FLUID-DYNAMICAL APPROACH TO COLLECTIVE MODES IN METAL-CLUSTERS

A simple variational method has recently been used to obtain the bulk- plasmon dispersion relation in a metal. In the present work we investi gate the eigenmodes of the valence electrons in a metal cluster consid ering a semiclassical version of the method presented by Ando and Nish izaki. As a variational function we consider the Slater determinant \ phi > which is related to the Slater determinant \ phi(0) >, describin g the ground state, by means of the unitary transformation \ phi > = e (l/($) over bar)S \ phi(0) >, where S(x, p, t) = (X)(x, t) + 1/2 [p.s( x, t).p]. We use a polynomial approximation to determine the dynamical cal fields (X)(x, t) and s(x, t). It is shown that the eigensolutions satisfy the energy weighted sum rule and the cubic energy weighted su m rule. The spectrum of excited energies, as well as transition densit ies and currents are obtained for the sodium, aluminum, and silver.