  We develop a theory for spontaneous decay of a quantum emitter (QE) situated
near metal-dielectric structure supporting localized surface plasmons. If
plasmon resonance is tuned close to the QE emission frequency, the emission is
enhanced due to energy transfer from the QE to a localized plasmon mode
followed by photon emission by plasmonic antenna. The emission rate is
determined by intimate interplay between the plasmon coupling to radiation
field and the Ohmic losses in metal. Here we develop plasmon Green's function
approach that includes plasmon's interaction with radiation to obtain explicit
expressions for radiative decay rate and optical polarizability of a localized
plasmon mode in arbitrary plasmonic nanostructure. Within this approach, we
provide consistent definition of plasmon mode volume by relating it to plasmon
mode density, which characterizes the plasmon field confinement, and recover
the standard cavity form of the Purcell factor, but now for plasmonic systems.
We show that, for QE placed at a "hot spot" near a sharp tip of a small metal
nanostructure, the plasmon mode volume scales with the metal volume while being
very sensitive to the proximity to the tip. Finally, we derive the enhancement
factor for radiated power spectrum for any nanoplasmonic system and relate it
to the Purcell factor for spontaneous decay rate. We illustrate our results by
numerical example of a QE situated near gold nanorod tip.
