{}^1{S}_0$--$5s5p{}^3{P}_1$) intercombination transition near the $5s5p{}^3{P}_1$--$5p^2{}^3{P}_2$ transition