Three-Body Correlations in Nuclear Matter

Abstract

The energy of nuclear matter which is due to the simultaneous interaction of three nucleons is calculated to all orders of Goldstone perturbation theory. The various orders form a divergent series with alternating signs. This series is summed by an integral equation due to Faddeev, and an approximate solution of this equation is found. According to this solution, the effect of the repulsive core on the potential energy of "particle" states is reduced to about one-third as compared with the usual third-order calculation, while the long-range attraction is essentially unchanged. The total potential energy of the important excited particle states is thereby reduced essentially to zero. Similarly, the total effect of three-body correlations on the energy of nuclear matter is very small, of the order of 3 to 6% of that of the two-body correlations. Thus the Goldstone series, if rearranged into a series in the number of interacting particles (which also corresponds roughly to powers of the density), converges very rapidly. The energy of nuclear matter is reduced substantially by our theory. When the theory is combined with Wong's idea of a "soft" repulsive core, the binding energy becomes roughly 13 MeV per particle, in much better agreement with observation than other recent estimates.