Validity of the Generalized Density Matrix Method for Microscopic Calculation of Collective/Bosonic Hamiltonian

TL;DR

This paper evaluates the generalized density matrix (GDM) method for microscopic calculation of collective bosonic Hamiltonians, demonstrating its accuracy in reproducing low-lying states compared to exact shell-model results.

Contribution

The study validates the GDM approach by comparing it with shell-model diagonalization, confirming its effectiveness across various nuclear shapes.

Findings

GDM reproduces low-lying energies accurately

Transition rates are well-matched by GDM

Effective across vibrational to deformed nuclei

Abstract

Recently a procedure by generalized density matrix (GDM) is proposed for calculating a collective/bosonic Hamiltonian microscopically from the shell-model Hamiltonian. In this work we examine the validity of the method by comparing the GDM results with that of the exact shell-model diagonalization in a number of models. It is shown that the GDM method reproduces the low-lying collective states quite well, both for energies and transition rates, across the whole region going from vibrational to gamma-unstable and deformed nuclei.