Self-consistent determination of the one-body density matrix and particle-hole excitations

We develop a procedure recently proposed for the treatment of correlations in finite Fermi systems in a more consistent way than the random phase appr oximation (RPA). The one-body density matrix in the correlated ground state is now no more assumed to be diagonal in the Hartree-Fock basis. An expres sion is rather provided where this quantity is expressed in terms of the X and Y amplitudes of the particle-hole phonon operators. A set of RPA-like e quations depending only on the one-body density matrix is then constructed by means of the method of linearized equations of motion and solved via an iterative procedure. The procedure is employed to calculate spectra and str ength distributions of several neutral and charged Na and Li metal clusters within the jellium approximation. Improvements are observed with respect t o standard RPA calculations. [S0163-1829(98)06947-1].