Relativistic description of regular and chaotic dynamics in the giant monopole resonances G.A. Lalazissis a, * , D. Vretenar b,c , N. Paar b , P. Ring b a Department of Theoretical Physics, Aristotle University of Thessaloniki, Thessaloniki GR 54006, Greece b Physik-Department der Technischen Universit€ atM€ unchen, D-85748 Garching, Germany c Department of Physics, Faculty of Science, University of Zagreb, 10000 Croatia Abstract Nonlinear dynamical properties of giant monopole resonances in atomic nuclei are investigated within the time- dependent relativistic mean-field model. The time-series analysis and reconstruction of the phase space display two types of collective vibrations: regular motion for the isoscalar oscillations, and chaotic dynamics for the isovector mode. Information entropy functionals disclose the underlying nonlinear dynamics in quantum systems that have spatial as well as temporal structure. Ó 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction Atomic nucleus represents a challenging quantum system for investigating nonlinear dynamical properties of many body system, and transitions from order to chaos. The studies of giant resonances are of particular interest, where large number of nucleons contributes to a collective oscillation. Their total strengths and widths are larger than the reso- nances generated by simple noncollective single-particle excitations. Different types of giant resonances are found all over the periodic table, and their excitation energies are smooth functions of nucleon mass number A [4–6]. Regular and chaotic dynamics of giant resonances has been investigated in many advanced theoretical and experimental studies in order to relate the nonlinear collective nuclear dynamics with single-particle motion [1–3,11]. Collective modes may coexist with chaotic single-particle motion, because the vibrating self-consistent mean field created by the same nu- cleons, averages out the random components of their motion. In the present study, the dynamics of isoscalar and isovector monopole collective modes is investigated, with protons and neutrons oscillating without changing its spherical shape. The nuclear dynamics is described in the framework of the time-dependent relativistic mean-field theory (TDRMFT). For an initial monopole deformation, time-dependent self-consistent calculations are performed in order to describe the collective dynamics of the giant monopole resonance. Since the time-evolution is evaluated in a self-consistent way, the system is nonlinear, therefore, chaotic regime of motion is to be expected for certain sets of mean-field and initial conditions. However, the frequencies of eigenmodes should be consistent with the available experimental data on monopole resonances. 2. Time-dependent relativistic mean-field model The relativistic mean-field model based on quantum hadrodynamics has been already successfully applied to de- scribe the properties of ground and excited states in spherical and deformed nuclei [1,4–6]. The TDRMFT has been * Corresponding author. 0960-0779/03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0960-0779(02)00401-0 Chaos, Solitons and Fractals 17 (2003) 585–590 www.elsevier.com/locate/chaos