Elastic scattering of 65 MeV polarized protons

Elastic scattering of 65 MeV polarized protons from 25 nuclei ($^{16}\mathrm{O}$---$^{209}\mathrm{Bi}$) has been measured. The volume integral of the real central part of the optical potential (${J}_{R}$) shows a behavior similar to the binding energy curve for the target mass number. The mean square radius of the real central part of the optical potential is found to obey the relation ${〈{r}^{2}〉}_{\mathrm{pot}}=(0.937\ifmmode\pm\else\textpm\fi{}0.012){A}^{\frac{2}{3}}+(6.42\ifmmode\pm\else\textpm\fi{}0.21)$ ${\mathrm{fm}}^{2}$. By comparing with the systematics of the charge distributions obtained from electron scattering data, it is found that the effective two-body interaction range between an incident proton and a nucleon in the target has a target mass number dependence given by ${〈{r}^{2}〉}_{\mathrm{int}}=(0.132\ifmmode\pm\else\textpm\fi{}0.013){A}^{\frac{2}{3}}+(4.24\ifmmode\pm\else\textpm\fi{}0.24)$ ${\mathrm{fm}}^{2}$. Assuming this relation, root mean square radii of the point nucleon distributions are obtained. The dependences of the ${J}_{R}$ value and the ${〈{r}^{2}〉}_{\mathrm{pot}}$ value on the mass number and energy obtained here are compared critically with recent microscopic optical potential calculations.NUCLEAR REACTIONS $^{16}\mathrm{O}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{40}\mathrm{Ar}$, $^{40,44,48}\mathrm{Ca}$, $^{46,48,50}\mathrm{Ti}$, $^{54,56}\mathrm{Fe}$, $^{58,60,62,64}\mathrm{Ni}$, $^{89}\mathrm{Y}$, $^{90}\mathrm{Zr}$, $^{98,100}\mathrm{Mo}$, $^{144}\mathrm{Sm}$, $^{208}\mathrm{Pb}$, $^{209}\mathrm{Bi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, p)$, $E=65$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$, $A(\ensuremath{\theta})$; deduced optical-model parameters, mean-square nuclear radii, and volume integrals for the real central potential.