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Finite field calculations of static polarizabilities and hyperpolarizabilities of In$^{+}$ and Sr

The finite field calculations are performed for two heavy frequency-standard candidates In$^+$ and Sr. The progressive hierarchy of electron correlations is implemented by the relativistic coupled-cluster and configuration interaction methods combined with basis set of increasing size. The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities are recommended for the ground state 5s$^2$ $^1S_0$ and low-lying states 5s5p $^3P^{\rm o}_{0,1,2}$ of In$^+$ and Sr. Comparative study of the fully and scalar relativistic electron correlation calculations reveals the effect of the spin-orbit interaction on the dipole polarizabilities of In$^{+}$ and Sr. Finally, the blackbody-radiation shifts due to the dipole polarizability, dipole hyperpolarizability, and quadrupole polarizability are evaluated for the clock transition 5s$^2$ $^1S_0$ - 5s5p $^3P^{\rm o}_0$ of In$^+$ and Sr.