Three-Nucleon Clusters in Nuclear Matter

The effect of three-body clusters on the binding energy of nuclear matter is studied. An attempt is made to treat all such clusters of the third order as self-energy diagrams and to include their effect into the single-particle energies, thereby improving the convergence of the Goldstone expansion considerably. For this purpose, an expression for off-diagonal reaction matrix elements is derived. One of the consequences of this procedure is that, to a good approximation, the contribution of all the third-order diagrams together is equal to that arising from just the even "$l$" states of the simplest of these diagrams. Many of the arguments and approximations used are based on the previous paper of this issue by Bethe et al.