Peeling Off Neutron Skins from Neutron-Rich Nuclei: Constraints on the Symmetry Energy from Neutron-Removal Cross Sections

An experimentally constrained equation of state of neutron-rich matter is fundamental for the physics of nuclei and the astrophysics of neutron stars, mergers, core-collapse supernova explosions, and the synthesis of heavy elements. To this end, we investigate the potential of constraining the density dependence of the symmetry energy close to saturation density through measurements of neutron-removal cross sections in high-energy nuclear collisions of 0.4 to 1 $\mathrm{GeV}/\mathrm{nucleon}$. We show that the sensitivity of the total neutron-removal cross section is high enough so that the required accuracy can be reached experimentally with the recent developments of new detection techniques. We quantify two crucial points to minimize the model dependence of the approach and to reach the required accuracy: the contribution to the cross section from inelastic scattering has to be measured separately in order to allow a direct comparison of experimental cross sections to theoretical cross sections based on density functional theory and eikonal theory. The accuracy of the reaction model should be investigated and quantified by the energy and target dependence of various nucleon-removal cross sections. Our calculations explore the dependence of neutron-removal cross sections on the neutron skin of medium-heavy neutron-rich nuclei, and we demonstrate that the slope parameter $L$ of the symmetry energy could be constrained down to $\pm 10\mathrm{MeV}$ by such a measurement, with a 2% accuracy of the measured and calculated cross sections.

Figure 1

Nucleon-nucleon (top) and total reaction cross sections for ${}^{12}\mathrm{C}$ on ${}^{12}\mathrm{C}$ (bottom) as a function of beam energy. The blue points display data from Refs. [26] (100 to $400\mathrm{MeV}/\mathrm{nucleon}$), [27] ($790\mathrm{MeV}/\mathrm{nucleon}$), and [28] ($950\mathrm{MeV}/\mathrm{nucleon}$). Black triangles display the result from a parameter-free eikonal calculation in the optical limit, while the red diamonds include the effect of Pauli blocking [29].

Figure 2

Neutron-skin thickness $\mathrm{\Delta }{r}_{np}$ (left) and corresponding neutron-removal cross sections ${\sigma }_{\mathrm{\Delta }N}$ (right) for Sn isotopes as predicted by RMF calculations based on variations [32] of the DD2 interaction [31]. The slope parameter $L$ has been systematically varied from 25 MeV ($\mathrm{DD}{2}^{--}$) to 100 MeV ($\mathrm{DD}{2}^{+++}$) [32].

Figure 3

Relation between ${\sigma }_{\mathrm{\Delta }N}$ (top) and $\mathrm{\Delta }{r}_{np}$ (bottom) with the slope parameter $L$ calculated based on RMF theory for ${}^{124}\mathrm{Sn}$ and ${}^{132}\mathrm{Sn}$. The lines indicate the sensitivity of the observables to $L$ for an $L$ range of 10 MeV.

Figure 4

Ratios of ${\sigma }_R$, ${\sigma }_{\mathrm{\Delta }Z}$, and ${\sigma }_{\mathrm{\Delta }N}$ for ${}^{134}\mathrm{Sn}$ projectiles incident on proton and ${}^{12}\mathrm{C}$ targets as a function of the bombarding energy.