  Using either quasi-static approximation or exact Mie expansion, we
characterize the localized surface plasmons supported by a metallic spherical
nanoparticle. We estimate the quality factor $Q_n$ and define the effective
volume $V_n$ of the $n^{th}$ mode in a such a way that coupling strength with a
neighbouring dipolar emitter is proportional to the ratio $Q_n/V_n$ (Purcell
factor). The role of Joule losses, far-field scattering and mode confinement in
the coupling mechanism are introduced and discussed with simple physical
understanding, with particular attention paid to energy conservation.
