Saturation of Nuclear Matter and Radii of Unstable Nuclei

Abstract

We systematically examine relations among the parameters characterizing the phenomenological equation of state (EOS) of nearly symmetric, uniform nuclear matter near the saturation density by comparing macroscopic calculations of radii and masses of stable nuclei with experimental data. The EOS parameters of interest here are the symmetry energy coefficient S0, the symmetry energy density derivative coefficient L and the incompressibility K0 at normal nuclear density. We estimate a range of (K0, L) from empirically reasonable values of the slope of the saturation line (the line joining the saturation points of nuclear matter at finite neutron excess) and find a strong correlation between S0 and L. In light of the uncertainties on the values of K0 and L, we perform macroscopic calculations of the radii of unstable nuclei expected to be produced in future facilities. We find that the matter radii depend appreciably on L, while being almost independent of K0. This dependence implies that if the matter radii are measured with an accuracy of ±0.01 fm for a sufficiently large number of neutron-rich nuclides to allow one to smooth out the expected staggering of the radii due to shell and pairing effects, it might be possible to derive the value of L within ±20 MeV.