Neutron transition densities for Ca48 from proton scattering at 200 and 318 MeV

Differential cross sections and analyzing powers for scattering of 200 and 318 MeV protons have been measured for states of Ca-48 up to 7 MeV of excitation. The data cover c.m. momentum transfers from approximately 0.4 to 3.0 fm-1. Neutron transition densities were extracted for the 2(1)+, 3(1)-, 3(2)-, 4(2)+, and 5(1)- states using density-dependent empirical effective interactions previously calibrated upon elastic and inelastic scattering data for O-16 and Ca-40. The corresponding proton transition densities were obtained from electron scattering data and held fixed during the analysis. Fits performed to the data for either energy provide excellent predictions for the other. Neutron densities fitted to data for either,energy independently agree very well with each other and with the densities fitted to both data sets simultaneously. These densities are also consistent with earlier data for 500 MeV protons. The energy independence of the extracted transition densities demonstrates that residual errors in the reaction model are compatible with the error bands estimated by the fitting procedure. Several additional tests of the model dependence of the results were performed also. The proton and neutron transition densities are compared with calculations based upon the extended random phase dominated by 1p1h configurations, whereas densities requiring substantial 2p2h contributions tend to be underestimated.