Coulomb energies of spherical nuclei

Abstract

A phenomenological Coulomb energy equation has been derived for spherical nuclei with diffuse surfaces. Contributions from the direct and exchange Coulomb energy and from the electromagnetic spin-orbit interaction are included explicitly. The experimental Coulomb displacement energies of 42 essentially spherical nuclei with Z ≧ 28 have been subjected to a least-squares analysis with the shape parameters of the ground state charge distributions required to agree with those obtained from electron scattering and muon capture X-ray experiments. Agreement between the experimental and calculated energies with a standard deviation of about 20 keV is obtained if (i) the ratio between the rms radii of the neutron excess and the proton core is taken between about 1.10 and 1.15, (ii) a smoothly A-dependent correction term which varies between about +450 keV in the light nuclei and +350 keV in the heavy nuclei is introduced, and (iii) an averaged contribution from the electromagnetic spin-orbit interaction is used rather than the expected shell-model contribution. Justification for this averaging may be provided by amounts of not less than 15 % of excitations into higher shellmodel orbits for all nuclei. The Coulomb displacement energies of vibrational and rotational nuclei are observed to be smaller by up to 200 keV than corresponding spherical nuclei. Neutron halos have been calculated and are found to be in very good agreement with the results of Hartree-Fock calculations, the droplet model of Myers and Swiatecki and the calculations by Nolen and Schiffer using wave functions generated in a Woods-Saxon potential well. The calculated neutron halo for 208Pb is 0.25±0.05 fm.