Properties of Nuclear Matter

Abstract

The properties of nuclear matter have been determined by the solution of the nuclear many-body problem, using the reaction matrix theory of Brueckner. The nonlinear integral equations characteristic of the theory have been solved with the aid of the fast electronic computer IBM 704. The two-body interaction assumed is the phenomenological potential of Gammel, Christian, and Thaler.It is found that the binding energy of nuclear matter, neglecting Coulomb forces, is 14.6 Mev per particle at a density corresponding to a radius parameter ${r}_{0}=1.00\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm. The Coulomb repulsion in a heavy nucleus is shown to drop the density by approximately 15%. The tensor force is shown to give approximately 6-Mev binding energy.The results are found to be very sensitive to the self-consistency requirements of the theory, the binding energy shifting from 14.6 Mev to 34.4 Mev if the velocity dependence of the single-particle potential is neglected. The actual solutions were made self-consistent by an iteration procedure which converged in five or six iterations, the final results being self-consistent to one part in ${10}^{5}$ or ${10}^{6}$.The effective mass for nucleon motion in the Fermi sea is found to vary from $0.56M$ for slow particles to $0.66M$ for particles near the Fermi surface. This velocity dependence of the potential is closely related to the symmetry energy which also depends, however, on the shifting in the spin populations as the neutronproton ratio is changed from unity. The symmetry energy computed is 10 to 15% larger than that deduced from experiment.