  We present analytical expressions for the resonance frequencies of the
plasmonic modes hosted in a cylindrical nanoparticle within the quasistatic
approximation. Our theoretical model gives us access to both the longitudinally
and transversally polarized dipolar modes for a metallic cylinder with an
arbitrary aspect ratio, which allows us to capture the physics of both
plasmonic nanodisks and nanowires. We also calculate quantum mechanical
corrections to these resonance frequencies due to the spill-out effect, which
is of relevance for cylinders with nanometric dimensions. We go on to consider
the coupling of localized surface plasmons in a dimer of cylindrical
nanoparticles, which leads to collective plasmonic excitations. We extend our
theoretical formalism to construct an analytical model of the dimer, describing
the evolution with the inter-nanoparticle separation of the resultant bright
and dark collective modes. We comment on the renormalization of the coupled
mode frequencies due to the spill-out effect, and discuss some methods of
experimental detection.
