Nucleon-Transfer Reactions and Coulomb Displacement Energies

Differential cross sections for several nucleon-transfer reactions on ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ are analyzed in distorted-wave Born approximation. It is shown that the values of the root-mean-square radius of the $1f_{\frac{7}{2}}$ proton in ${}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}$ and the $1f_{\frac{7}{2}}$ neutrons in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ are quite well determined. These values are in a reasonable agreement with theoretical results obtained from shell-model and Hartree-Fock calculations, but imply Coulomb displacement energies which differ from experimental results by about 0.6 MeV. It is concluded that the anomaly observed in nuclear matter radii, as derived from Coulomb displacement energies, is probably due to difficulties in calculating these energies.