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The dipole polarizability ₃ and the quadrupole polarizability ₐ have been calculated for several ions by solving the Schr\"odinger equation satisfied by the first-order perturbation of the wave functions of the electrons of the core. The results for ₃ of the helium-like ions are in good agreement with those obtained previously by an analytic method. The calculated quadrupole polarizability ₐ of the alkali ions increases very rapidly with increasing Z, from 0. 056 A^5 for Na^+ to 7. 80 A^5 for Cs^+.
R. M. Sternheimer (Sun,) studied this question.