The scattering of 79.1 MeV $\alpha$ 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 $\Delta R$, the difference between the ${}_{}{}^{40,48}{}_{}{}^{}\mathrm{Ca}$ rms matter radii, is $\Delta R=0.05\mathrm{}\pm 0.04$ 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 $\Delta R$ with the results of electromagnetic experiments yields the relative neutron-proton radius difference in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$; $R_n\mathrm{}\left(48\right)-R_p\mathrm{}\left(48\right)=0.03\mathrm{}\pm 0.08$ fm. These results are compared with Hartree-Fock calculations which tend to produce larger differences. Possible reasons for this discrepancy are discussed.

NUCLEAR REACTIONS ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(\alpha , \alpha )$ $E=79.1\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; $\theta =10-45\mathrm{}°$, enriched targets. Microscopic optical model analysis; deduced rms matter radii.

• Received 7 October 1974

DOI:https://doi.org/10.1103/PhysRevC.12.778