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

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 $C_6\left(0_u\right)=3771\left(32\right)$ a.u. and $C_6\left(1_u\right)=4001\left(33\right)$ 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 ${}^1{S}_0\text{−}{}^3{P}_1^o$ transition vanishes. The accuracy of calculations is analyzed and uncertainties are assigned to all quantities reported in this work.