The static quadrupole polarizabilities for hydrogen-like ions from Z = 1 to Z = 100 in the 1S 1/2 ground state are calculated to high precision by solving the Dirac equation using the B-spline Galerkin method. The results are consistent with the expression of Kaneko [J. Phys. B 10 (1977) 3347] at low Z. The quadrupole oscillator strength sum ? nf (2) gn is computed to be zero to a very high degree of precision.
Zhang, Y-H., Tang, L-Y., Zhang, X-Z., Shi, T-Y., & Mitroy, J. (2012). Relativistic Quadrupole Polarizability for the Ground State of Hydrogen-Like Ions. Chinese Physics Letters, 29(6), 063101-1-063101-4. https://doi.org/10.1088/0256-307X/29/6/063101