A−16Dependence of Giant Dipole Energies

Goldhaber and Teller suggested a model for the giant $E1\mathrm{}$ transition resonance in which the sphere of neutrons oscillates against the sphere of protons. Using simple arguments they showed such a model predicts an $A^{\frac{-1\mathrm{}}{6}}$ dependence of the dipole energy on atomic weight. However, Steinwedel and Jensen introduced a hydrodynamic model of the nucleus with a rigid nuclear surface that predicted an $A^{\frac{-1\mathrm{}}{3}}$ behavior. They obtained a semiqualitative estimate of the energy by using as the restoring force the symmetry energy term in the semiempirical mass formula. We present a hydrodynamic model which includes a realistic nuclear surface and show that an $A^{\frac{-1\mathrm{}}{6}}$ behavior is again predicted. A plot of the data for nuclei from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ to ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ shows that the $log\overline{\omega }$ values, where $\overline{\omega }$ is the average energy of absorption for a given nucleus, fall on a straight line with slope of $-\frac{1}{6}$.