Z. Phys. A 356, 113-118 ~1996) ZEITSCHRIFT FOR PI-h'SIK A (~) Springer-Verlag 1996 Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei V. Lopac I, S. Brant 2, V. Paar 2 i Facultyof Chemical Engineering and Technology,Department of Physics, University of Zagreb, Croatia 2 Facultyof Sciences, Department of Physics, Universityof Zagreb, Croatia Received: 23 March 1996 Communicated by X. Campi Abstract. Statistical properties of the realistic energy spec- tra of the odd-odd nuclei J°6Ag, 198Au, 134Cs, 4°K and 94Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of the A 3 statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the tran- sitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics. PACS: 5.45.+b; 21.60.Fw; 21.10.Ma 1 Introduction Level density fluctuations in a quantum-mechanical energy spectrum contain important information on the quantal sys- tem itself and on its classical counterpart. Introduced first as a means to decipher complex features of nuclear and atomic spectra [1], investigations of level density fluctuations have been extended to a large class of quantum-mechanical sys- tems, especially after they have been recognized as a possi- ble signature of quantum chaos [2-6]. At present, the investigations of the level density fluctua- tions are concentrated around three leading subjects: theories of random matrices [7-11], investigations of low- dimen- sional model systems such as billiards or driven oscillators [ 12-16], and the energy spectra of realistic systems - atoms, molecules and nuclei - obtained from experiments or in the realistic model calculations [17-23]. Authors investigating typical low-dimensional model quantal systems with classical counterparts consider that there are three universality classes of spectral fluctuations: Poisson statistics in the classically integrable cases, Wigner (GOE) statistics of the Random Matrix Theory, and the in- termediate statistics typical for the KAM-generic systems with mixed chaotic and regular dynamics [12, 24]. In these investigations great care is taken of the quantitative and pre- cise characterization of the degree of chaos [12, 25], and their results had influenced remarkably the investigations of the realistic physical systems. In accordance with the seminal work of Percival [26], Berry and Tabor[27] and Bohigas, Giannoni and Schmit [28], it has been largely accepted that the Wigner(GOE) distri- bution of the energy level spacings is typical for quantum systems whose classical counterparts are chaotic, whereas the Poisson distribution describes the level fluctuations of systems which are classically integrable. However, results questioning the universality of this conjecture have also been reported [29-31]. The importance of symmetry for su- pressing chaos has been pointed out [6,32-37]. It has been suggested that the integrability in the quantum-mechanical sense, where it is defined with the help of the symmetry concept, may not mean the integrability (regularity) for the classical system [38]. Therefore we use the notion of reg- ularity and chaos as conjectured by Bohigas, Giannoni and Schmit [28], but have in mind that this issue has still not been completely cleared. Great attention has been paid to the statistics which is intermediate between the Wigner(GOE) and Poisson limits. The typical Hamiltonian responsible for the transitional be- havior is of the form H = Ho + AV (1) where by increasing A one obtains the transition from regular to chaotic behavior. In this paper we investigate statistical properties of the energy spectra of several odd-odd nuclei, calculated within the Interacting Boson Fermion Fermion Model. In Sect. 2 we briefly review the properties and implications of the nuclear model and explain their relevance for the statistical spectral analysis. In Sect. 3 we discuss statistical methods used in the analysis and propose the new level spacing distribution function P(s). Section 4 presents the calculations and dis- cussion of the results, whereas the conclusions are briefly stated in Sect. 5. 2 Properties of the nuclear model The Interacting Boson Fermion Fermion Model (IBFFM) [39, 40] incorporates three important dynamical concepts: