  This article presents and discusses the general features and aspects
regarding the electromagnetic scattering by a small core-shell plasmonic
sphere. First, the thickness effects on the plasmonic resonances are presented
in the electrostatic (Rayleigh) limit, utilizing the MacLaurin expansion of the
Mie coefficients of hollow scatterers. Several aspects regarding the core
effects are given, illustrating the enabling mechanisms and peculiarities of
its resonant scattering response on it electrostatic limit. The electrodynamic
aspects of the scattering process are revealed through the newly introduced
Pad\'e expansion of the Mie coefficients. Additionally we expose how the core
material affects the dynamic mechanisms, such as the dynamic depolarization and
radiative damping. The described method can be expanded for other type of
resonances and canonical shapes, while the general characteristics presented
here are expected to stimulate further studies regarding the functionalities of
the core-shell scatterers.
