Analytical relations between nuclear symmetry energy and single-nucleon potentials in isospin asymmetric nuclear matter

TL;DR

This paper derives analytical relations linking nuclear symmetry energy components to single-nucleon potentials, aiding understanding of uncertainties at high densities, with applications to common nuclear models.

Contribution

It introduces a formalism based on the Hugenholtz-Van Hove theorem to connect symmetry energies with single-nucleon potentials in asymmetric nuclear matter.

Findings

Derived general expressions for symmetry energies.

Applied formalism to widely used nuclear models.

Provided insights into uncertainties at supra-saturation densities.

Abstract

Using the Hugenholtz-Van Hove theorem, we derive general expressions for the quadratic and quartic symmetry energies in terms of single-nucleon potentials in isospin asymmetric nuclear matter. These analytical relations are useful for gaining deeper insights into the microscopic origins of the uncertainties in our knowledge on nuclear symmetry energies especially at supra-saturation densities. As examples, the formalism is applied to two model single-nucleon potentials that are widely used in transport model simulations of heavy-ion reactions.