Isoscaling, Symmetry Energy and Thermodynamic Models

TL;DR

This paper investigates the isoscaling parameter in nuclear reactions, comparing theoretical models including mean field and thermodynamic approaches, and demonstrates the importance of the canonical ensemble for finite systems and experimental deviations.

Contribution

It introduces a detailed comparison of grand canonical and canonical ensemble models for isoscaling, highlighting the canonical model's effectiveness for finite systems and experimental data.

Findings

Canonical ensemble better describes finite systems.

Grand canonical model fails with experimental deviations.

Canonical model explains non-isoscaling data.

Abstract

The isoscaling parameter usually denoted by $\alpha$ depends upon both the symmetry energy coefficient and the isotopic contents of the dissociating systems. We compute $\alpha$ in theoretical models: first in a simple mean field model and then in thermodynamic models using both grand canonical and canonical ensembles. For finite systems the canonical ensemble is much more appropriate. The model values of $\alpha$ are compared with a much used standard formula. Next we turn to cases where in experiments, there are significant deviations from isoscaling. We show that in such cases, although the grand canonical model fails, the canonical model is capable of explaining the data.