Neutron skin thickness in droplet model with surface width dependence: indications of softness of the nuclear symmetry energy

TL;DR

This study uses the droplet model with surface width dependence to analyze neutron skin thickness, revealing a preference for a softer symmetry energy and constraining the density derivative of the symmetry energy in finite nuclei.

Contribution

It introduces a correlation between the symmetry energy slope and the J/Q ratio, emphasizing surface width effects in neutron skin calculations with effective interactions.

Findings

Neutron skin sizes suggest a soft symmetry energy at subsaturation densities.

The J/Q ratio correlates with the density derivative of the symmetry energy.

A narrow range of L ~ 45-75 MeV is compatible with various experimental constraints.

Abstract

We analyze the neutron skin thickness in finite nuclei with the droplet model and effective nuclear interactions. The ratio of the bulk symmetry energy J to the so-called surface stiffness coefficient Q has in the droplet model a prominent role in driving the size of neutron skins. We present a correlation between the density derivative of the nuclear symmetry energy at saturation and the J/Q ratio. We emphasize the role of the surface widths of the neutron and proton density profiles in the calculation of the neutron skin thickness when one uses realistic mean-field effective interactions. Next, taking as experimental baseline the neutron skin sizes measured in 26 antiprotonic atoms along the mass table, we explore constraints arising from neutron skins on the value of the J/Q ratio. The results favor a relatively soft symmetry energy at subsaturation densities. Our predictions are compared with the recent constraints derived from other experimental observables. Though the various extractions predict different ranges of values, one finds a narrow window L ~ 45-75 MeV for the coefficient L that characterizes the density derivative of the symmetry energy which is compatible with all the different empirical indications.