Electron Scattering by Calcium at 250 MeV

The doubly magic nucleus of ${\mathrm{Ca}}^{40}$ has been investigated by the electron scattering technique at an incident energy of 250 MeV. The elastic scattering behavior has been resolved from the inelastic scattering, and absolute data on cross sections have been obtained for both types of events. In the case of the elastic scattering, the first and second diffraction features have been observed and measured. It has been possible to make a comparison of the elastic data with theoretical calculations based on a phase-shift analysis for certain assumed models of the nuclear charge density distribution. The combination of such an analysis with the present data, and also with earlier data on the same nucleus, permits the determination of the radius and skin thickness of the ${\mathrm{Ca}}^{40}$ nucleus with a precision greater than has been attainable heretofore. An investigation of the dependence of the density distribution on a third parameter indicates that a Fermi distribution, or models close to this type, are required to fit the experimental data. A Fermi radial charge density distribution with radius $c=3.60\mathrm{}$ F and skin thickness $t=2.50\mathrm{}$ F fits the data extremely well.