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arXiv:nucl-th/9906046 · Physical Review C

Dominance of JP=0+ ground states in even-even nuclei from random two-body interactions

R. Bijker, Alejandro Frank, Stuart Pittel

Published Jul 19, 1999• 61 citations
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Abstract

Recent calculations using random two-body interactions showed a preponderance of ${J}^{P}{=0}^{+}$ ground states, despite the fact that there is no strong pairing character in the force. We carry out an analysis of a system of identical particles occupying orbits with $j=1/2,$ 3/2, and 5/2 and discuss some general features of the spectra derived from random two-body interactions. We show that for random two-body interactions that are not time-reversal invariant the dominance of ${0}^{+}$ states in this case is more pronounced, indicating that time-reversal invariance cannot be the origin of the ${0}^{+}$ dominance.

DOI
10.1103/physrevc.60.021302

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Recent calculations using random two-body interactions showed a preponderance of JP=0+{J}^{P}{=0}^{+}JP=0+ ground states, despite the fact that there is no strong pairing character in the force. We carry out an analysis of a system of identical particles occupying orbits with j=1/2,j=1/2,j=1/2, 3/2, and 5/2 and discuss some general features of the spectra derived from random two-body interactions. We show that for random two-body interactions that are not time-reversal invariant the dominance of 0+{0}^{+}0+ states in this case is more pronounced, indicating that time-reversal invariance cannot be the origin of the 0+{0}^{+}0+ dominance.
We apply a two-body random ensemble to a hypothetical system of spinless fermions occupying a one-dimensional rotationally invariant orbit in order to study the statistical tendencies of spins of ground states for a random two-body interaction. We also investigate the origin of the dominance of spin-zero ground states of a single-j shell in the nuclear shell model, which can be interpreted geometrically as a particular case of the simple hypothetical model we consider. Assuming a specific symmetry, or the doublet structure due to time-reversal symmetry, it is found that the ensemble has a preference for a ground state whose spin is zero. We demonstrate how the time-reversal symmetry and its doublet structure affect this ground state tendency.
The ground states of all even-even nuclei have angular momentum equal to zero, I = 0, and positive parity, π = +. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, a predominance of I π = 0 + ground states was discovered in 1998 using the two-body random ensemble. Since then many efforts have been devoted to understanding and solving this problem from a lot of viewpoints. Still, the underlying physical origin of the I π = 0 + dominance has not been fully understood. Our recent progress in understanding the 0 + dominance of many-body systems is shown.
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.
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.
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.