Chinese Physics C

Level statistics for the even-even Yb isotopes

Fangqi Chen, Yang Sun, Xian-Rong Zhou

Published Mar 1, 2009• 1 citation

Abstract

The level statistics of the even-even Yb isotopes are studied by using the energy levels calculated by the projected shell model. The spectrum of intrinsic states and band energies are also studied to discuss the generation of chaoticity. The energy dependence of the chaoticity is investigated, and a chaos to order transition is found.

DOI: 10.1088/1674-1137/33/s1/008

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Chinese Physics C

Level statistics for the even-even Yb isotopes

Fangqi Chen, Yang Sun, Xian-Rong Zhou

Published Mar 1, 2009• 1 citation

Publisher

Abstract

DOI: 10.1088/1674-1137/33/s1/008

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The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the

J-T

scheme for 12 particles in the

sd

-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90\% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.

The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution

P(s)

as a function of interaction strength U and the excitation energy $\ensuremath{\epsilon}$ above the Fermi level. As U increases,

P(s)

undergoes a transition from Poissonian (nonchaotic) to Wigner-Dyson (chaotic) statistics and the transition is described by a single scaling parameter given by $Z=(U{\ensuremath{\epsilon}}^{\ensuremath{\alpha}}\ensuremath{-}{u}_{0}){\ensuremath{\epsilon}}^{1/(2\ensuremath{\nu})},$ where

{u}_{0}

is a constant. While the exponent $\ensuremath{\alpha},$ which determines the global change of the chaos border, is indecisive within a broad range of $0.9\ensuremath{\sim}2.0,$ the finiteness of $\ensuremath{\nu},$ which comes from the increase of the Fock space size with $\ensuremath{\epsilon},$ suggests that the transition becomes sharp as $\ensuremath{\epsilon}$ increases.