Surface symmetry energy

Abstract

Abstract Binding energy of symmetric nuclear matter can be accessed straightforwardly with the textbook mass-formula and a sample of nuclear masses. We show that, with a minimally modified formula (along the lines of the droplet model), the symmetry energy of nuclear matter can be accessed nearly as easily. Elementary considerations for a macroscopic nucleus show that the surface tension needs to depend on asymmetry. That dependence modifies the surface energy and implies the emergence of asymmetry skin. In the mass formula, the volume and surface and (a)symmetry energies combine as energies of two connected capacitors, with the volume and surface capacitances proportional to the volume and area, respectively. The net asymmetry partitions itself into volume and surface contributions in proportion to the capacitances. A combination of data on skin sizes and masses constrains the volume symmetry parameter to 27 MeV≲ α ≲31 MeV and the volume-to-surface symmetry-parameter ratio to 2.0≲ α / β ≲2.8. In Thomas–Fermi theory, the surface asymmetry-capacitance stems from a drop of the symmetry energy per nucleon S with density. We establish limits on the drop at half of normal density, to 0.57≲ S ( ρ 0 /2)/ S ( ρ 0 )≲0.83. In considering the feeding of surface by an asymmetry flux from interior, we obtain a universal condition for the collective asymmetry oscillations, in terms of the asymmetry-capacitance ratio.