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arXiv:nucl-th/0211033 · Physical Review C

Energy level statistics of the U(5) and O(6) symmetries in the interacting boson model

Jing Shu, Ying Ran, Tao Ji, Yu‐xin Liu

Published Apr 25, 2003• 11 citations
arXivHTMLPDF

Abstract

We study the energy level statistics of the states in U(5) and O(6) dynamical symmetries of the interacting boson model and the high spin states with backbending in U(5) symmetry. In the calculations, the degeneracy resulting from the additional quantum number is eliminated manually. The calculated results indicate that the finite boson number N effect is prominent. When N has a value close to a realistic one, increasing the interaction strength of subgroup O(5) makes the statistics vary from Poisson type to Gaussian orthogonal ensemble type and further recover to Poisson type. However, in the case of $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ they all tend to be Poisson type. The fluctuation property of the energy levels with backbending in high spin states in U(5) symmetry involves a signal of shape-phase transition between spherical vibration and axial rotation.

DOI
10.1103/physrevc.67.044304

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We study the energy level statistics of the states in U(5) and O(6) dynamical symmetries of the interacting boson model and the high spin states with backbending in U(5) symmetry. In the calculations, the degeneracy resulting from the additional quantum number is eliminated manually. The calculated results indicate that the finite boson number N effect is prominent. When N has a value close to a realistic one, increasing the interaction strength of subgroup O(5) makes the statistics vary from Poisson type to Gaussian orthogonal ensemble type and further recover to Poisson type. However, in the case of N\ensuremath→\ensuremath∞,\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},N\ensuremath→​\ensuremath∞, they all tend to be Poisson type. The fluctuation property of the energy levels with backbending in high spin states in U(5) symmetry involves a signal of shape-phase transition between spherical vibration and axial rotation.
We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd- A nucleus using the interacting boson–fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (Δ 3 ) are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SO B (5) and SO BF (5) and the spin play important roles in the energy level statistics, however, along with the increase of N , the statistics distribution would tend to be in Poisson form.
We study the energy level statistics of the SO(5) limit of super-symmetry U(6/4) in odd-A nucleus using the interacting boson-fermion model. The nearest neighbor spacing distribution (NSD) and the spectral rigidity (△3)are investigated, and the factors that affect the properties of level statistics are also discussed. The results show that the boson number N is a dominant factor. If N is small, both the interaction strengths of subgroups SOB(5) and SOBF(5)and the spin play important roles in the energy level statistics, however, along with the increase of N, the statistics distribution would tend to be in Poisson form.
We investigate the finite-size scaling exponents for the critical point at the shape-phase transition from U(5) (spherical) to O(6) (deformed \ensuremath{\gamma}-unstable) dynamical symmetries of the interacting boson model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading-order correction to the ground-state energy, the gap, the expectation value of the d-boson number in the ground state and the E2E2E2 transition probability from the ground state to the first excited state and determine the corresponding finite-size scaling exponents.
The spectral degeneracies emerging in the critical region of the interacting boson model are systematically investigated. The results indicate that the level crossings in the transitions from the U(5) to the SU(3) quasidynamical symmetry can induce the approximate spectral degeneracies along the first-order transitional line for large boson number NNN. The remnants of these types of degeneracies in finite-NNN systems have been preliminarily identified from the low-lying spectra of 150Nd^{150}\mathrm{Nd}150Nd. In addition, the similar approximate degeneracies emerging in the phase transition between the U(5) and SO(6) quasidynamical symmetries are parallel emphasized and those in other critical models are also mentioned.
The quantum phase transitional behavior of an alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model is explored. Specifically, the usual SU(3) quadrupole-quadrupole interaction is replaced by an O(6) cubic interaction, and the transitional behaviors of the low-lying energy levels, eigenstates, isomer shifts, $E$2 transition rates, and expectation values of shape variables across the entire transitional region are all examined within this context. A comparison with outcomes of the usual U(5)-SU(3) transitional description shows that the spherical to axially deformed shape-phase transition can also be described within this alternative context, especially near the critical point. However, with the O(6) cubic interaction the transition is considerably smoother than for the U(5)-SU(3) case, but with the nuclear shape less well defined, even in the axially deformed limit. It is also shown that the new scheme seems better than the usual U(5)-SU(3) scheme in describing the low-lying spectrum of 152{}^{152}152Sm with X(5) critical point symmetry.
We study quasicritical phenomena in transitions between two "quantum phases" of a finite boson system, described by the interacting boson model 1 used in nuclear physics. The model is formulated in the algebraic framework and has a simple geometrical interpretation; the "phases" represented by dynamical symmetries U(5) and SU(3) correspond to spherical and deformed nuclear shapes. The quasicriticality of the U(5)-SU(3) transition is shown to be connected with the following phenomena simultaneously occurring in a narrow parameter region between the symmetries: (a) abrupt structural changes of eigenstates, (b) multiple avoided crossing of levels, (c) peaked density of exceptional points, (d) qualitative changes of the corresponding classical potential. We show that these spectroscopic features influence the dynamics of intersymmetry transitions in the model parameter space if the parameters themselves become dynamical variables.