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

TL;DR

This study investigates how chaos emerges in a classical nuclear billiard system by analyzing the transition from order to chaos through intermittency and various qualitative methods, focusing on different vibrational modes and their effects.

Contribution

It introduces a detailed qualitative analysis of chaos onset in a nuclear billiard model considering dissipation and vibrational multipolarities, highlighting intermittency near resonance.

Findings

Divergence of trajectories increases near resonance.

Intermittency observed in monopole oscillations.

Multiple qualitative measures confirm transition to chaos.

Abstract

We analyze on a simple classical billiard system the onset of chaotical behaviour in different dynamical states. A classical version of the "nuclear billiard" with a 2D deep Woods-Saxon potential is used. We take into account the coupling between the single-particle and the collective degrees of freedom in the presence of dissipation for several vibrational multipolarities. For the considered oscillation modes an increasing divergence of the nucleonic trajectories from the adiabatic to the resonance regime was observed. Also, a peculiar case of intermittency is reached in the vicinity of the resonance, for the monopole case. We examine the order-to-chaos transition by performing several types of qualitative analysis including sensitive dependence on the initial conditions, single-particle phase space maps, fractal dimensions of Poincare maps and autocorrelation functions.