Density dependence of isospin observables in spinodal decomposition

TL;DR

This paper models isotopic fluctuations during nuclear spinodal decomposition, linking the isotopic content of emerging clusters to the symmetry energy and density, providing insights into the early stages of nuclear fragmentation.

Contribution

It introduces a quasi-analytical approach to study density-dependent isotopic fluctuations in spinodal decomposition, connecting cluster properties to the symmetry energy.

Findings

Average charge asymmetry decreases with density.

Width of isotopic distributions narrows as density increases.

Results pertain to early system break-up stages.

Abstract

Isotopic fluctuations in fragment formation are investigated in a quasi-analytical description of the spinodal decomposition scenario. By exploiting the fluctuation-dissipation relations the covariance matrix of density fluctuations is derived as a function of the wave vector for nuclear matter at given values of density, charge asymmetry, temperature, and of the time that the system spends in the instability region. Then density fluctuations in ordinary space are implemented with a Fourier transform performed in a finite cubic lattice. Inside this box, domains with different density coexist, from which clusters of nucleons eventually emerge. Within our approach, the isotopic distributions are determined by the N/Z ratio of the leading unstable isoscalarlike mode and by isovectorlike fluctuations present in the matter undergoing the spinodal decomposition. Hence the average value of the N/Z ratio of clusters and the width of the relative distribution reflect the properties of the symmetry energy. Generating a large number of events, these calculations allow a careful investigation of the cluster isotopic content as a function of the cluster density. A uniform decrease of the average charge asymmetry and of the width of the isotopic distributions with increasing density is observed. Finally we remark that the results essentially refer to the early break--up of the system.