Intermittency route to chaos for the nuclear billiard - a quantitative study

TL;DR

This study quantitatively analyzes the intermittency and chaos in a classical nuclear billiard system, revealing how vibrational modes and coupling influence the transition to chaos.

Contribution

It extends previous qualitative work by providing detailed quantitative analyses, including power spectra, entropies, and Lyapunov exponents, to better understand chaos in nuclear billiards.

Findings

Chaos increases with oscillation frequency shift from adiabatic to resonance.

Intermittency pattern observed in monopole deformation case.

Coupling between nucleonic and collective degrees of freedom is crucial for chaos.

Abstract

We extended a previous qualitative study of the intermittent behaviour of a chaotical nucleonic system, by adding a few quantitative analyses: of the configuration and kinetic energy spaces, power spectra, Shannon entropies, and Lyapunov exponents. The system is regarded as a classical "nuclear billiard" with an oscillating surface of a 2D Woods-Saxon potential well. For the monopole and dipole vibrational modes we bring new arguments in favour of the idea that the degree of chaoticity increases when shifting the oscillation frequency from the adiabatic to the resonance stage of the interaction. The order-chaos-order-chaos sequence is also thoroughly investigated and we find that, for the monopole deformation case, an intermittency pattern is again found. Moreover, coupling between one-nucleon and collective degrees of freedom is proved to be essential in obtaining chaotic states.