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Physical Review C

Robustness of “noncollective” rotational behavior for nuclei in the presence of random interactions

Jiajie Shen, Hui Jiang, G. J. Fu

Published Nov 29, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physrevc.104.054319

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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)I(I+1)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-Imax{I}_{\mathrm{max}}Imax​ 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.
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.
A variable combination of realistic and random two-body interactions allows the study of collective properties [such as the energy spectra and B(E2)B(E2)B(E2) transition strengths] in 44Ti,{}^{44}\mathrm{Ti},44Ti, 48Cr,{}^{48}\mathrm{Cr},48Cr, and 24Mg.{}^{24}\mathrm{Mg}.24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2)B(E2)B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.
Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of JP=0+J^P=0^+JP=0+ ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.
Nuclei at low excitation energy exhibit such well-ordered behavior, such as rotational and vibrational bands as well as pairing gaps, that they are commonly described with algebraic models; but does such order originate in the details of the nuclear force, or are they emergent properties of dense fermion systems? To answer this, I consider ensembles of random two-body shell-model interactions and examine the low-lying spectra and wavefunctions. Some striking regularities emerge: in particular, pairing appears to be a ubiquitous phenomenon, even in the absence of explicit pairing interactions! These results are remarkably insensitive to the detailed definition of the ensemble.
We apply a two-body random ensemble to a hypothetical system of spinless fermions occupying a one-dimensional rotationally invariant orbit in order to study the statistical tendencies of spins of ground states for a random two-body interaction. We also investigate the origin of the dominance of spin-zero ground states of a single-j shell in the nuclear shell model, which can be interpreted geometrically as a particular case of the simple hypothetical model we consider. Assuming a specific symmetry, or the doublet structure due to time-reversal symmetry, it is found that the ensemble has a preference for a ground state whose spin is zero. We demonstrate how the time-reversal symmetry and its doublet structure affect this ground state tendency.
The energy systematics of medium and heavy even-even nuclei shows very regular features, such as for example the tripartite classification of nuclear structure into seniority, anharmonic vibrator and rotor regions [1,2]. Traditionally, this regular behavior has been interpreted as a consequence of particular interactions, such as an attractive pairing force in semimagic nuclei and an attractive neutron-proton quadrupole-quadrupole interaction for deformed nuclei. It came as a surprise, therefore, that recent studies of even-even nuclei in the nuclear shell model [3–5] and in the interacting boson model (IBM) [6–8] with random interactions also displayed a high degree of order. Both models showed a statistical preference for L = 0 ground states, despite the random nature of the interactions. In addition, in the shell model evidence was found for the occurrence of pairing properties [5], and in the IBM for vibrational and rotational bands [6,7]. These unexpected results have sparked a large number of investigations to try to understand their origin [9]. In this contribution, we discuss the phenomenom of emerging regular spectral features from the IBM with random interactions, and its