Systematic analysis on spectral statistics of odd-A nuclei

Majarshin, A. Jalili; Pan, Feng; Sabri, H.; Draayer, J. P.

doi:10.1016/j.aop.2019.05.002

Cited by 12 publications

(16 citation statements)

References 43 publications

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“…Depending on the details of the chaoticity, some simple distributions have been proposed for describing the spectral statistics of nuclei [72][73][74][75][76][77][78] with less fitting parameters. For example, in what follows we use the socalled Berry-Robnik Distribution (BRD), which interpolates between Poisson statistics with q=1 and GOE with q=0, respectively.…”

Section: B Spectral Statistics Of Dipole Resonancesmentioning

confidence: 99%

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Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

et al. 2021

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In this paper, we report on a study of the spectral features associated with dipole resonances in medium mass nuclei (E ≤ 12 MeV), as revealed in the framework of the spd -interacting boson model. The effect of pairing correlations on the theory follows from solutions obtained through an application of the Bethe Ansatz Equation. In general, calculated spectra around the critical point of the vibrational to γ-soft transitions appears to approach that of a Gaussian Orthogonal Ensemble, while near the rotational and vibrational limits of the theory the spectra show more regular behavior. Specifically, the results reveal that the statistical features of the spectra are sensitive to the vector boson pairing strength, cp, in the transition region; that is, when cp is zero, or when the system approaches one of its dynamical symmetries limits the spectrum display regular features, while for stronger cp values, or when near to the critical phase transition region, the spectral feature show more chaotic behavior. Overall, our results indicate that the statistical features are governed by the interplay between dipole resonant energies, pairing correlations, and interactions between and among the single and vector bosons modes of the theory. As part of this work we also found out that chaoticity occurs when results were fit to a Berry-Robnik distribution. Throughout our analyses, we used experimentally known information about both positive and negative parity states. Our findings suggest that dipole resonances appear to be best-described by Poisson statistics for A ≈ 32-138 nuclei.

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Section: B Spectral Statistics Of Dipole Resonancesmentioning

confidence: 99%

“…In the transition from one limit to another limit for the spd -IBA, values of the chaoticity range between 0 and 1 with intermediate statistics showing more or less regular behavior as one departs from the two limits. Specifically, In what follows, our use of BRD is defined as advance in [73,79]…”

Section: B Spectral Statistics Of Dipole Resonancesmentioning

confidence: 99%

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

et al. 2021

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“…, for the chaotic system, and as well an unfolding procedure to calculate the spectral statistics [18][19][20]. In Cd isotopes, the lengths of J π sequences are short, and therefore a much better measure is to use the ratio of consecutive spacings of adjacent energy levels, and recognize that there will be uncertainties associated with the unfolding.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…In particular, to gain spectral convergence, as many as eight valence ph-excitations may be required. For a more complete discussion of these matters see: [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Random Matrix Theory in Cd isotopes

Majarshin¹,

Luo²,

Pan³

et al. 2021

J. Phys. G: Nucl. Part. Phys.

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Random matrix theory (RMT) is used to provide a measure of the chaoticity (q) of calculated results for the spectra for various Cd isotopes. The goal is to gain a better understanding of the internal dynamics in play; namely, whether it tracks with regular or irregular (chaotic) behavior as determined through an RMT analyses of calculated spectra. The basis-state configurations used to determine the spectra includes all positive, negative, natural (J π = 1 − , 2 + , . . .), and unnatural parity configurations (J π = 0 − , 1 + , 2 − , . . .), unless suppressed for comparative purposes. The results show that when intruder-state configurations are in play, regular behavior emerges, but when not in play, chaotic behavior seems to dominate the dynamics.

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“…Different nuclei's statistical properties have been studied in another type of literature and get some obvious dependence of chaotic properties to nuclear structure properties such as mass, spin, and dynamical symmetries 21 – 30 . Rotational bands are not the subject of individual consideration, and we can suggest some references, such as 27 – 36 , which compare the spectral statistics of such states versus deformed ones. On the other hand, Guhr et al have stated in their paper 37 , that degeneracy makes irregular statistics in the energy spectra of atomic nuclei.…”

Section: Introductionmentioning

confidence: 99%

Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

Sabri

Mobarakeh

Majarshin

et al. 2021

Sci Rep

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Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $$R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$$ R 4 1 + / 2 1 + ≥ 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $$2_{\gamma }^{ + }$$ 2 γ + band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

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Systematic analysis on spectral statistics of odd-A nuclei

Cited by 12 publications

References 43 publications

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

Properties of giant dipole resonances within an extended pairing model with a focus on spectral statistics

Random Matrix Theory in Cd isotopes

Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

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