Isoscaling properties for neutron-rich fragments in highly asymmetric heavy ion collision systems*

Abstract

Historically, isoscaling has often been understood and applied under the grand canonical ensemble, assuming that the fragments are produced after the statistical equilibrium state is achieved. However, the influence of the symmetry energy may lead to differences in the neutron and density distribution in neutron-rich nuclei, potentially impacting the isoscaling parameters (usually denoted by $\alpha$ and $\beta$. We study the isoscaling properties for neutron-rich fragments produced in very asymmetric systems on inverse kinematics, namely $^{40,48}$Ca and $^{58,64}$Ni + $^{9}$Be at 140 MeV per nucleon. We evaluate the $\alpha$ and $\beta$ value and sort them as a function of the neutron excess $I \equiv N-Z$. The significant differences in $\alpha$ extracted from fragments within different range of $I$ emphasize the importance of understanding the isoscaling parameters dependence of fragments produced in different collision regions. Furthermore, the $|\beta(N)| / \alpha(Z)$ value for a specific fragment in small size and highly isospin asymmetry systems can serve as a probe to detect the variations of neutron density and proton density in different regions of the nucleus and point out the limitations of theoretical models in investigating these issues.