Model calculations of doubly closed-shell nuclei in the integro-differential equation approach

The binding energies and root mean square radii obtained from the Integro-Differential Equation Approach (IDEA) and from the Weight-Function Approximation (WFA) of the IDEA for an even number of bosons and for C-12, O-16 and Ca-40 are compared to those recently obtained by the Variational Monte Carlo, Fermi Hypernetted Chain and Coupled Cluster expansion methods with model potentials. The IDEA provides numbers very similar to those obtained by other methods although it takes only two-body correlations into account. The analytical expression of the wave function for the WFA is given for bosons in the ground state when the interacting pair is outside the potential range. Due to its simple structure, the equations of the IDEA can easily be extended to realistic interactions for nuclei as has already been done for the trinucleon and He-4.