  Inspired by recent measurements on individual metallic nanospheres that can
not be explained with traditional classical electrodynamics, we theoretically
investigate the effects of nonlocal response by metallic nanospheres in three
distinct settings: atomic spontaneous emission, electron energy loss
spectroscopy, and light scattering. These constitute two near-field and one
far-field measurements, with zero-, one-, and two-dimensional excitation
sources, respectively. We search for the clearest signatures of hydrodynamic
pressure waves in nanospheres. We employ a linearized hydrodynamic model and
Mie-Lorenz theory is applied for each case. Nonlocal response shows its mark in
all three configurations, but for the two near-field measurements we predict
especially pronounced nonlocal effects that are not exhibited in far-field
measurements. Associated with every multipole order is not only a single
blueshifted surface plasmon, but also an infinite series of bulk plasmons that
has no counterpart in a local-response approximation. We show that these
increasingly blueshifted multipole plasmons become spectrally more prominent at
shorter probe-to-surface separations and for decreasing nanosphere radii. For
selected metals we predict hydrodynamic multipolar plasmons to be measurable on
single nanospheres.
