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

TL;DR

This paper revisits the generalized density matrix method to microscopically derive collective Hamiltonian parameters, emphasizing anharmonicities in soft spherical nuclei for stability, validated through three progressively complex models.

Contribution

It introduces a consistent microscopic approach to calculate anharmonicities in collective Hamiltonians for soft nuclei, integrating mean field, harmonic potential, and higher order effects.

Findings

Successfully applied to three models of increasing complexity.

Demonstrated importance of anharmonicities for nuclear stability.

Validated approach against known models.

Abstract

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