The dispersion properties of high- and low-frequency electrostatic oscillations of a spherical metallic plasma consisting of hot electrons and cold ions are investigated. The main interest and the key first applications of this system are the spherical metal nanoparticles. General expressions of dispersion relations are obtained for the so-called surface and bulk plasmon waves, and surface and bulk ion-acoustic waves in spherical geometry, using hydrodynamic equations and Poisson equation with appropriate boundary conditions. Numerical results show that dispersion effects become large for metallic particles of small radii, particularly in the range of few nanometers.
