Intrinsic radial sensitivity of nucleon inelastic scattering

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Abstract
A linear expansion analysis of the folding model transition amplitude is used to study the intrinsic sensitivity of the inelastic scattering of intermediate energy nucleons to the radial form of the neutron transition density, given known proton transition densities from electron scattering. Realistic density-dependent effective interactions are used to construct pseudodata. These pseudodata are then reanalyzed and the error matrix is used to calculate an error band for the radial transition density. This approach reveals the sensitivity of the extracted transition density to absorption, medium modifications of the interaction, and the extent and quality of the data in a manner that is largely free of the residual inaccuracies in reaction theory that complicate the analysis of real data. We find that the intrinsic radial sensitivity of nucleon inelastic scattering is best for projectile energies between 200 and 500 MeV, but is adequate to resolve the radial dependence of neutron transition densities even in the interior of heavy nuclei throughout the energy regime 100–800 MeV. We have also compared our method with scale-factor analyses which assume proportionality between neutron and proton densities. For states whose transition densities are similar in the surface, we find scaling to be accurate at the 20% level. However, for light nuclei substantial deviations beyond the first peak of the differential cross section reveal sensitivity to shape differences. This sensitivity is reduced for heavy nuclei. The model dependence of radial densities is also studied. A high-q constraint is used to analyze the contribution of incompleteness error to the deduced error bands and to reduce the model dependence.