Analysis of bulk and surface contributions in the neutron skin of nuclei

Abstract

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy and has multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult to obtain. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.

Density dependence of the symmetry energy from neutron skin thickness in finite nuclei

“…On the basis of our findings in recent years [30][31][32][33][34], in the next sections we will discuss two of these estimates of the L parameter. Namely, we will study the constraints that can be derived from the analysis of neutron skins in antiprotonic atoms, and the constraints that may be provided by parity-violating elastic electron scattering in a heavy neutron-rich nucleus such as 208 Pb.…”

“…[32,33]. That is, in order to obtain the predictions of the mean-field models for the central radius and diffuseness of the nucleon densities, we fit 2pF functions to the self-consistently calculated nucleon densities of the various models studied in the previous section.…”

“…Following refs. [32,33], we fit the parameters of eq. (33) to reproduce the zeroth, second, and fourth moments of the actual self-consistent mean-field density distributions.…”

Temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains

“…The latter is commonly defined in terms of the difference between the neutron and proton root-mean-square (rms) radii and is found to be closely related to the density dependence of the NSE, with the EOS of pure neutron matter and properties of neutron stars [39][40][41][42][43][44][45][46]. It is also related to a number of observables in finite nuclei, including the NSE (see, e.g., [4,8,9,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]), although its precise measurement is difficult. As examples, in Ref.…”

Density dependence of the nuclear symmetry energy from measurements of neutron radii in nuclei

“…Further details of these studies can be found in Refs. [34,35,36,37,38]. Part of the relevance of the extraction of the neutron radius lies on the fact that there exists a nice correlation between the neutron radius in a heavy nucleus such as 208 Pb and the slope of the symmetry energy at saturation L that links an observable of finite nuclei with a property of the symmetry energy.…”