Correlations of excited states forsdbosons in the presence of random interactions

Abstract

In this work we study the yrast states of sd-boson systems in the presence of random interactions. It is found that the yrast states with spin-zero ground states among the random ensemble exhibit strong correlations, characterized by anharmonic vibration, s-boson or d-boson condensation, as well as vibrational and rotational motions. We study these correlations explicitly based on their wave functions and the features of two-body interactions in the random ensemble.Challenges of modern science reflect the twin themes of complexity and simplicity in many-body systems, and the structure of atomic nuclei provides us with an appropriate laboratory to study both the complexity out of simple building blocks and simplicity out of the complexity [1]. The low-lying states of nuclei often exhibit a pattern suggestive of symmetries for collective motions (e.g., vibration and rotation). One thus asks to what extent the low-lying states acquire order from the basic properties of interactions (e.g., rotational invariance). This can be studied by permitting the interactions to be more and more arbitrary.In 1998, Johnson, Bertsch, and Dean discovered [2] that spin-zero ground-state (g.s.) dominance in even-even nuclei can be obtained by using random two-body interactions. This result is called the 0-g.s. dominance. Many efforts have been devoted to understand this observation; see Refs. [3-5] for reviews. For recent studies of random Hamiltonians for sd bosons, see Refs. [6][7][8][9][10][11][12].In Ref.[7], Bijker and Frank pointed out that the vibration and rotation are two important motions in sd-boson systems, even if random interactions are assumed. These two motions are characterized by the ratio of the first 4 + state energy with respect to the first 2 + state energy, that is, R 4 = E 4 + 1 /E 2 + 1 (in this paper, we define R I = E I + 1 /E 2 + 1 ). For vibrations R 4 2.0, and for rotations R 4 3.3. The predominance of vibrational and rotational motions is characterized by the sharp peaks in the distribution of R 4 at R 4 2.0 and 3.3.In contrast, the random samples with R 4 = 2.0 or 3.3 have not been paid enough attention to date, because they look like statistical "noise" to the dominant modes (i.e., vibrational and rotational motions) in the two-body random ensemble. There were two studies of R 4 = 2.0 or 3.3: In Ref.[6], Kusnezov and collaborators indicated a pattern of the anharmonic vibrator (AHV) [13] with random interactions, and in Ref.[11], Johnson and Nam noticed the correlation with R I R 4 1 (called the "seniority"-type correlation and denoted by "S" therein), in addition to vibrational and rotational spectra, by the distributions of (R I , R 4 ) for boson number N B = 16.

Regularity of nuclear structure under random interactions

“…In this part I present two recent results obtained by our group with random interactions [2]. The first result is on collective motion in sd-boson systems, and the second is on evaluation of eigenvalues [3].…”

“…For random Hamiltonians, we studied relevance of generalized seniority under random interactions in single-closed shell nuclei in the sd and the p f shell [1], and the collective motions of sd bosons with random interactions [2]. Concerning the fourth topic, Prof. Arima, Mr. Shen (one of my graduate students), Prof. Yoshinaga, and I, have been working very hard to evaluate eigenvalues of the nuclear shell model Hamiltonian without diagonalizing the full matrices [3,4].…”

“…(1) Nucleon Pair Approximation of the shell model; (2) Description and prediction of mass, residual neutron-proton interaction; (3) Random Hamiltonians; (4) Eigenvalues of the shell model Hamiltonian. The third topic is the main subject which Prof. Arima suggested me to work under his guidance during my stay in Japan for about seven years, as one of his post-docs.…”

Correlations between low-lying yrast states forsdbosons with random interactions

“…There are problems remaining to be solved. The correlation a is not yet understood; this correlation is not understood for the case of spin-zero ground states, although one can derive this correlation in terms of the anharmonic vibrator model [11,17,18], Another correlation close to (/?6,7?4) = (7,3.3) [{Rs,R4) = (12,3.…”

“…[7][8][9] in which the dominance of spin-zero ground states and robustness of vibrational and rotational bands were studied with an analysis of the mean field method as well as its dependence of F spin; and Refs. [10,11] in which correlations among yrast excitation energies were investigated for random samples with spin-zero ground states.…”