Three-Body Correlations in Reaction-Matrix Calculations

Abstract

An improved method of treating three-body cluster correlations in reaction-matrix calculations is presented and applied to nuclear matter. A three-particle reaction matrix is defined which allows three particles to interact with each other in all possible ways after specifying the particles involved in the initial and terminal interactions. The method is similar to that proposed by Bethe but, since all off-energy-shell terms can be treated separately, full advantage can be taken of the Faddeev formalism as applied to the three-nucleon system. The Pauli exclusion operator is included in calculating on-energy-shell reaction-matrix elements but is neglected in the off-energy-shell terms. Numerical calculations are presented for two spin-independent, $s$-state, separable potentials, one of which contains a hard-shell repulsive term. Higher-order terms are found to be important for the hard-shell potential but not for the simple attractive potential. In both cases the total three-body correlation energy is found to be small.