Electron Scattering Studies of Calcium and Titanium Isotopes

Experimental results are presented on the scattering of 250-MeV electrons by ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{42}$, ${\mathrm{Ca}}^{44}$, ${\mathrm{Ca}}^{48}$, and ${\mathrm{Ti}}^{48}$, and of 500-MeV electrons by ${\mathrm{Ca}}^{40}$ and ${\mathrm{Ca}}^{48}$. An analysis is made in terms of a phenomenological three-parameter shape, and a new, more accurate charge distribution is obtained for ${\mathrm{Ca}}^{40}$. The experiments also lead to a detailed exploration of the radial dependence of the differences in charge distributions of the various isotopes. Implications for nuclear theory are discussed. Comparison is made with the results of other electron scattering and of muonic x-ray experiments. The latter comparison permits an independent determination of an upper limit on the muon electromagnetic radius ${{〈{r}^{2}〉}_{\ensuremath{\mu}}}^{\frac{1}{2}}\ensuremath{\lesssim}0.35$ F.