Possible Connection Between the Iwamoto-Yamada Cluster Expansion and the Reaction-Matrix Perturbation Theory

A partial-wave decomposition of the Iwamoto-Yamada cluster energy ${\mathcal{E}}_2$ is used to show that the cluster energy ${\mathcal{E}}_1+{\mathcal{E}}_2$ is consistently more attractive than the reaction-matrix energy $W_1+W_2$ by several MeV per nucleon at all densities. The differenee between these two types of calculations is shown to come from the absence in ${\mathcal{E}}_2$ of the dispersion effect in $W_2$ due to self-consistent hole energies. The necessity for imposing subsidiary conditions on the correlation function for ${\mathcal{E}}_2$— conditions not explicitly required in reaction-matrix calculations—is traced to the absence of the same dispersion effect. This result suggests a possible starting point for a formal comparison of the two expansions.