A novel approach to Isoscaling: the role of the order parameter m = (N-Z)/A

TL;DR

This paper introduces m-scaling, a new approach to isoscaling based on the Landau O(m^6) theory, emphasizing the role of the order parameter m = (N-Z)/A and the external field H in nuclear reactions.

Contribution

It proposes a novel theoretical framework linking isoscaling to the Landau O(m^6) model and the order parameter m, offering a different interpretation from traditional methods.

Findings

Isoscaling depends mainly on the order parameter m and the external field H.

The approach highlights differences in interpreting experimental results.

The framework connects isoscaling with phase transition theories.

Abstract

Isoscaling is derived within a recently proposed modified Fisher model where the free energy near the critical point is described by the Landau O(m^6) theory. In this model m = (N-Z)/A is the order parameter, a consequence of (one of) the symmetries of the nuclear Hamiltonian. Within this framework we show that isoscaling depends mainly on this order parameter through the 'external (conjugate) field' H. The external field is just given by the difference in chemical potentials of the neutrons and protons of the two sources. To distinguish from previously employed isoscaling relationships, this approach is dubbed: m - scaling. We discuss the relationship between this framework and the standard isoscaling formalism and point out some substantial differences in interpretation of experimental results which might result. These should be investigated further both theoretically and experimentally.