Statistics of 2+ levels in even–even nuclei

Abul-Magd, A. Y.; Harney, H. L.; Simbel, M. H.; Weidenmüller, Hans A.

doi:10.1016/j.physletb.2003.07.092

Cited by 37 publications

(58 citation statements)

References 36 publications

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“…the review articles [30,31]. We analyzed the fluctuation properties of the energy levels using two models, where one is based on a RMT ensemble [32][33][34] and the other one on the method of Bayesian inference [35][36][37]. Both provide quantitative measures for the chaoticity in terms of a parameter which interpolates between the Poisson statistics and GOE statistics.…”

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confidence: 99%

“…2-4 where we compare the NNSD, the ∆ 3 statistics and the ratio distributions of the experimental and calculated levels (histograms and circles) with those of Poissonian random numbers (dash-dotted lines) and of random matrices from the GOE (dashed lines). Superimposed subspectra.-For the analysis of the composite spectra we proceeded as described in [35][36][37]. Ac- …”

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Chaos and Regularity in the Doubly Magic NucleusPb208

et al. 2017

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High resolution experiments have recently lead to a complete identification (energy, spin, and parity) of 151 nuclear levels up to an excitation energy of Ex = 6.20 MeV in 208 Pb [Heusler et al., Phys. Rev. C 93, 054321 (2016)]. We present a thorough study of the fluctuation properties in the energy spectra of the unprecedented set of nuclear bound states. In a first approach we grouped states with the same spin and parity into 14 subspectra, analyzed standard statistical measures for short-and long-range correlations, i.e., the nearest-neighbor spacing distribution, the number variance Σ 2 , the Dyson-Mehta ∆3 statistics, and the novel distribution of the ratios of consecutive spacings of adjacent energy levels in each energy sequence and then computed their ensemble average. Their comparison with a random matrix ensemble which interpolates between Poisson statistics expected for regular systems and the Gaussian Orthogonal Ensemble (GOE) predicted for chaotic systems shows that the data are well described by the GOE. In a second approach, following an idea of Rosenzweig and Porter [Phys. Rev. 120, 1698Rev. 120, (1960] we considered the complete spectrum composed of the independent subspectra. We analyzed their fluctuation properties using the method of Bayesian inference involving a quantitative measure, called the chaoticity parameter f , which also interpolates between Poisson (f = 0) and GOE statistics (f = 1). It turns out to be f ≈ 0.9. This is so far the closest agreement with GOE observed in spectra of bound states in a nucleus. The same analysis has also been performed with spectra computed on the basis of shell model calculations with different interactions (SDI, KB, M3Y). While the simple SDI exhibits features typical for nuclear many-body systems with regular dynamics, the other, more realistic interactions yield chaoticity parameters f close to the experimental values.

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Chaos and Regularity in the Doubly Magic NucleusPb208

et al. 2017

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“…For nuclear systems with time reversal symmetry which spectral spacing follows Gaussian Orthogonal Ensemble (GOE) statistics, the NNSD probability distribution function is well approximated by Wigner distribution[1-2] Different analyses which investigate the spectral statistics of nuclear systems propose a transitional behavior between these limits. To compare the fluctuation properties with regular and chaotic limits quantitatively, different distribution functions have been used [34][35][36][37][38]. One of popular distribution is Abul-Magd distribution [38] which was derived by assuming that, the energy level spectrum is a product of the superposition of independent subspectra, which are contributed respectively from localized eigenfunctions onto invariant (disjoint) phase space.…”

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confidence: 99%

Pairing effect on spectral statistics of even and odd mass nuclei

et al. 2013

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The interplay of pairing is explored for the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distributions by employing the kernel density and maximum likelihood estimation techniques. Different sequences prepared by all the available empirical data for low-lying energy levels of even and odd-mass nuclei in the 34 < 206 A ≤ mass region. A deviation to more regular dynamics is apparent for even-mass nuclei in compare to odd-mass ones, and there are suggestions of effects due to unclosed proton shells on more chaotic dynamics.

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“…Analyses done in Ref. [44] show that the NNS distribution for each group vary strongly with R 4/2 and takes a more regular shape in nuclei that have one of the dynamical symmetries of the interacting Boson model [45]. Figure 6 shows the result of comparison between the histograms for each group with the predictions of Eq.…”

Section: Statistics Of 2 + Levels In Even-even Nucleimentioning

confidence: 97%

Kappa-Deformed Random-Matrix Theory Based on Kaniadakis Statistics

Abul-Magd

Abdel-Mageed

2012

Mod. Phys. Lett. B

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We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index κ (Boltzmann-Gibbs entropy is recovered in the limit κ → 0), we propose the non-Gaussian deformations (κ = 0) of the conventional orthogonal and unitary ensembles of random matrices. The joint eigenvalue distributions for the κ-deformed ensembles are derived by applying the principle maximum entropy to Kaniadakis entropy. The resulting distribution functions are base independent as they depend on the matrix elements in a trace form. Using these expressions, we introduce a new generalized form of the Wigner surmise valid for nearly-chaotic mixed systems, where a basis-independent description is still expected to hold. We motivate the necessity of such generalization by the need to describe the transition of the spacing distribution from chaos to order, at least in the initial stage. We show several examples about the use of the generalized Wigner surmise to the analysis of the results of a number of previous experiments and numerical experiments. Our results suggest the entropic index κ as a measure for deviation from the state of chaos. We also introduce a κ-deformed Porter-Thomas distribution of transition intensities, which fits the experimental data for mixed systems better than the commonly-used gamma-distribution.

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Statistics of 2+ levels in even–even nuclei

Cited by 37 publications

References 36 publications

Chaos and Regularity in the Doubly Magic NucleusPb208

Chaos and Regularity in the Doubly Magic NucleusPb208

Pairing effect on spectral statistics of even and odd mass nuclei

Kappa-Deformed Random-Matrix Theory Based on Kaniadakis Statistics

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