Finite-field calculation of static polarizabilities and hyperpolarizabilities of In+ and Sr

The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities of the 5s(2) S-1 and 5s5p(3)P(o) states of In+ and Sr are calculated by using the finite-field method. The electron correlation effect and the basis set convergence are investigated in the relativistic coupled-cluster and configuration interaction calculations in order to obtain polarizabilities of high accuracy. Comparative study of the fully and scalar relativistic calculations reveals the effect of the spin-orbit coupling on the dipole polarizabilities of In+ and Sr. The blackbody-radiation shifts of the clock transition 5s(2) S-1(0)-5s5fp P-3(0)o due to the dipole polarizabilities, quadrupole polarizabilities, and dipole hyperpolarizabilities are evaluated to be 0.017, 8.33x10(-10), and 1.93x10(-17) Hz for In+ and 2.09 and 5.82x10(-8), and 1.69x10(-15) Hz for Sr. The blackbody-radiation shifts from the quadrupole polarizabilities and dipole hyperpolarizabilities are significantly less than that from the dipole polarizabilities and therefore can be safely omitted for the quoted 10(-18) uncertainty of the optical frequency standard of In+ and Sr.