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Chaos and regularity in the excitation spectrum of the doubly magic nucleus 208Pb

Achim Richter

Jeudi 18 mai

à 11h, en salle C. BROT

High resolution experiments [1] have recently lead to a complete identification (energy, spin, and parity) of 151 nuclear levels up to an excitation energy of E_x = 6.20 MeV in 208Pb. Subsequently a thorough study of the fluctuation properties of the levels in the energy spectra of the unprecedented set of nuclear bound states has been made [2] and is reported upon. 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 -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 [3] 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.

[1] A. Heusler, R. V. Jolos, T. Faestermann, R. Hertenberger, H.-F. Wirth, P. von Brentano, Phys. Rev. C 93, 054321 (2016).

[2] B. Dietz, A. Heusler, K. H. Maier, A. Richer, B. A. Brown, Phys. Rev. Lett. 118, 012501 (2017).

[3] N. Rosenzweig and C. E. Porter, Phys. Rev. 120, 1698 (1960).

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centers 634 and 1245.