The scattering problem within a multilayered spherically symmetric medium due to a source of perturbation located in the external region is considered. Assuming that the refractive index and its derivative vary continuously, with the exception of a finite number of jump discontinuities, the electromagnetic field vectors are represented in terms of various well-known potentials suitable for describing the azimuthal dependence of the incident wave. The linear dependence between the permittivity and the specific conductivity is proved to be equivalent to the vanishing of the electric charge density. Exact expressions for the field energy characteristics in the external region have been derived without any supplementary suppositions with respect to the wave zone. Scattering from a dielectric coated sphere, whose refractive index is a continuous function while its derivative has two jump discontinuity points (a modified Mie problem), has been studied. The generalized van de Hulst phase angle transformation is introduced and used to show the coincidence of the cross sections for scattering and extinction for the transparent spherical shell mentioned.
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