Fluctuation properties of spacings of low-lying nuclear levels

Shriner, J. F.; Mitchell, G. E.; Egidy, T. von

doi:10.1007/bf01288195

Cited by 90 publications

(132 citation statements)

References 79 publications

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“…Thus the similarities with GOE are certainly limited. The result ω = 0.68 ± 0.02 is similar to the value ω = 0.72 ± 0.16 for nuclei with A < 50 [10]. Therefore we may wonder whether it represents more or less a practical limit of possible chaos in nuclear bound states.…”

Section: B Short-range Level Fluctuations In 208 Pbsupporting

confidence: 62%

“…This step, called unfolding, is delicate and of utmost importance, because some of the unfolding procedures used in the literature can lead to completely wrong results on the behavior of level fluctuations [11]. In this work we have used the constant temperature formula [10],…”

Section: B Short-range Level Fluctuations In 208 Pbmentioning

confidence: 99%

“…But to improve statistics, level spacings from different nuclei can be combined into a single set to analyze the behavior of the NNS distribution P (s). An extensive analysis of low-lying energy levels was performed by Shriner et al [10] using experimental data along the whole nuclear chart. A total of 988 spacings from 60 different nuclei were included in the analysis.…”

Section: A Spectral Fluctuations In Experimental Nuclear Bound Statesmentioning

confidence: 99%

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Examination of experimental evidence of chaos in the bound states of Pb208

et al. 2017

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We study the spectral fluctuations of the 208 Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of 6.20 MeV recently identified at the Maier-Leibnitz Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of random matrix theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter ω, which takes the value ω = 0 for regular systems and ω 1 for chaotic systems. We obtain ω = 0.85 which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in 208 Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition, our results show that chaotic and nonchaotic nuclear states coexist in the same energy region of the spectrum.

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Section: B Short-range Level Fluctuations In 208 Pbsupporting

confidence: 62%

Section: B Short-range Level Fluctuations In 208 Pbmentioning

confidence: 99%

Section: A Spectral Fluctuations In Experimental Nuclear Bound Statesmentioning

confidence: 99%

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Examination of experimental evidence of chaos in the bound states of Pb208

et al. 2017

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“…However, in the region closer to the ground state the situation is still unclear because of the experimental difficulty in obtaining complete sequences of levels. Even if data coming from different nuclei are properly studied, the results are less than conclusive [3][4][5]. More work is needed to completely understand the statistical properties of low-energy nuclear spectra.…”

Section: Introductionmentioning

confidence: 99%

Power spectrum of nuclear spectra with missing levels and mixed symmetries

et al. 2007

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Sequences of energy levels in nuclei are often plagued with missing levels whose number and position are unknown. It is also quite usual that all the quantum numbers of certain levels cannot be experimentally determined, and thus levels of different symmetries are mixed in the same sequence. The analysis of these imperfect spectra (from the point of view of spectral statistics) is unavoidable if one wants to extract some statistical information. The power spectrum of the δ q statistic has emerged in recent years as an important tool for the study of quantum chaos and spectral statistics. We derive analytical expressions for the observed power spectrum in terms of the fraction of observed levels and the number of mixed sequences. These expressions are tested with large shell model spectra simulating realistic experimental situations. A good estimation of the number of mixed symmetries and the fraction of missing levels is obtained by means of a least-squares fit in a wide set of different situations.

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“…Instead, a statistical description, called Statistical Nuclear Spectroscopy (SNS), is used, based on the division into global and local nuclear properties [9][10][11][12][13][14][15][16][17]. A typical example of this is the separation of the level density into a global component, the secular variation, and a local component, the fluctuations, which are well described by the random matrix ensembles [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%