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Quadrupole coherence with displaced random ensembles

Víctor Velázquez, A. P. Zuker

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Displaced two body random ensembles are built with numbers extracted from normal distributions whose peaks are centered off zero (DT-BRE). Exact diagonalizations in the f 7 / 2 p 3 / 2 space show the evolution of the ratioR = E 4 + /E 2 + and B(E2) values of even-even nuclei for different displaced centroids. We find that displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced B(E2) transitions.

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Displaced two body random ensembles are built with numbers extracted from normal distributions whose peaks are centered off zero (DT-BRE). Exact diagonalizations in the f 7 / 2 p 3 / 2 space show the evolution of the ratioR = E 4 + /E 2 + and B(E2) values of even-even nuclei for different displaced centroids. We find that displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced B(E2) transitions.
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.
We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular, we calculate probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory frame) quadrupole moments, and discuss $\ensuremath{\alpha}$ clustering in the ground states. We find that the probability distribution for the parity of the ground states obtained by a two-body random ensemble simulates that of realistic nuclei with $A\ensuremath{\geqslant}70$: positive parity is dominant in the ground states of even-even nuclei, while for odd-odd nuclei and odd-mass nuclei we obtain with almost equal probability ground states with positive and negative parity. In addition, assuming pure random interactions, we find that, for the ground states, low seniority is not favored, no dominance of positive values of spectroscopic quadrupole deformation is observed, and there is no sign of $\ensuremath{\alpha}$-clustering correlation, all in sharp contrast to realistic nuclei. Considering a mixture of a random and a realistic interaction, we observe a second-order phase transition for the $\ensuremath{\alpha}$-clustering correlation probability.
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
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in the spectra, ground state spins, and isospins is discovered. In even-particle systems the strong preponderance of spin zero ground states is observed with three, four, and higher-order random many-body interactions, and similar trends are discovered in systems that possess both rotational and isospin symmetry. Various types of correlations from pairing to spectral sequences and correlations across different masses are explored. A search for an interpretation is presented.