To model elastic and inelastic light scattering on a metal nanosphere with spatially dispersive permittivity, an extension of the Lorenz–Mie theory is applied. The theory takes into account longitudinal vector spherical harmonics inside the sphere and determines the generalized Mie coefficients using a condition of vanishing electron flow through the sphere surface. In general, this condition is distinct from the conventional additional boundary condition of the continuity of the normal component of the electric field. Therefore, contrary to the common belief, the problem of divergence of the local density of electromagnetic states at the surface of an absorbing sphere is not solved by considering the spatial dispersion of the permittivity. We illustrate the theory by a study of the optical properties of a silver nanosphere using a hydrodynamic model for the dielectric function of the electron gas. Predictions of the nonlocal theory differ markedly from those of the local one if the sphere’s radius or the distance to the surface is smaller than a few nanometers. In particular, we demonstrate a shift of the Fröhlich resonance of nanometer-sized Ag particles caused by the spatial dispersion. Excitation of high-order spherical harmonics in larger particles is discussed. We show how the spatial dispersion decreases the rate of fluorescence quenching in close proximity to the particle surface.
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