Three-Body Problem in Nuclear Matter

Abstract

This work reviews some recent developments in the theory of nuclear matter. Assuming familiarity with the basic Brueckner-Goldstone theory described in the preceding article by B. Day, it is first shown that the Brueckner-Goldstone series does not converge in powers of the reaction matrix, and that the perturbation series for the binding energy has to be rearranged in powers of the density $\ensuremath{\rho}$. Physical reasons and actual estimates are provided for expecting convergence in powers of $\ensuremath{\rho}$.A detailed theory is outlined for the evaluation of the three-body energy, which gives the ${\ensuremath{\rho}}^{2}$ term. Attention is paid to both the momentum dependence of the reaction matrix and the tensor nature of nuclear forces. Finally, the last section is devoted to the choice of the single-particle potential energies, suitably designed so as to absorb most of the four-body and higher cluster terms.