Quantum chaos in the two-center shell model

Milek, B.; Nörenberg, W.; Rozmej, P.

doi:10.1007/bf01284549

Cited by 9 publications

(19 citation statements)

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“…The important role of the type of avoided level crossings for order-to-chaos transitions was demonstrated. It follows from the results of the papers [7,8] that chaotic dynamics in a large fraction of the phase space can be expected only for very large deformations. Such deformations of the mean field take place in large amplitude nuclear motion, for example in fission events or in heavyion collisions where the neck degree of freedom plays an important role.…”

Section: Introductionmentioning

confidence: 89%

“…Could it be that the results are an artifact of the numerical calculations and that the classical dynamics is fully regular, independently of the LSD? In order to answer these questions we perform in the following an analysis of the classical phase space for parameter values (A = 260, R = 10 fro, c~ = 1.3 and e = 0.6; no deformation of the fragments) where signatures of quantum chaos were found in [8].…”

Section: Two-center Oscillator Shell Modelmentioning

confidence: 99%

“…Locally averaged level-spacing distributions for this potential were calculated in [8] for a large parameter region varying R, e and e. In very heavy nuclear systems with mass numbers between 260 and 400 nearly ideal Wigner distributions for the LSD were found. This feature is correlated with a strong interaction of adiabatic levels of the same symmetry.…”

Section: Two-center Oscillator Shell Modelmentioning

confidence: 99%

“…In order to estimate the statistical error in the calculations, we have taken into account (i) level sets with positive and/or negative parity, (ii) level sets with/without the real parts of low lying resonances. As usual [8,18], the statistics was improved by overlaying different LSD for slightly different deformation parameters around the main one. The energy dependence of the level density was corrected by introducing bins of size of 15 MeV.…”

Section: P(s) = Exp ( -S) (212)mentioning

confidence: 99%

“…The detailed structure of the phase space depends sensitively on the deformation parameter as well as on the kinematical quantities, the binding energy and the component of the orbital angular momentum along the symmetry axis. In another paper [8] the quantum aspect of the question under consideration was studied for the two-center oscillator potential including spin-orbit forces and a neck degree of freedom. A clear occurrence of a nearly ideal Wigner distribution was found for the single-particle LSD.…”

Section: Introductionmentioning

confidence: 99%

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Classical versus quantum chaos in strongly deformed nuclear potentials

Milek

Reif²

1991

Z. Physik A - Hadrons and Nuclei

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The correspondence of classical dynamical chaos and statistical properties of the energy spectrum has been investigated for the single-particle motion in strongly deformed nuclear potentials with axial symmetry. The properties of the classical and of the quantized system were analyzed for two potentials: the two-center well potential of finite depth and the two-center oscillator shell model. It has been found that in such mean fields the occurrence of fully developed random matrix statistics is a generic feature corresponding to a global instability of classical trajectories. But due to the absence of scaling invariance, for the general case with a mixed phase space a significant energy dependence of the chaotic phase-space volume has been obtained so that the over-all level-spacing distribution cannot be specified by the chaotic volume as a single parameter. The reason for the appearance ofchaoticity turns out to be rather complex. Besides the expected important role of large deformations of high multipolarity, including the neck degree of freedom, the spin-orbit part of the nuclear interaction can also be responsible for the occurrence of dynamical chaos.

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Section: Introductionmentioning

confidence: 89%

Section: Two-center Oscillator Shell Modelmentioning

confidence: 99%

Section: Two-center Oscillator Shell Modelmentioning

confidence: 99%

Section: P(s) = Exp ( -S) (212)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Classical versus quantum chaos in strongly deformed nuclear potentials

Milek

Reif²

1991

Z. Physik A - Hadrons and Nuclei

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Level density fluctuations in the generalized interacting boson model

Lopac

Paar

1992

Z. Physik A - Hadrons and Nuclei

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Abstract. Level density fluctuations are calculated within the generalized interacting boson model proposed for even-even nuclei, in dependence on the truncation parameter ~c. For the case z=2 corresponding to the SU(3) dynamical symmetry of the interacting boson model the fluctuation pattern is close to Poissonian. For cases z r 2, including the anharmonic vibrator model for which z = oo, a rapid transition to the fluctuation pattern close to GOE is obtained. PACS: 24.60.Ky; 21.60.Ev; 21.60.Fw Fluctuations of the energy level density in quantum systems have received much attention in recent years [1][2][3]. This interest is mostly due to the conjecture expressed by Bohigas et al. [4] stating that the distribution of the level spacings within the quantum energy spectrum reflects the nature of the corresponding classical system. According to this conjecture, the systems exhibiting the regular behaviour in the classical limit, have the Poissonian distribution of the quantum energy levels, and the quantum systems whose classical counterparts behave chaotically conform to the Gaussian orthogonal ensemble (GOE, Wigner) type of the level spacing distribution.A number of recent investigations made it clear that there are many quantum systems which belong to the intermediate class, exhibiting a pattern lying between the two limits [3,5,6]. The importance of an interaction parameter controlling the transition between Poisson and GOE limits has been stressed in different contexts [7,8]. It has also been emphasized that the absence of the coupling results in a high degree of degeneracy and leads to a pattern exceeding the values of the Poisson limit [9,10].All of the mentioned features are typical also for the nuclear spectra [11]. The transition from regularity to chaos -in the sense of the conjecture of Bohigas et al. -has been clearly identified both in the experimental level spacings [12][13][14][15][16] and in the model calculations for the realistic nuclei [17][18][19][20][21][22][23][24][25][26][27]. It can be summarized in the statement that the realistic nuclear spectra are intermediate between Poisson and GOE type of fluctuations, showing the tendency to be closer to the GOE limit. The role of collectivity in this tendency is currently being investigated.In the present paper we investigate the level density fluctuations of spectra for even-even nuclear systems described by the generalized interacting boson model (generalized truncated quadrupole-boson model), which will be referred to as the GTQM model. The GTQM Hamiltonian in the quadrupole boson representation reads , h4L[(b + b2+)L(s163 9 L=0,2,4 (1)Here, b+u and b2u denote the creation and annihilation operators, respectively, of the quadrupole bosons, Ho=hlN. These can be denoted as INvI) where N is the quadrupole boson number, I stands for the angular momentum and v is an additional quantum number necessary in some cases to distinguish between the states of the same/. We consider the truncation function operator f (N) defined as

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