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Surface and volume plasmons excited in a metal cluster by moving electron andcorresponding inelastic scattering spectra are studied based on thehydrodynamic approach. Along with the bulk losses traditionally taken intoaccount, the surface and radiative ones are also considered as the physicalmechanisms responsible for the plasmon damping. The second and third mechanismsare found to be essential for the surface plasmons and depend very differentlyon the multipole mode order. The differential equations are obtained whichdescribe the temporal evolution of every particular mode as that one of alinear oscillator excited by the given external force, and the electron energyloss spectra are calculated. The changes in spectrum shape with the impactparameter and with the electron passage time are analyzed and found to be ingood enough agreement with the data of scanning transmission electronmicroscopy (STEM) experiments. It is shown that, in the general case, apronounced contribution to the formation of the loss spectrum is given by theboth surface and volume plasmons with low and high multipole indices. Inparticular, at long electron passage time, the integral loss spectrum which iscalculated for the free-electron cluster model contains two main peaks: a broadpeak from merging of many high-order multipole resonances of the surfaceplasmons and a narrower peak of nearly the same height from merged volumeplasmons excited by the electrons that travel through the central region of thecluster. Comparatively complex dependences of the calculated excitationcoefficients and damping constants of various plasmons on the order of theexcited multipole result in wide diversity of possible types of the lossspectrum even for the same cluster material and should be taken into account ininterpretation of corresponding electron energy loss spectroscopy (EELS)experiments.

Excitation of surface and volume plasmons in metal nanocluster by fast electrons