Self-Consistent Nuclear Model

A Hamiltonian proposed by Duerr is applied to carry out self-consistent calculations for atomic nuclei. Average exchange forces, calculated from a plane-wave model, are included in the Hartree potential. In order to obtain agreement with the empirical data, two coupling constants and one constant representing the range of the interaction have to be adjusted. The range turns out to be 3.23×${10}^{-14\mathrm{}}$ cm. Because this range is very short the calculations may not be justified and must be considered as a formal procedure. Having adjusted the three parameters, reasonable neutron and proton binding energies and nucleon densities are obtained for the nuclei ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ce}}^{140}$, and ${\mathrm{Pb}}^{208}$.