Naotaka Yoshinaga

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.

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

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

Strong correlation between eigenvalues and diagonal matrix elements

I_{max}

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

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.

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

We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. For two-body random ensemble, we find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the smaller values to larger ones. By using this linear correlation we are able to predict reasonably all eigenvalues of a given Hamiltonian matrix without complicated iterations. For Gaussian orthogonal ensemble matrices, the hyperbolic tangent function improves the accuracy of predicted eigenvalues near the minimum and maximum.

Shell Model Estimate of Nuclear Electric Dipole Moments

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 a 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 Agreater than or equal to70: 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 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 a-clustering correlation probability.

The structure of the 168Er nucleus and the 166Er(t,p)168 Er reaction in terms of the sdg interacting boson model☆

The probability of a state with spin I to be the ground state in many-body systems is studied. Single-j shells with four-particle systems are examined in detail. It is shown that the structure coefficients give a clue to understand the problem why the spin-0 state is most likely to be the ground state.

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

Nuclear electric dipole moments (EDMs) and Schiff moments for the lowest 1/2 + states around the mass 130 are calculated in terms of the nuclear shell model. We estimate the upper limits of the nuclear EDMs, which may be directly measured through ionic atoms. The nuclear EDM of each nucleus is slightly quenched from its single-particle estimate due to many-body effects. We also estimate the upper limit for the EDM of neutral 129 Xe atom using the Schiff moment. Subject Index: 203

Lowest eigenvalues of random Hamiltonians

Abstract Extending the interacting boson model by incorporating besides s and d, also the g-boson, we can describe the population of positive parity states of 168Er in the 166Er(t,P)168Er reaction rather well. In particular, the excitation of I,K π i = 4,3 + 1 ; 2,2+2; 0,0+3 and 0,0+4 states is much improved over the sd-IBM approach.