arXiv:nucl-th/0404041 · Physical Review C

Patterns of the ground states in the presence of random interactions: Nucleon systems

Y. M. Zhao, A. Arima, Noritaka Shimizu, K. Ogawa, Naotaka Yoshinaga, Olaf Scholten

Published Nov 29, 2004• 18 citations

Abstract

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.

DOI: 10.1103/physrevc.70.054322

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arXiv:nucl-th/0404041 · Physical Review C

Patterns of the ground states in the presence of random interactions: Nucleon systems

Y. M. Zhao, A. Arima, Noritaka Shimizu, K. Ogawa, Naotaka Yoshinaga, Olaf Scholten

Published Nov 29, 2004• 18 citations

arXiv HTML PDF

Abstract

\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.

DOI: 10.1103/physrevc.70.054322

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Physical Review CNov 29, 20211 citation

\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

\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.

In this paper we discuss in detail the

P(I)'\mathrm{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)'\mathrm{s}

with those obtained by diagonalizing a TBRE Hamiltonian. We begin with a few solvable cases, such as fermions in a small single-

j

shell and d boson systems, where elegant agreements between the predicted

P(I)'\mathrm{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-

j

shell or a many-

j

shell,

\mathrm{sd}

-boson or

\mathrm{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)

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-

j

shells and j g.s. probabilities of odd numbers of fermions in a single-

j

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-

j

shell. Some interesting results taking a displaced two-body random ensemble are presented for the I ground state probabilities.

Z

, odd-

N

systems with isospin conservation have relatively fewer J=0 ground states.

In this paper, we report our systematic calculations of angular momentum I ground state probabilities

P(I)

of boson systems with spin l in the presence of random two-body interactions. It is found that the

P(0)

dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the

P(0)

dominance is partly connected to the even number of identical particles. It is also noticed that the

{P(I}_{\mathrm{max}})

's of bosons with spin l do not follow the

1/N

(N=l+1,

referring to the number of independent two-body matrix elements) relation. The properties of the

P(I)

's obtained in boson systems with spin l are discussed.

We investigate the robustness of ``noncollective'' rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal

I(I+1)

behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin-

{I}_{\mathrm{max}}

ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.