Three-Body Effect in Nuclear Matter to All Orders of Perturbation

Abstract

It is shown that there are three-body clusters in all orders of the Goldstone expansion for the binding energy of nuclear matter and that they converge extremely poorly. A $\ensuremath{\Gamma}$ matrix is defined which, on expansion, is shown to generate this infinite sequence of three-nucleon clusters. It is shown that the $\ensuremath{\Gamma}$ matrix can be evaluated in terms of a three-body correlation function for which a differential equation is derived. Solving this equation leads to the evaluation of $\ensuremath{\Gamma}$. This demonstrates that a finite sum does exist for these cluster diagrams, and gives a method for finding it. Finally, it suggests that for strong short-range potentials it is better to expand the binding energy in powers of the density rather than in powers of the interaction.