The quantum theory of nucleon correlation in finite nuclei. II. Higher order correlation effects and additive pair approximation

In the first part of this article it was shown that the variational solution of the Schroedinger equation of a finite Fermion system can be written as a finite sum of A terms (for A particles) the first of which is the Hartree-Fock energy, while the rest represent the correlation effects. In the first part explicit formulas for the 2-particle correlation energy were given. In this paper explicit formulas are given for the higher order correlation energies. It is shown that two different models can be developed depending on the orthogonality condition used. Beginning with the 4th order effects the “linked” and “unlinked” correlation terms are separated. An exact formula is given for the case in which only the 2-particle effects, linked and unlinked are taken into account. The “additive pair approximation” in which the correlation energy is given as the sum of 2-particle energies is investigated and it is shown to be related to the exact formula by a clearly defined set of approximations. Various possible applications of the model are discussed.