Relative Sizes of Ca-40,48 from Scattering of 79 Mev Alpha-Particles

The scattering of 79.1 MeV $\ensuremath{\alpha}$ particles from $^{40,48}\mathrm{Ca}$ has been measured with high relative accuracy and analyzed with a folding model for the optical potential. The result for $\ensuremath{\Delta}R$, the difference between the $^{40,48}\mathrm{Ca}$ rms matter radii, is $\ensuremath{\Delta}R=0.05\ifmmode\pm\else\textpm\fi{}0.04$ fm. This result appears smaller than most previous measurements which employed Woods-Saxon potentials or diffraction analyses. Most of the discrepancies are removed when the definition of the matter radius used in each analysis is scrutinized. Combining $\ensuremath{\Delta}R$ with the results of electromagnetic experiments yields the relative neutron-proton radius difference in $^{48}\mathrm{Ca}$; ${R}_{n}(48)\ensuremath{-}{R}_{p}(48)=0.03\ifmmode\pm\else\textpm\fi{}0.08$ fm. These results are compared with Hartree-Fock calculations which tend to produce larger differences. Possible reasons for this discrepancy are discussed.NUCLEAR REACTIONS $^{48}\mathrm{Ca}(\ensuremath{\alpha}, \ensuremath{\alpha})$ $E=79.1$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$; $\ensuremath{\theta}=10\ensuremath{-}45\ifmmode^\circ\else\textdegree\fi{}$, enriched targets. Microscopic optical model analysis; deduced rms matter radii.