Coulomb energies and nuclear radii in the energy density formalism Academic Article uri icon


  • The relation between Coulomb displacement energies, ΔEc, and Δr=rn-rp, the difference between the rms radii of neutrons and protons in nuclei, is investigated within the energy density formalism (EDF). The variational equation, obtained by minimizing the Coulomb plus symmetry energies, is solved assuming the symmetry interaction is a simple functional of the local nuclear matter density. Varying parameters of the model, rather unique relation between ΔEc and Δr is obtained (within ±50 keV). ΔEc is independent of rex, the rms radius of the excess neutrons distribution. Using the experimental values of rp and adjusting the model to reproduce the recent data on Δr (Δr{reversed tilde}~0.05 fm for48Ca and208Pb), which are significantly smaller than those obtained from current Hartree-Fock calculations, the calculated ΔEc agree with the experimental results. Using the value of Δr∼0.05 fm and the experimental values of rex, a small compression (<0.02 fm) of the proton core in the analogue state relative to its parent state emerges, thus contributing an additional electrostatic term to the Coulomb displacement energy. The size of this relative core-compression effect depends on the values assumed for Δr and rex, it increases with the decreasing of Δr and the increasing of rex. If Δr∼0.05 fm the effect is large enough to remove the long standing Coulomb energy anomaly. The main result of the present work is the correlation between ΔEc and Δr, suggesting that the difficulties of current Hartree-Fock calculations in reproducing isotope shifts of rp, the small value of rn-rp and the values of ΔEc may all be different manifestations of some missing residual p n effective interaction. © 1977 Springer-Verlag.

author list (cited authors)

  • Friedman, E., & Shlomo, S.

citation count

  • 10

publication date

  • March 1977