Collective pair model

Microscopic investigation of collective models is illustrated with the study of the multilevel pairing force model. The coherent-state description of pairing excitations through the variation of the pairing field and the classification of generators into collective and noncollective modes are discussed. Numerical calculations are performed for collective pairing rotations and vibrations built on the ground state. The coupling to the noncollective state is studied. Exact results from the Richardson method are given for comparison.Microscopic investigation of collective models is illustrated with the study of the multilevel pairing force model. The coherent-state description of pairing excitations through the variation of the pairing field and the classification of generators into collective and noncollective modes are discussed. Numerical calculations are performed for collective pairing rotations and vibrations built on the ground state. The coupling to the noncollective state is studied. Exact results from the Richardson method are given for comparison.

Physical Review CMar 1, 19913 citations

Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

Fang Ni, Takashi Nakatsukasa

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.

arXiv:1712.02954Physical Review CApr 12, 20183 citations

Collective Model

WORLD SCIENTIFIC eBooksMay 2, 20070 citations

Generic rotation in a collective SD nucleon-pair subspace

Y. M. Zhao, Stuart Pittel, R. Bijker +2 more

The low-lying collective states involving many nucleons interacting by the two-body random ensemble (TBRE) interactions are investigated in a collective $\mathrm{SD}$ -pair subspace, with the collective pairs defined by the two-nucleon system. It is found that in this truncated pair subspace, collective vibrations arise naturally for a general TBRE Hamiltonian whereas collective rotations do not. A Hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the Hamiltonian is key to producing generic collective rotation.The low-lying collective states involving many nucleons interacting by the two-body random ensemble (TBRE) interactions are investigated in a collective $\mathrm{SD}$-pair subspace, with the collective pairs defined by the two-nucleon system. It is found that in this truncated pair subspace, collective vibrations arise naturally for a general TBRE Hamiltonian whereas collective rotations do not. A Hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the Hamiltonian is key to producing generic collective rotation.

arXiv:nucl-th/0206042Physical Review COct 17, 200228 citations

Collective Model

WORLD SCIENTIFIC eBooksFeb 1, 20080 citations

The low-lying collective states involving many nucleons interacting by the two-body random ensemble (TBRE) interactions are investigated in a collective

\mathrm{SD}

-pair subspace, with the collective pairs defined by the two-nucleon system. It is found that in this truncated pair subspace, collective vibrations arise naturally for a general TBRE Hamiltonian whereas collective rotations do not. A Hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the Hamiltonian is key to producing generic collective rotation.