Matter radii of the even tin isotopes from elastic $\alpha$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering

The elastic scattering of $\alpha$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ particles from ${}_{}{}^{116,118,120,122,124}{}_{}{}^{}\mathrm{Sn}$ has been measured at $\alpha$ energies between 9 and 17 MeV and at ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ energies between 46 and 59 MeV. Fits have been made to the data with the optical and the incoming wave boundary condition models. The radius at which the nuclear potential is 2% of the Coulomb potential is minimally sensitive to the ambiguities of the fit. The increases in nuclear matter size as $A$ increases over the tin isotopes, measured by $\alpha$ and by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ scattering, agree reasonably well with each other and with the increase measured by proton scattering. However, the increase in the size of the matter distribution is 2 to 3 times larger than that of the charge distribution as observed in muonic atom and electron scattering studies.

NUCLEAR REACTIONS ${}_{}{}^{116,118,120,122,124}{}_{}{}^{}\mathrm{Sn}(\alpha , \alpha )$,, $E=9-17\mathrm{}$ MeV; ${}_{}{}^{116,118,120,122,124}{}_{}{}^{}\mathrm{Sn}$(${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$), $E=46-59\mathrm{}$ MeV; measured $\sigma (E, \theta )$. Deduced nuclear size. Enriched targets.