  The kinetic approach is applied to calculate oscillations of a surface
plasmon linewidth in a spheroidal metal nanoparticle embedded in any dielectric
media. The principal attention is focused on the case, when the free electron
path is much greater than the particle size.
  The linewidth of the plasmon resonance as a function of the particle radius,
shape, dielectric constant of the surrounding medium, and the light frequency
is studied in detail. It is found that the resonance plasmon linewidth
oscillates with increasing both the particle size and the dielectric constant
of surrounding medium.
  The main attention is paid to the electron surface-scattering contribution to
the plasmon decay.
  All calculations the plasmon resonance linewidth are illustrated by the
example of the Na nanoparticles with different radii.
  The results obtained in the kinetic approach are compared with the known ones
from other models.
  The role of the radiative damping is discussed as well.
