The order to chaos transition in axially symmetric nuclear shapes

Błocki, J.; Brut, F.; Srokowski, T.; Świa̧tecki, W.J.

doi:10.1016/0375-9474(92)90489-7

Cited by 40 publications

(31 citation statements)

References 15 publications

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“…There we display the final radial coordinate at a time t of one chosen particle vs. the one at t = 0 for three cases: a) the wall is not coupled to the particles' motion and always oscillates at the same frequency [2] thus giving energy to the gas, b) coupling is taken into account and the Hamilton's equations (2-4) are solved respectively for b) one particle and c) ten particles. The idea these plots are based on is the following : if the dynamics is regular, two initially close points in space stay close even at later times, but if the dynamics is chaotic the two points will soon separate due to the exponential divergence induced by chaos.…”

Section: T Mrmentioning

confidence: 99%

Chaoticity in vibrating nuclear billiards

et al. 1995

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We study the motion of classical particles confined in a two-dimensional "nuclear" billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle Hamiltonian between the particle motion and the collective coordinate generates a fully selfconsistent dynamics. We consider in particular monopole oscillations and demonstrate that self-consistency is essential in order to induce chaotic single-particle motion. We also discuss the dissipative behaviour of the wall motion and its relation with the order-to-chaos transition in the dynamics of the microscopic degrees of freedom. Analogous considerations can be extended to higher multipolarities.

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Section: T Mrmentioning

confidence: 99%

Chaoticity in vibrating nuclear billiards

et al. 1995

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“…In a classical picture, this will be given as the average fraction of the nucleon trajectories within the nucleus which are chaotic when the sampling is done uniformly over the nuclear surface. The value of the chaoticity for a given nuclear shape is evaluated by sampling over a large number of classical nucleon trajectories while each trajectory is identified either as a regular or as a chaotic one by considering the magnitude of its Lyapunov exponent and the nature of its variation with time [14]. The shape-dependence of the chaoticity, thus obtained, is shown in fig.1.…”

Section: Nuclear Dissipationmentioning

confidence: 99%

“…The prescission particle multiplicity and fission probability will be obtained by sampling over a large number of Langevin trajectories. The chaos-weighted wall friction coefficient is obtained following a specific procedure [14] which explicitly considers particle dynamics in phase space in order to calculate the chaoticity factor µ of eq.(1). There is no free parameter in this calculation of friction.…”

Section: Introductionmentioning

confidence: 99%

Evaporation residue cross-sections as a probe for nuclear dissipation in the fission channel of a hot rotating nucleus

Chaudhuri

Pal

2003

Eur. Phys. J. A

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Evaporation residue cross-sections are calculated in a dynamical description of nuclear fission in the framework of the Langevin equation coupled with statistical evaporation of light particles. A theoretical model of one-body nuclear friction which was developed earlier, namely the chaosweighted wall formula, is used in this calculation for the 224 Th nucleus. The evaporation residue cross-section is found to be very sensitive to the choice of nuclear friction. The present results indicate that the chaotic nature of the single-particle dynamics within the nuclear volume may provide an explanation for the strong shape-dependence of nuclear friction which is usually required to fit experimental data.

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“…In applying this model to studying mass-energy distributions of fragments of compound nuclei, we decided to use, in addition to constant values of k s = 0.25 and 1.0, the the elongation-dependent reduction factor for the contribution from the wall formula, ks = µ(q 1 ), where, we recall, q 1 is the elongation parameter, which is the main fission coordinate. In order to calculate this dependence, we follow [17][18][19], relying on the idea that the reduction factor for the contribution from the wall formula is intimately related to the measure of chaoticity of nucleons motion within a nucleus as this nucleus evolves from the ground state to separated shapes [17,18]. The explicit form of the function µ(q 1 ) was taken from [19].…”

Section: Introductionmentioning

confidence: 99%

Mass-energy distribution of fragments in Langevin dynamics of fission induced by heavy ions

Anischenko

Vanin

Адеев

2012

EPJ Web of Conferences

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Abstract. Four-dimensional Langevin equation was employed to calculate mass-energy distributions of fission fragments of highly excited compound nuclei. The research took into account not only three shape collective coordinates introduced on the basis of {c, h, α}-parametrization but also orientation degree of freedom (K-state) -spin about the symmetry axis. Overdamped Langevin equation was used to describe the evolution of the K-state. Friction tensor was calculated using the "wall+window" model of the modified one-body dissipation mechanism with a reduction coefficient from the "wall" formula k s . The calculations have been performed with k s = 0.25 and k s = 1.0. To learn more about the role of the dissipation effects the calculations have also been done with use of the chaoticity measure of nucleon movements in the nuclear shape configuration as k s parameter. Calculations were performed for the large number of compound nuclei with Z 2 /A parameter in the range 21 Z 2 /A 44. The goal was to study the mass-energy distributions not only for heavy nuclei but also for light nuclei close to the Businaro-Gallone point. Mass-energy distributions and variances of the mass fragments are well reproduced in the applied calculations for all considered compound nuclei. It was shown that inclusion of the K-state in the dynamical model produces considerable increase of the mass and energy variances. Inclusion of the chaoticity measure to the friction tensor provides a better agreement with the experiment results on mass variances.

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The order to chaos transition in axially symmetric nuclear shapes

Cited by 40 publications

References 15 publications

Chaoticity in vibrating nuclear billiards

Chaoticity in vibrating nuclear billiards

Evaporation residue cross-sections as a probe for nuclear dissipation in the fission channel of a hot rotating nucleus

Mass-energy distribution of fragments in Langevin dynamics of fission induced by heavy ions

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