Power spectrum of nuclear spectra with missing levels and mixed symmetries

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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 delta(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.
© 2006 Elsevier B.V. All rights reserved. R.A.M. would like to thank E. Grosse, A.Wagner and G. Rusev of the Fz. Rossendorf for suggesting this work. A.R. is supported by the Spanish “Juan de la Cierva” program. This work is supported in part by Spanish Government grants BFM2003-04147-C02 and FTN2003-08337-C04-04.
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