Density dependence of isospin observables in spinodal decomposition

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.Comment: Revtex4, 19 pages, 8 eps figures, to be published in Phys. Rev.

Nuclear Matter and Nuclear Dynamics

“…One can see that, both the average N/Z and the isovector variance decrease as the density increases, leading to a more symmetric and less fluctuating liquid phase. However, fluctuations are rather large in the Asysoft case (circles and triangles) [31].…”

“…Left Panel: Correlation between the N/Z and the density of the domains, obtained with the two asy-EOS in the decomposition of unstable nuclear matter, with asymmetry β = 0.1 (squares and circles) and β = 0.2 (triangles and stars). Right: Variance of the (N-Z) content of the density domains as a function of their volume[31].…”

Fluctuations and Symmetry Energy in Nuclear Fragmentation Dynamics

“…3). More precisely, the quantities ÁðZ=AÞ 2 and ÁðN=AÞ 2 go approximately as 0 @C sym @ j ¼ 0 [31], counterbalancing the density dependence of F v eff . In the case of a linear behavior of F v eff , i.e., close to the conditions of our stiff case, the isoscaling parameters, Eq.…”

“…Indeed, isovectorlike oscillations are characterized by a much shorter time scale, with respect to the growth of the unstable modes [31]. Thus, important coupling effects between isoscalar and isovector oscillations are emerging from the solution of the full nonlinear equations (1).…”