Nuclear level repulsion and order vs. chaos

Garrett, J.D.; Robinson, J.Q.; Foglia, A.J.; Jin, H. Q.

doi:10.1016/s0370-2693(96)01528-6

Cited by 41 publications

(32 citation statements)

References 12 publications

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“…That of 116 Sn has been termed "nearly complete" by the authors of Ref. [41,42]. Furthermore, the analysis of the spectral properties of experimentally determined bound states of nuclei did not yield the results expected in nuclear many-body systems exhibiting a chaotic dynamics.…”

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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

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“…In the rare cases when nearly complete spectroscopic information exists for some nuclei [20][21][22], one can see onset of spectral chaos at excitation energy about 4 MeV for even-even nuclei and even lower for odd-A and odd-odd nuclei. Because of strong pairing correlations, the level density in even-even nuclei is reduced below pair breaking threshold; energy of 3-4 MeV is needed to break two pairs; the interaction of four unpaired nucleons is already sufficiently strong to build a chaotic spectrum.…”

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confidence: 99%

Chaos, spins and symmetries in nuclear structure

Zelevinsky

2002

Czech J Phys

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A pedagogic introduction to recent developments in "many-body quantum chaos", complicated dynamics at high level density in a finite quantum system with strong interaction between constituents, is given. Topics relating chaotic dynamics to the concept of symmetry are discussed: spectral statistics, extreme sensitivity to perturbations violating the symmetry, correlations between the states of different symmetry, and many examples of applications to nuclear structure. One of manifestations is the strikin~ predominance of ground states with zero spin in a system with arbitrary but rotationally invariant two-body interactions.1 Many-body quantum chaos 1.1 Does quantum chaos exist?The expression "quantum chaos" is controversial. The routine viewpoint [1] is that one' can speak only on "quantum signatures of classical chaos", and quantum chaos does not exist. Let us first try to understand what is the real meaning of such statements.Classical chaos is nowadays a well studied phenomenon that has found its way to the modern textbooks [2]. Moreover, the standard stuff of books in classical mechanics (two-body problem, small amplitude oscillations, rigid body rotation and so on) seems to cover only very exceptional cases of regular (integrable) motion. The majority of realistic problems, starting with the classical three-body problem, include domains of chaotic motion. There are different degrees of chaoticity [3], but for our purpose it is sufficient to characterize typ!cal features of classical chaotic dynamics in very general terms.The symmetry arguments play a key role in all considerations of chaos. Usually the idea of chaotic motion implies that all symmetries of the problem are destroyed. The simplest example can be that of a billiard, a two-dimensional area where a particle moves freely being elastically reflected from the boundaries. In a billiard of good symmetry, as round or rectangular, motion is integrable; it is characterized, apart from energy, by an additional integral of motion, angular momentum or linear momentum of the unfolded trajectory (Fig. 1), respectively. In coordinate space one trajectory can cover uniformly the entire available area; but in momentum space we keep the fixed constant of motion. In a billiard of arbitrary shape, such conservation laws are destroyed. In fact it suffices to match rectilinear and round pieces of the boundary (a stadium billiard, Fig. 2) in order to come to chaotic motion. Now a single trajectory covers an area in phase space.

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“…It has been realized that the nuclear dynamics interpolates between the Poisson (integrable) and Wigner (chaotic) distributions. The analysis of spectra of nuclei in the ground-state domain shows intermediate behavior [7][8][9][10][11][12][13][14][15][16][17].Parameterizing isotopes of the nuclear chart according to their collective behavior in a single control parameter is an interesting field of research. Many parameters are introduced to take such a role, for example, the number of protons Z, number of neutrons N , mass number A, quadrupole deformation parameter β 2 , R 4/2 ratio, and P factor.…”

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Autocorrelation studies for the first 2+nuclear energy levels

Alsayed

2012

Phys. Rev. C

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The autocorrelation function, and the correlation time are calculated for a series of the first 2 + states of 466 even-even nuclei classified by different parameters related to nuclear structure. The results indicate enhanced values for the P factor compared with other classifying parameters to cumulate nuclei having similar properties nearby each other.Introduction. The introduction of random matrix theory (RMT) to describe the fluctuation properties of nuclear energy states has gained a considerable interest with many physicists [1,2]. Bohigas et al. [3] conjectured that RMT could be used to model the fluctuation properties of quantum systems which are fully chaotic in the classical limit. RMT provides analytical results for the spacing distributions, the level number variance, and the spectral rigidity of quantum systems. Comparing these expressions with the corresponding experimental results has been used as a signature of chaotic dynamics [4][5][6]. It has been realized that the nuclear dynamics interpolates between the Poisson (integrable) and Wigner (chaotic) distributions. The analysis of spectra of nuclei in the ground-state domain shows intermediate behavior [7][8][9][10][11][12][13][14][15][16][17].Parameterizing isotopes of the nuclear chart according to their collective behavior in a single control parameter is an interesting field of research. Many parameters are introduced to take such a role, for example, the number of protons Z, number of neutrons N , mass number A, quadrupole deformation parameter β 2 , R 4/2 ratio, and P factor.The aim of the present work is to answer the following question: which of the previously mentioned parameters can be used to describe the collective behavior of nuclei best? In other words, we search for the parameter that is capable of arranging nuclei of similar collective behavior nearby each other.In order to achieve this aim, we select even-even nuclei for their abundance and simplicity to be described by nuclear models. For each nucleus the first 2 + energy state is takenmost even-even nuclei have 2 + levels as the first excited state. In this way, we collect a series of 466 even-even nuclei ranging between 10 A 256, are taken from National Nuclear Data Center [18] up to August 2010.It is well known that-neglecting the shell closure effectlight nuclei having higher excitation energies of the first 2 + levels on the order of a few MeV. On the other hand, as the mass number A increases, the 2 + excitation energies decrease to be on the order of several tenths of a KeV. Consequently, in general the first 2 + level energy of each nucleus can be used as an indicator of collective behavior.A recent approach proposed by Relaño et al. [19] considers the spectrum of any quantum system as a set of discrete eigenvalues placed along the real energy axis. This set is ordered as any sequence of events occurring at different

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Nuclear level repulsion and order vs. chaos

Cited by 41 publications

References 12 publications

Chaos and Regularity in the Doubly Magic NucleusPb208

Chaos and Regularity in the Doubly Magic NucleusPb208

Chaos, spins and symmetries in nuclear structure

Autocorrelation studies for the first 2+nuclear energy levels

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