N-Block Separable Random Phase Approximation: Application to metal clusters and C60 fullerene

Starting from the Random Phase Approximation (RPA), we generalize the schematic model of separable interaction defning subspaces of ph excitations with different coupling constants between them. This ansatz simplifies the RPA eigenvalue problem to a finite, small dimensional system of equations which reduces the numerical effort. Associated dispersion relation and the normalization condition are derived for the new defined unknowns of the system. In contrast with the standard separable approach, the present formalism is able to describe more than one collective excitation even in the degenerate limit. The theoretical framework is applied to neutral and singly charged spherical sodium clusters and C60 fullerene with results in good agreement with full RPA calculations and experimental data.