  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.

Atomic and Molecular Clusters;Mesoscale and Nanoscale Physics;Quantum Physics