Neutron skin uncertainties of Skyrme energy density functionals

TL;DR

This paper evaluates the uncertainties in neutron-skin thickness predictions using Skyrme energy density functionals, highlighting the importance of precise measurements to constrain nuclear symmetry energy parameters.

Contribution

It systematically assesses statistical and systematic uncertainties in neutron-skin predictions and links them to the nuclear symmetry energy parameters using advanced density functional theory.

Findings

Errors increase with neutron excess.

Statistical errors surpass systematic errors.

Uncertainty in the slope L of symmetry energy is the main source.

Abstract

Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of neutron-skin thickness and relate them to the equation of state of nuclear matter, and in particular to nuclear symmetry energy parameters. Methods: We use the nuclear superfluid Density Functional Theory with several Skyrme energy density functionals and density dependent pairing. To evaluate statistical errors and their budget, we employ the statistical covariance technique. Results: We find that the errors on neutron skin increase with neutron excess. Statistical errors due to uncertain coupling constants of the density functional are found to be larger than systematic errors, the latter not exceeding 0.06 fm in most neutron-rich nuclei across the nuclear landscape. The single major source of uncertainty is the poorly determined slope L of the symmetry energy that parametrizes its density dependence. Conclusions: To provide essential constraints on the symmetry energy of the nuclear energy density functional, next-generation measurements of neutron skins are required to deliver precision better than 0.06 fm.