A. Arima

Regularities of many-body systems interacting by a two-body random ensemble

Abstract The ground states of all even–even nuclei have angular momentum, I , 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, in the presence of two-body random interactions, the predominance of I π = 0 + ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single- j shells for small j , there are a few approaches to predict and/or explain spin I ground state ( I g.s.) probabilities. An empirical approach to predict I g.s. probabilities is available for general cases, such as fermions in a single- j ( j > 7 2 ) or many- j shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random two-body interactions, such as the odd–even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced two-body random ensemble.

Simple approach to the angular momentum distribution in the ground states of many-body systems

We propose a simple approach to predict the angular momentum I ground state (I g.s.) probabilities of many-body systems that does not require the diagonalization of hamiltonians with random interactions. This method is found to be applicable to {bf all} cases that have been discussed: even and odd fermion systems (both in single-j and many-j shells), and boson (both sd and sdg) systems. A simple relation for the highest angular momentum g.s. probability is found. Furthermore, it is suggested for the first time that the 0g.s. dominance in boson systems and in even-fermion systems is given by two-body interactions with specific features.

One-Pion Exchange Current Corrections for Nuclear Magnetic Moments in Relativistic Mean Field Theory

The one-pion exchange current corrections to isoscalar and isovector magnetic moments of double-closed shell nuclei plus and minus one nucleon with

The pseudo-spin symmetry in a Dirac equation

A=15,17,39

Many-body systems interacting via a two-body random ensemble. I. Angular momentum distribution in the ground states

and 41 have been studied in the relativistic mean field (RMF) theory and compared with previous relativistic and non-relativistic results. It has been found that the one-pion exchange current gives a negligible contribution to the isoscalar magnetic moments but a significant correction to the isovector ones. However, the one-pion exchange current doesnt improve the description of nuclear isovector magnetic moments for the concerned nuclei.

Many-body systems interacting via a two-body random ensemble. II. Average energy of each angular momentum

We have found the root of the pseudo-spin symmetry to the Dirac equation. We found two kinds of conditions for the pseudo-spin approximation both for the case of the spherical potential and for the deformed potential.

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

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum

The 0+ predominance in nuclear physics: single-j shell study

I_{max}

General pairing interactions and pair truncation approximations for fermions in a single-jshell

is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by 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 fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.

Lowest eigenvalues of random Hamiltonians

In this paper, we discuss the regularities of average energies with a fixed angular momentum I (denoted as