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

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