Shape of the Nuclear Symmetry Potential

The form factor of the real symmetry potential is explicitly calculated from a simple microscopic model of isobaric analog resonances. Numerical results are presented for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{132}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. For ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ the symmetry potential turns out to be of the surface type, while for ${}_{}{}^{132}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ it is of the volume type. The magnitude depends only on the strength of the $n-p$ interaction.