The Symmetry Energy: Current Status of Ab Initio Predictions vs. Empirical Constraints

Abstract

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation.

The Neutron Skin of 48Ca and 208Pb: A Critical Analysis

“…Analyses of hadronic scattering experiments, in particular, require modeling of the nuclear potential. Based on previous measurements of the skin in 48 Ca, we see no strong reasons to deem the CREX result surprising or unexpected, whereas the opposite is true for 208 Pb. These observations are well captured in Figure 1, the content of which we have extracted from Figure 8 of ref.…”

“…Indirect measurements of the neutron skin in 208 Pb and 48 Ca have been performed using a variety of techniques, such as those listed below. Parity-violating electron scattering will be addressed separately.…”

“…In Table 1, we summarize values for 208 Pb and 48 Ca neutron skins deduced from the indicated experiments. There is a considerable spread, as the result of a multitude of methods and theoretical input over decades.…”

“…The purpose of this article is to review and critically examine modern predictions and empirical constraints as well as the different points of view currently being debated. A special focus is placed on the recently reported value of the neutron skin in 48 Ca extracted from the CREX experiment [2], relative to the findings from the PREX-II [3] experiment. We end with thoughts and suggestions on the best way forward to strengthen the link between experiment and ab initio theory.…”

The Neutron Skin of ⁴⁸Ca and ²⁰⁸Pb: A Critical Analysis

“…In fact, from analyses including luminosities and ages determined from observations of isolated neutron stars [46], one may conclude that the direct Urca process, although possible at the central densities of neutron stars with masses between 1.7 and 2.0 solar masses, is unlikely around M = 1.7M ⊙ , and is likely, but not the principal cooling mechanism, for the M = 2.0M ⊙ stars. The importance of a realistic isovector component of the nuclear force (that is, carefully calibrated through freespace NN data), on the density dependence of the symmetry energy has been demonstrated [44,47]. Relaxing the constraint of accurate phase shifts for the isospin-1 S and P waves leads to drastic variations of the pressure in NM [47] and, consequently, the neutron skin.…”