  The symmetry energy in nuclei is studied using a monopole-monopole two boby
interaction which has an isospin dependent term. A Hartree theory is developed
for this interaction which has an oscillator shell model basis with
corresponding shell structure. The role of shell structure on the symmetry
energy is then studied. We also find that the strength of the Heisenberg
interaction is very important for understanding the difference between proton
and neutron radii and features associated with halo nuclei.
  PACS numbers: 21.10.Sf, 21.65Cd, 21.65Ef
