The dipole polarizability αd and the quadrupole polarizability αq 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 αd of the helium-like ions are in good agreement with those obtained previously by an analytic method. The calculated quadrupole polarizability αq of the alkali ions increases very rapidly with increasing Z, from 0.056 A⁵ for Na⁺ to 7.80 A⁵ for Cs⁺.
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R. M. Sternheimer (1957) studied this question.
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