J. M. G. Gómez

Quantum chaos in A = 46–50 atomic nuclei

Abstract The spectral statistics of low-lying states of several fp shell nuclei are studied with realistic shell-model calculations. For Ca isotopes, we find significant deviations from the predictions of the random-matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.

Statistical theory versus shell model in a large pf configuration space

Spectral distribution method and exact shell-model predictions for the strength sums of different transition operators are compared in detail for the J=0, T−Tz=0 states of 46V and 50Sc using the full pf shell. Good agreement of both models is observed in the high level density region of the energy spectrum, where chaotic motion is dominant, and larger discrepancies are observed in the ground state region, where nuclear motion is more regular. The agreement in the chaotic region becomes especially good in the 5986 dimensional space of 50Sc, illustrating the quality of the statistical theory in large configuration spaces.

Examination of experimental evidence of chaos in the bound states of Pb 208

We study the spectral fluctuations of the Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of 6.20 MeV recently identified at the Maier-LeibnitzLaboratorium at Garching, Germany. For natural parity stat e the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbo r spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter ω, which takes the value ω = 0 for regular systems andω ≃ 1 for chaotic systems. We obtain ω = 0.85± 0.02 which is, to our knowledge, the closest value to chaos ever observed in experimental bound s tates of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We int rpret these results as a consequence of the strength of the residual interaction in Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In ad dition our results show that chaotic and non-chaotic nuclear states coexist in the same energy regio n of the spectrum.

Shell-Model studies of chaos and statistical properties in nuclei

Shell-model calculations with realistic empirical interactions constitute an excellent tool to study statistical properties of nuclei. Using large-scale shell-model calculations in pf- shell nuclei, we study how the onset of chaos depends on different properties of the nuclear interaction and on excitation energy. We make use of classical random matrix theory and other theoretical developments based on information theory and time series analysis. We show that besides energy-level statistics, other statistical properties like the complexity of wave functions are fundamental for a proper determination of the dynamical regime of nuclei. Important deviations from GOE are observed in level fluctuations and in the complexity of wave functions.

Recent results in quantum chaos and its applications to atomic nuclei

A survey of chaotic dynamics in atomic nuclei is presented, using on the one hand standard statistics of quantum chaos studies, and on the other a new approach based on time series analysis methods. The study of shell-model spectra in the pf shell shows that nuclear chaos is strongly isopin dependent and increases with excitation energy. On the other hand, it is found that chaotic quantum systems exhibit 1/f noise and regular systems exhibit 1/f2 behaviour. It is shown that the time series approach can be used to calculate quite accurately the fraction of missing levels and the existence of mixed symmetries in experimental level spectra.

Spectral distribution studies of fp shell nuclei with a modified Kuo-Brown interaction

The structure of nuclei in the lower half of the fp shell is investigated by the spectral distribution method using the modified Kuo-Brown interaction. This interaction recently showed success in reproducing observed properties through detailed shell model studies. Spectral distribution studies avoid explicit diagonalization and hold promise for applications to astrophysics. {copyright} {ital 1997} {ital The American Physical Society}

Chaos and 1/f noise in nuclear spectra

Many complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum S(f) which is a power function of the frequency f. Examples with this behavior are the Sun spot activity, the human heartbeat, the DNA sequence, or Bach’s First Brandenburg Concert. In this work, we show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series, with energy playing the role of time. Because of this analogy, the fluctuations of quantum energy spectra can be studied using traditional methods of time series, like calculating the Fourier transform and studying the power spectrum. We present the results for paradigmatic quantum chaotic systems like atomic nuclei (by means of large scale shell‐model calculations) and the predictions of random matrix theory. We have found a surprising general property of quantum systems: The energy spectra of chaotic quantum systems are characterized by 1/f noise, while regular quantum systems exhibit...

Spectral distribution studies with a modified Kuo-Brown interaction in the upper half of thefpshell

The spectral distribution method with modified Kuo-Brown interaction is extended to the study of the upper half as well as to odd-A nuclei, of the fp shell. The calculations show similar success to that obtained for the lower half.

Chaos in nuclei: Theory and experiment

During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.

Perspectives on 1/f noise in quantum chaos

The power spectrum of the ?n statistic of quantum spectra presents 1/f? noise. For chaotic systems ? = 1 while for regular systems ? = 2. Although the transition from regularity to chaos is non universal, for a wide variety of systems with a mixed phase space the value of ? is intermediate between 1 and 2 and can be related to the fraction of regular or chaotic orbits in the total phase space. This statistic can be a very useful tool for the analysis of experimental spectra, specially in the case of missing levels or spectral sequences with mixed symmetries.