Surface plasmons in small metal particles

The dielectric response of a small metal particle to a perturbing potentialv _L =r ^L Y _LM e ^iωt is considered within the random phase approximation (RPA). The static dielectric polarizability is found and the size dependence of the surface plasmon frequencies are then determined from sum rule calculations. When the particle radiusa is large compared to the Thomas-Fermi screening lengthr ₀ the RPA equation is transformed into a form appropriate for an analytical solution. The dynamic electric polarizability, the position and the width of the surface plasma resonance are found in the limita/r ₀?1.