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The generalized density matrix (GDM) method is used to calculatemicroscopically the parameters of the collective Hamiltonian. Higher orderanharmonicities are obtained consistently with the lowest order results, themean field [Hartree-Fock-Bogoliubov (HFB) equation] and the harmonic potential[quasiparticle random phase approximation (QRPA)]. The method is applied tosoft spherical nuclei, where the anharmonicities are essential for restoringthe stability of the system, as the harmonic potential becomes small ornegative. The approach is tested in three models of increasing complexity: theLipkin model, model with factorizable forces, and the quadrupole plus pairingmodel.

Generalized Density Matrix Revisited: Microscopic Approach to Collective Dynamics in Soft Spherical Nuclei