INTEGRODIFFERENTIAL EQUATION APPROACH EXTENDED TO LARGER NUCLEI

We extend the integro-differential equation approach (IDEA) from few-nucleon to closed-shell and closed-subshell nuclei and outline the analytical methods required for the calculation of the density functions, which enter into the integro-differential equations. These contain all the physics for a system of fermions associated with the Pauli principle. In order to test the accuracy of the IDEA comparisons are made of the binding energies of He-4, C-12 and O-16 obtained with effective potentials using thc hypercentral approximation (HCA) providing a variational solution without correlations, the IDEA which fully includes the two-body correlations, the S-state integro-differential equation (SIDE) valid for potentials operating only on pairs in the S-state and those calculated by several variational or perturbative methods in the literature. We find that the IDEA is in general in reasonably good agreement with the best results in the literature but that the difference between the binding energies calculated with SIDE and IDEA increases with the number of particles A. This implies that the approximation, where the potential operates only on pairs in the S-state (thc SIDE), is not suitable for local potentials operating on all orbitals which shows the importance of the contribution of motions where pairs are not in the S-state, We also emphasize the speed and efficiency of the numerical computations in the IDEA.