On the macroscopic theory of the giant dipole state

A macroscopic theory of isovector states is derived from a reduction of the random phase approximation. Using Skyrme interactions and assuming a dipole transition density of the Goldhaber-Teller shape, we find reasonable agreement with experimental excitation energies for the light nucleus ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The theoretical excitation energies for heavy nuclei are too high by a couple of MeV. The transition density may be given a general parametric form which includes the hydrodynamic model as well as the Goldhaber-Teller model. A variational calculation of the form of the transition density gives the Goldhaber-Teller shape for light nuclei, and a shape between the hydrodynamic and Goldhaber-Teller models for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.