On the basis of a vectorial integral equation for the local field inside a so-called quantum particle the local-field correction to the optical polarizability of the particle is studied in the limit for which the particle diameter is much less than the wavelength of the externally impressed field (electric dipole–electric dipole polarizability). From the point of view that the transverse and the longitudinal self-field contributions to the electromagnetic propagator dominate the electrodynamics of the quantum particles, the diamagnetic and paramagnetic contributions to the optical polarizability are investigated. In the regime of dominating paramagnetic coupling it is demonstrated that the basic vectorial integral equation can be solved exactly if a limited number of energy levels participate in the dynamics. A new and computationally simple expression is obtained for the diamagnetic polarizability with the transverse self-field assumed to dominate the interaction. The model displays quantum-size effects, and comparison with experimental data on small Au particles shows good agreement.
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