Abstract

Perturbing fluids of neutrons and protons (nuclear matter) may lead, as the most catastrophic effect, to the rearrangement of the fluid into clusters of nucleons. A similar process may occur in a single atomic nucleus undergoing a violent perturbation, like in heavy-ion collisions tracked in particle accelerators at around 30 to 50 MeV per nucleon: in this conditions, after the initial collision shock, the nucleus expands and then clusterises into several smaller nuclear fragments.Microscopically, when violent perturbation are applied to nuclear matter, a process of clusterisation arises from the combination of several fluctuation modes of large-amplitude where neutrons and protons may oscillate in phase or out of phase. The imposed perturbation leads to conditions of instability, the wavelengths which are the most amplified have sizes comparable to small atomic nuclei. We found that these conditions, explored in heavy-ion collisions, correspond to the splitting of a nucleus into fragments ranging from Oxygen to Neon in a time interval shorter than one zeptosecond (10−21s). From the out-of-phase oscillations of neutrons and protons another property arises, the smaller fragments belonging to a more volatile phase get more neutron enriched: in the heavy-ion collision case this process, called distillation, reflects in the isotopic distributions of the fragments.The resulting dynamical description of heavy-ion collisions is an improvement with respect to more usual statistical approaches, based on the equilibrium assumption. It allows in fact to characterise also the very fast early stages of the collision process which are out of equilibrium. Such dynamical description is the core of the Boltzmann-Langevin One Body (BLOB) model, which in its latest development unifies in a common approach the description of fluctuations in nuclear matter, and a predictive description of the disintegration of nuclei into nuclear fragments. After a theoretical introduction, a few practical examples will be illustrated.This paper resumes the extended analysis of fluctuations in nuclear matter of ref. [2] and briefly reviews applications to heavy-ion collisions.

Highlights

  • The most catastrophic process which can occur in a nuclear complex is its splitting into clusters and fragments when undergoing a violent external action

  • We want to address this process, which can be probed in a dissipative heavy-ion collision, from the point of view of dynamics, moving from nuclear matter to nuclei, which are finite open self-bound systems

  • We constructed a microscopic dynamical framework from applying the theory of Fermi liquids to clusterisation in nuclei; within this framework, we explore how the clusterisation progresses from zero-sound propagation

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Summary

Introduction

The most catastrophic process which can occur in a nuclear complex is its splitting into clusters and fragments when undergoing a violent external action. The independent-particle scheme (i.e. mean field) is applied to nucleonic single-particle wavefunctions ψi, so that manybody correlations in both mean field and scattering can be achieved from the localisation of ψi (a coherent-state subspace is used in FMD [6] and an even stronger localisation is imposed in AMD [4, 5] by fixing the widths of ψi) Such treatment is successful for final-state correlations, but it may approximate collective behaviour and 0-sound propagation. We consider a second simplified approach to solve the BL equation, Eq (3), based on the SMF [14] treatment, where fluctuations are injected from an external stochastic contribution Uext and projected on spacial density In both cases, in all following calculations, a simplified SKM* effective interaction, with momentum dependence omitted, is used [15, 16]. Before carrying on a study on heavy-ion collisions, we require that fluctuation amplitudes are consistent with analytic expectations from Fermi liquids: for this purpose, we study nuclear matter in initially homogeneous conditions

Fluctuations in two-component nuclear matter
Relating isovector fluctuations to the symmetry energy
Relating zero-sound propagation to instability growth
Spinodal clusters from density ripples at Fermi energies
Conclusions
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