Certain physical mechanisms contributing to the Brueckner pair dispersion energy
W2D are reviewed. This
W2D is found to appear also in the Iwamoto-Yamada cluster expansion if the same Brueckner state- and momentum-dependent correlation operators are used. It does not appear in the two-body Iwamoto-Yamada energy, however, but in the three-body energy. Up to this point, a Brueckner triplet dispersion energy
W3D has not yet appeared. This
W3D depends on a triplet excitation parameter ${\ensuremath{\kappa}}_{3}$, which is calculated using Jastrow correlation functions. We find that ${\ensuremath{\kappa}}_{3}$ is small when ${\ensuremath{\kappa}}_{2}$ is small (\ensuremath{\lesssim} 0.1), and large when ${\ensuremath{\kappa}}_{2}$ is large (\ensuremath{\gtrsim} 0.4). Since ${\ensuremath{\kappa}}_{2}\ensuremath{\approx}0.2$ in nuclear matter, there is hope that both Brueckner and Iwamoto-Yamada expansions converge to the same answer at fairly low orders.NUCLEAR STRUCTURE Fermion fluids, nuclear matter; compared Brueckner and IY expansions; calculated triplet excitation parameter.
We develop diagrammatic methods which give the explicit expression for the n th order term of the linked Iwamoto-Yamada cluster expansion in terms of the cluster integrals. The method applies independently of the number A of particles of the system. We carry through partial summations which for finite A result in a representation of the expansion by skeleton diagrams, whereas in the limit A → ∞ the expansion is reduced to two analytical equations. In addition, for finite A the renormalization establishes a connection between the expectation value of an arbitrary operator and the probability to find n hole states, 1 ≤ n ≤ A, occupied. Simple considerations raise some doubts concerning the convergence of the unrenormalized expansion.