Neutron Scattering Studies of the Doubly Magic Calcium Nuclei, CALCIUM-40 and CALCIUM-48, in the Low Energy Resonance Region.

Measurements of neutron elastic and inelastic scattering differential cross sections from ^ {48}Ca at 2.35, 2.43, 2.71, 3.15, 3.55, 4.70, 6.00, and 7.97 MeV are presented. These data are combined with n + ^{48}Ca total cross sections taken at Oak Ridge National Laboratory to form a rather extensive set of scattering data for ^{48}Ca between 80 keV and 20 MeV incident neutron energy. Coupled-channels analyses of these data with a first-order vibrational model described both the neuron inelastic cross sections at 7.97 MeV and intermediate structure resonances observed in the total cross sections below 3 MeV. Particle-core coupled resonance configurations were determined for four intermediate structure resonances from the coupled-channels calculations. The present calculations are compared to earlier shell model calculations which used a smaller model space to determine the resonance configurations. The expanded model space used in the present analysis was found to give a more complete description of the resonance configurations. Also measured at each of the energies listed above were neutron elastic and inelastic cross sections from ^{40}Ca. These measurements were made to examine the scattering from the two doubly magic Ca nuclei in a consistent way. Coupled-channels calculations, again using a first-order vibrational model, were used in analyzing the ^{40} Ca data. Results of these analyses show that, although the ^{40}Ca differential scattering cross sections vary rather smoothly with energy, they are influenced by resonance structure. In addition to the above coupled-channels analysis of ^{48}Ca, the mean field potential used to describe the bound-state and scattering data of ^{48}Ca was determined using a dispersion relation to connect the real and imaginary components of the optical model potential. The importance of the dispersion corrections in describing the scattering from 50 keV to 20 MeV is presented. Finally, differential scattering cross sections measured between 2 and 3.5 MeV from ^{48 }Ca are compared to calculations using phase shifts from an evaluation of the total cross sections. The agreement between the measured and calculated differential scattering cross sections was excellent at some energies.