© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:nucl-th/0206042 · Physical Review C

Generic rotation in a collective SD nucleon-pair subspace

Y. M. Zhao, Stuart Pittel, R. Bijker, Alejandro Frank, A. Arima

Published Oct 17, 2002• 28 citations

Abstract

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.

DOI: 10.1103/physrevc.66.041301

Related papers

Collective behavior in random interaction

Calvin W. Johnson, Hai Ah Nam

Recent investigations have looked at the many-body spectra of random two-body interactions. In fermion systems, such as the interacting shell model, one finds pairing-like spectra, while in boson systems, such as IBM-1, one finds rotational and vibrational spectra. We discuss the search for random ensembles of fermion interactions that yield rotational and vibrational spectra, and in particular present results from a new ensemble, the ``random quadrupole-quadrupole ensemble''

arXiv:nucl-th/0601093•Revista Mexicana de Física•Jan 30, 2006•1 citation

Quadrupole collectivity in the two-body random ensemble

Volha Abramkina, Alexander Volya

We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with two-body random interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities in the many-body spectra and their dependence on the underlying two-body interaction Hamiltonian. The quadrupole-quadrupole interaction component appears to be dynamically dominating in the two-body random ensemble. This quadrupole coherence leads to rotational spectral features and thus suggests the formation of the deformed mean-field of a specific geometry.

arXiv:1105.1669•Physical Review C•Aug 25, 2011•6 citations

Collective states in nuclei and many-body random interactions

R. Bijker, Alejandro Frank

Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of ${L}^{P}{=0}^{+}$ ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.

arXiv:nucl-th/0004002•Physical Review C•Jun 1, 2000•50 citations

Order out of chaos in the shell model

Calvin W. Johnson

Nuclei at low excitation energy exhibit such well-ordered behavior, such as rotational and vibrational bands as well as pairing gaps, that they are commonly described with algebraic models; but does such order originate in the details of the nuclear force, or are they emergent properties of dense fermion systems? To answer this, I consider ensembles of random two-body shell-model interactions and examine the low-lying spectra and wavefunctions. Some striking regularities emerge: in particular, pairing appears to be a ubiquitous phenomenon, even in the absence of explicit pairing interactions! These results are remarkably insensitive to the detailed definition of the ensemble.

AIP conference proceedings•Jan 1, 2000•0 citations

Nuclear structure from random interactions

R. Bijker, Alejandro Frank, Stuart Pittel

Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of $J^P=0^+$ ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.

arXiv:nucl-th/0004032•Revista Mexicana de Física•Apr 12, 2000•2 citations

Generalized seniority from random Hamiltonians

Calvin W. Johnson, G. F. Bertsch, David J. Dean +1 more

We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored $J=0$ ground states and an energy gap, but the relationship between ground-state wave functions of neighboring nuclei shows signatures of pairing as well. Matrix elements of pair creation-annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required.

arXiv:nucl-th/9908037•Physical Review C•Dec 20, 1999•75 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.

We conduct a systematic investigation of the nuclear collective dynamics that emerges in systems with two-body random interactions. We explore the development of the mean field and study its geometry. We investigate multipole collectivities in the many-body spectra and their dependence on the underlying two-body interaction Hamiltonian. The quadrupole-quadrupole interaction component appears to be dynamically dominating in the two-body random ensemble. This quadrupole coherence leads to rotational spectral features and thus suggests the formation of the deformed mean-field of a specific geometry.

Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of

{L}^{P}{=0}^{+}

ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.

Nuclei at low excitation energy exhibit such well-ordered behavior, such as rotational and vibrational bands as well as pairing gaps, that they are commonly described with algebraic models; but does such order originate in the details of the nuclear force, or are they emergent properties of dense fermion systems? To answer this, I consider ensembles of random two-body shell-model interactions and examine the low-lying spectra and wavefunctions. Some striking regularities emerge: in particular, pairing appears to be a ubiquitous phenomenon, even in the absence of explicit pairing interactions! These results are remarkably insensitive to the detailed definition of the ensemble.

Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of

J^P=0^+

ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.

We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored

J=0

ground states and an energy gap, but the relationship between ground-state wave functions of neighboring nuclei shows signatures of pairing as well. Matrix elements of pair creation-annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required.