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arXiv:1105.1669 · Physical Review C

Quadrupole collectivity in the two-body random ensemble

Volha Abramkina, Alexander Volya

Published Aug 25, 2011• 6 citations
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Abstract

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.

DOI
10.1103/physrevc.84.024322

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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.
A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and B(E2)B(E2)B(E2) transition strengths] in 44Ti,{}^{44}\mathrm{Ti},44Ti, 48Cr,{}^{48}\mathrm{Cr},48Cr, and 24Mg.{}^{24}\mathrm{Mg}.24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2)B(E2)B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.
The energy systematics of medium and heavy even-even nuclei shows very regular features, such as for example the tripartite classification of nuclear structure into seniority, anharmonic vibrator and rotor regions [1,2]. Traditionally, this regular behavior has been interpreted as a consequence of particular interactions, such as an attractive pairing force in semimagic nuclei and an attractive neutron-proton quadrupole-quadrupole interaction for deformed nuclei. It came as a surprise, therefore, that recent studies of even-even nuclei in the nuclear shell model [3–5] and in the interacting boson model (IBM) [6–8] with random interactions also displayed a high degree of order. Both models showed a statistical preference for L = 0 ground states, despite the random nature of the interactions. In addition, in the shell model evidence was found for the occurrence of pairing properties [5], and in the IBM for vibrational and rotational bands [6,7]. These unexpected results have sparked a large number of investigations to try to understand their origin [9]. In this contribution, we discuss the phenomenom of emerging regular spectral features from the IBM with random interactions, and its
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 LP=0+{L}^{P}{=0}^{+}LP=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.
The low-lying collective states involving many nucleons interacting by the two-body random ensemble (TBRE) interactions are investigated in a collective SD\mathrm{SD}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.