  A quantum-mechanical model to calculate the electron energy-loss spectra
(EELS) for the system of a closely located metallic nanoshell and a molecule
has been developed. At the resonance between the molecular excitation and
plasmon modes in the nanoshell, which can be provided by a proper choice of the
ratio of the inner and outer nanoshell radii, the cross-section of inelastic
electron scattering at the molecular excitation energy is shown to grow
significantly, because the molecular transition borrows the oscillator strength
from a plasmon. The enhancement of the inelastic electron scattering by the
molecule makes it possible to observe molecular transitions with an electron
microscope. The dependences of the EEL spectra on the relative arrangement of
the molecule and the nanoshell, the ratio between the inner and outer nanoshell
radii, and the scattering angle are plotted and analyzed.
