Nucleon-nucleus optical model potential: (II). Finite nuclei

Abstract

The complex nucleon-nucleus optical potential for finite nuclei is calculated from the Hamada-Johnston internucleon interaction. The first term of a multiple scattering series is used and a diagonal representation in coordinate space of the t-matrix is calculated in a nuclear matter approximation. The resulting potential consists of a local part which is similar to the often used folding model together with a non-local part. The local part is large and repulsive and the non-local part is large and attractive. The complex t-matrix has a complicated radial variation as well as strong density and energy dependence and it is unlikely that they can be well approximated by phenomenological forms or, for instance, by the t-matrix obtained from bound state calculations. The optical potential has a radial dependence which differs markedly from those used in phenomenological analysis and we conclude that such analysis may easily give misleading results. A particular example is given of proton scattering from 40Ca at 30.3 MeV where our potential gives a good fit with none of the extra terms claimed to be required in phenomenological analysis. We also obtain good fits for protons on 40Ca at 40 MeV, protons on 208Pb at 30.3, 40 and 100.4 MeV and for neutrons on 40Ca at 7.91 MeV. In all cases the fit is of similar quality to that obtained in phenomenological analysis despite the fact that our theory contains very few adjustable parameters. We conclude that our theory presents an approach which is far more satisfactory than phenomenological fitting of scattering data.