Symmetry Energy for Nuclei Beyond the Stability Valley

TL;DR

This paper investigates the symmetry energy in neutron-rich nuclei beyond the stability valley using variational methods and Skyrme forces, analyzing neutron coats, spinodal instability, and isospin effects.

Contribution

It introduces a method to derive the isospin symmetry energy from chemical potential shifts in finite nuclei beyond beta stability.

Findings

Neutron coat and isospin symmetry energy are characterized for neutron-rich nuclei.

Spinodal instability regions depend on mass number, asymmetry, and Skyrme parameters.

A procedure is proposed to extract symmetry energy from chemical potential differences.

Abstract

We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Using the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from analysis of the isospin shift of chemical potential $\Delta\lambda = \lambda_n - \lambda_p$ beyond the beta-stability line.