Three-body correlations in nuclear matter

A momentum-space method is developed for the calculation of three-body terms in the Brueckner-Bethe method for nuclear matter. The method is similar to one used earlier for central $S$-wave potentials. Here we extend it to the full nuclear force, including tensor forces, spin-orbit forces, etc. Furthermore, we show how the method can be used to investigate the possibility of long-range correlations in nuclear matter by summing the generalized ring series. The numerical accuracy obtainable with various mesh parameters and cut-offs in momentum space, and with various truncations of partial-wave expansions, is thoroughly explored. Several angle-average approximations are used, and the estimated numerical accuracy in the three-body cluster energy is 10-15%. The method is applied to a central potential $v_2$, a semirealistic potential $v_6$ (Reid), which has a tensor force, and to the Reid potential, augmented by an interaction that is consistent with empirical scattering phase shifts in two-body partial waves with $j\ge 3$. In all cases the three-body contribution to the energy is correctly given in order of magnitude by ${\kappa }_2{D}_2$, where $D_2$ is the two-body contribution and ${\kappa }_2$ is the usual convergence parameter of the Brueckner-Bethe method. The generalized ring series is found to converge rapidly, indicating that long-range correlations are not very important for the binding energy of nuclear matter. The Reid potential is found to saturate at the right energy but at too high a density.