Interplay of Three-Body Interactions in the EOS of Nuclear Matter

Abstract

The equation of state of symmetric nuclear matter has been investigated within Brueckner approach adopting the charge-dependent Argonne $V_{18}$ two-body force plus a microscopic three-body force based on a meson-exchange model. The effects on the equation of state of the individual processes giving rise to the three-body force are explored up to high baryonic density. It is found that the major role is played by the competition between the strongly repulsive $(σ, ω)$ exchange term with virtual nucleon-antinucleon excitation and the large attractive contribution due to $(σ, ω)$ exchange with $N^*(1440)$ resonance excitation. The net result is a repulsive term which shifts the saturation density corresponding to the only two-body force much closer to the empirical value, while keeping constant the saturation energy per particle. The contribution from $(π, ρ)$ exchange 3BF is shown to be attractive and rather small. The analysis of the separate three-body force contributions allows to make a comparison with the prediction of Dirac-Brueckner approach which is supposed to incorporate via the {\it dressed} Dirac spinors the same virtual nucleon-antinucleon excitations as in the present three-body force. The numerical results suggest that the three-body force components missing from the Dirac-Brueckner approach are not negligible, especially at high density. The calculation of the nuclear mean field and the effective mass shows that the three-body force affects to a limited extent such properties.

12 pages 7 figures