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arXiv:nucl-th/9911067 · Physical Review Letters

Band Structure from Random Interactions

R. Bijker, Alejandro Frank

Published Jan 17, 2000• 99 citations
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Abstract

The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one- and two-body interactions. We find a predominance of L(P) = 0(+) ground states, as well as strong evidence for the occurrence of both vibrational and rotational band structures. This remarkable result suggests that such band structures represent a far more general (robust) property of the collective model space than is generally thought.

DOI
10.1103/physrevlett.84.420

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The anharmonic vibrator and rotor regions in nuclei are investigated in the framework of the interacting boson model using an ensemble of random one- and two-body interactions. We find a predominance of L(P) = 0(+) ground states, as well as strong evidence for the occurrence of both vibrational and rotational band structures. This remarkable result suggests that such band structures represent a far more general (robust) property of the collective model space than is generally thought.
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.
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 JP=0+J^P=0^+JP=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.
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
We investigate the origin of the regular features observed in numerical studies of the interacting boson model with random interactions, in particular the dominance of L=0L=0L=0 ground states and the occurrence of vibrational and rotational band structures. It is shown that all of these properties can be interpreted and explained in terms of a Hartree-Bose mean-field analysis, in which different regions of the parameter space are associated with geometric shapes. The same conclusions hold for the vibron model.