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Journal of Physics Conference Series

0+ dominance with random interactions

A. Arima, Naotaka Yoshinaga, Yilin Zhao

Published Jan 1, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/20/1/026

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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.
The dominance (preponderance) of the 0+ ground state for random interactions is shown to be a consequence of certain random interactions with chaotic features. These random interactions, called chaotic random interactions, impart a symmetry property to the ground-state wave function: an isotropy under an appropriate transformation, such as zero angular momentum for rotation. Under this mechanism, the ground-state parity and isospin can also be predicted in such a manner that positive parity is favored over negative parity and the isospin T = 0 is favored over higher isospins. As chaotic random interaction is a limit with no particular dynamics at the level of two interacting particles, this realization of isotropic symmetry in the ground state can be considered as the ultimate case of many-body correlations. A possible relation to the isotropy of the early universe is mentioned.
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.
All nuclei with even numbers of protons and of neutrons have ground states with zero angular momentum. This is ascribed to the pairing force between nucleons, but simulations with random interactions suggest a much broader many-body phenomenon. In this Letter I project out random Hermitian matrices that have good quantum numbers and, computing the width of the Hamiltonian in subspaces, find ground states dominated by low quantum numbers, e.g. J=0. Furthermore I find odd-ZZZ, odd-NNN systems with isospin conservation have relatively fewer J=0 ground states.
In this paper we discuss in detail the P(I)′s,P(I)'\mathrm{s},P(I)′s, angular momentum I probabilities in the ground states, of many-body systems interacting via a two-body random ensemble (TBRE). In particular, we extensively apply an approach introduced in an earlier paper and compare the predicted P(I)′sP(I)'\mathrm{s}P(I)′s with those obtained by diagonalizing a TBRE Hamiltonian. We begin with a few solvable cases, such as fermions in a small single-jjj shell and d boson systems, where elegant agreements between the predicted P(I)′sP(I)'\mathrm{s}P(I)′s and those obtained by diagonalizing a TBRE Hamiltonian are achieved. We find that d boson systems systematically present counterexamples of angular momentum 0 ground state dominance when the number of d bosons is $6\ensuremath{\kappa}\ifmmode\pm\else\textpm\fi{}1$ with $\ensuremath{\kappa}$ a natural number, which suggests that certain fundamental symmetry (say, time reversal invariance) of the Hamiltonian cannot ensure the occurrence of angular momentum 0 ground state dominance. Next, we apply the same approach to more complicated cases, such as even or odd number of fermions in a large single-jjj shell or a many-jjj shell, sd\mathrm{sd}sd-boson or sdg\mathrm{sdg}sdg-boson systems, etc. We find that the simple approach proposed in an earlier paper is also well applicable, and thus it is a universal approach. The numerical experiments provide a guideline to tell which interactions are essential to produce a sizable P(I)P(I)P(I) in a many-body system. This disproves a popular idea that the angular momentum 0 ground state (0 g.s.) dominance may be independent of two-body interactions. Some matrix elements which are useful to understand the observed regularities are given or addressed in detail. In this paper we also report a synchronous staggering between the 0 g.s. probabilities of even numbers of fermions in a single-jjj shells and j g.s. probabilities of odd numbers of fermions in a single-jjj shell when j is small. The low seniority chain of 0 g.s. using the same set of two-body interactions is confirmed, but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even numbers of fermions in a single-jjj shell. Some interesting results taking a displaced two-body random ensemble are presented for the I ground state probabilities.