Semiclassical theory of surface plasmons in spheroidal clusters

A microscopic theory of linear response based on the Vlasov equation is ext ended to systems having spheroidal equilibrium shape. The solution of the l inearized Vlasov equation, which gives a semiclassical version of the rando m-phase approximation, is studied for electrons moving in a deformed equili brium mean field. The deformed field has been approximated by a cavity of s pheroidal shape, both prolate, and oblate. Contrary to spherical systems, t here is now a coupling among excitations of different multipolarity induced by the interaction among constituents. Explicit calculations are performed for the dipole response of deformed clusters of different size. In all cas es studied here, the photoabsorption strength for prolate clusters always d isplays a typical double-peaked structure. For oblate clusters we find that the high-frequency component of the plasmon doublet can became fragmented in the medium size region (N similar to 250). This fragmentation is related to the presence of two kinds of three-dimensional electron orbits in oblat e cavities. The possible scaling of our semiclassical equations with the va lence electron number and density is investigated.