Rotational-Optical Model for Scattering of Neutrons

The scattering of neutrons by a deformed, rotating, even-even nucleus has been investigated with a diffuse-surfaced complex potential employed. Two essential approximations, for which justification is presented, are made: (1) Nuclear excitations corresponding to $I\ge 6$ are ignored. (2) In the expansion of the nuclear potential, $V(r, {\theta }^{\prime })=\Sigma v_{\lambda }\mathrm{}\left(r\right)\mathrm{}{P}_{\lambda }\left({cos\theta }^{\prime }\right)$, terms with $\lambda \ge 4$ are omitted. Comparison with earlier calculations by other authors, employing a distorted-wave Born approximation and $\delta$-function interaction, indicates that the earlier work seriously overestimated direct excitation. At low energies (≲1 Mev), the excitation cross section given by the direct process is small compared with excitation through the compound nucleus, but the direct process may contribute significantly to the angular distribution due to its arge anistropy. The relevance of this work to the measurements of the differential cross section for excitation of the $I=2\mathrm{}$ first excited level of ${\mathrm{U}}^{238}$ is discussed in some detail. The general features of the experimental variation of the strength function $\frac{{{\overline{\Gamma }}_n}^0}{D}$ and potential-scattering length $R^{\prime }$ with mass number at low energy have been reproduced by a calculation with suitably varying deformation.