A formalism is proposed for microscopic calculation of the collective nuclear Hamiltonian from the underlying nucleonic Hamiltonian, based on the generalized density matrix. It goes beyond the well-known random phase approximation, which calculates only the harmonic terms in the collective Hamiltonian. Many nuclei, including those at the gamma-unstable and rotational limits, have a vanishing or negative harmonic potential; there the anharmonic terms calculated by the generalized density matrix method are indispensable restoring the stability of the system. The proposed formalism is tested in several models by comparing with the exact results. Realistic applications on tin isotopes are discussed.
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