  Interactions between elementary excitations are of great interest from a
fundamental aspect and for novel applications. While plasmon-exciton have been
extensively studied, the interaction mechanisms between acoustic vibrations
(phonons) and localized surface plasmons (LSPs) remain quite unexplored. Here,
we present a new theoretical framework for the investigation of the interaction
between confined acoustic vibrations and LSPs involved in resonant acoustic
Raman scattering. We express the Raman scattering process in the framework of
Fermi's golden rule and introduce the concept of Raman energy density (RED).
Similarly to the Raman-Brillouin electronic density (RBED) introduced for
semiconductors, this physical quantity is used as a theoretical tool for the
interpretation of resonant Raman scattering mediated by LSPs in metallic
nanoparticles. The RED represents the electromagnetic energy density excited in
the Raman scattering process and modulated by the acoustic vibrations of the
nanoparticle. We show that, similarly to the LDOS and the RBED, the RED can be
mapped in the near-field region, and provides a clear picture of the
interaction between LSPs and acoustic vibrations giving rise to inelastic
scattering measurable in the far-field. We use the newly introduced RED concept
to investigate elastic (an)isotropy effects and extract the Raman selection
rules of spherical nanoparticles embedded in a dielectric environment.
