Shell-model Coulomb energies

Analytical expressions have been derived for the total Coulomb energies, for isoscalar, isovector and isotensor Coulomb energies, and for Coulomb energy differences of nuclei with protons and neutrons in equivalent and in different major shell regions. The approach is related to earlier theoretical treatments of Carlosn and Talmi and of Hecht. A simple A-dependence is assumed to account for the increase in radius. Introducing average matrix elements for the Coulomb interactions between valence-valence, valence-core, and core-core protons in each of the six major shell regions as adjustable parameters, a global fit with 21 parameters to 288 experimental Coulomb displacement energies with 4<A<240 gives good agreement with a standard deviation of sigma=45 keV. The interaction energies display discontinuities particularly at major proton shell crossings, and they generally decrease within shells less rapidly than Asup(-1/3). The average decrease, however, follows approximately an Asup(-1/3) dependence which explains the success of Coulomb energy equations based on liquid-drop models. (orig.)