  A classical way for exploring the scattering behavior of a small sphere is to
approximate Mie coefficients with a Taylor series expansion. This ansatz
delivered a plethora of insightful results, mostly for small spheres supporting
localized plasmonic resonances. However, many scattering aspects are still
uncharted, especially with regards to magnetic resonances. Here, an alternative
system ansatz is proposed based on the Pad\'e approximants for the Mie
coefficients. The result reveal the existence of a self-regulating radiative
damping mechanism for the first magnetic resonance and new general resonating
aspects for the higher order multipoles. Hence, a systematic way of exploring
the scattering behavior is introduced, sharpening our understanding about the
sphere's scattering behavior and its emergent functionalities.
