Giant multipole resonances in the deformed fissionable nucleus ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$

The deformed, fissionable nucleus ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ was studied with inelastic scattering of 87.5 MeV electrons between 5 and 40 MeV excitation energy with inelastic momentum transfers ranging from 0.32 ${\mathrm{fm}}^{-1\mathrm{}}$ to 0.58 ${\mathrm{fm}}^{-1\mathrm{}}$ for an excitation energy of 15 MeV. Resonance cross sections extracted were compared with distorted-wave Born-approximation calculations using the Goldhaber-Teller, Steinwedel-Jensen, and Myers-Swiatecki models of the giant resonance. It is demonstrated that up to the first minimum of the form factor the cross section is nearly completely determined by one parameter, the transition radius $R_{\mathrm{tr}}$. Using the known systematics of various multipole resonances in other, nonfissionable nuclei as a guide, it was found that the assumed ground state radius of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ had to be enlarged by about 10% for all multipolarities, to bring the strength found into agreement with the systematics and with other experiments in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. In particular, while the model-independent values for position and width of the giant dipole resonance agree well with photon experiments, a scaled version of the Myers-Swiatecki model had to be used to produce agreement in strength. Similarly a scaled Goldhaber-Teller model was used for the isoscalar $E2\mathrm{}$ resonance at 9.9 MeV. The situation for the isovector states above the giant dipole resonance, $E2\mathrm{}$, and $E3\mathrm{}$ (or $E0\mathrm{}$ is even more complicated. It is argued that with proper caution and consideration of other available data the use of the collective models mentioned above may give valuable insight into the charge distribution of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ at higher excitation energies.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(e,e^{\prime })$, $E_0=87.5\mathrm{}$ MeV. Measured $\frac{d^2\sigma }{d\Omega d{E}_x}$, bound and continuum states (giant resonances). Deduced multipolarity, reduced matrix element $B\left(E\lambda \right)$, radiative width ${\Gamma }_{\gamma }^0$, sum rule exhaustion of giant resonances, total width of continuum and clustered states.