Symmetry and Surface Symmetry Energies in Finite Nuclei

A study of properties of the symmetry energy of nuclei is presented based on density functional theory. Calculations for finite nuclei are given so that the study includes isospin dependent surface symmetry considerations as well as isospin independent surface effects. Calculations are done at both zero and non-zero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of $\beta$ stability. Differences of several MeV are shown over a good fraction of the total mass range in $A$. Also given are calculations for the bulk, surface and Coulomb terms.