Nuclear Matter from Effective Quark-Quark Interaction

We study neutron matter and symmetric nuclear matter with the quark-meson model for the two-nucleon interaction. The Bethe-Bruckner-Goldstone many-body theory is used to describe the correlations up to the three hole-line approximation with no extra parameters. At variance with other nonrelativistic realistic interactions, the three hole-line contribution turns out to be non-negligible and to have a substantial saturation effect. The saturation point of nuclear matter, the compressibility, the symmetry energy, and its slope are within the phenomenological constraints. Since the interaction also reproduces fairly well the properties of the three-nucleon system, these results indicate that the explicit introduction of the quark degrees of freedom within the considered constituent quark model is expected to reduce the role of three-body forces.

Figure 1

Different Goldstone diagrams contributing to the nuclear matter equation of state (EOS). The wavy line indicates Brueckner $G$-matrix. Diagrams corresponding to the two hole-line approximation are labeled (a) and (b). Diagram (d) is the first potential insertion in the hole-line expansion. Diagram (e) is the ring diagram, which includes long range correlations. The box labelled $T^{(3)}$ is the in-medium three-body scattering matrix. Diagram (c), usually indicated as ’’bubble diagram", is the first term of the set of diagrams obtained once the expansion of $T^{(3)}$ is inserted in (f) and it has been singled out for numerical convenience.

Figure 2

EOS of symmetric nuclear matter at the two-hole level of approximation (open symbols) and at the three hole-line level (full symbols) for the continuous (squares) and the gap (circles) choices, respectively.

Figure 3

The EOS of pure neutron matter at the three hole-line level of approximation with the QM potential in the continuous (full squares) and gap (full circles) choices. For comparison, one BHF EOS from Ref. [5] (dashed line) and the one of Ref. [9] (stars) are also reported. The latter two include three-body forces.

Figure 4

Blowup of Fig. 3 in the low density region. For comparison, the EOS from the chiral expansion of Ref. [40] (dashed-dotted line) has been reported. The area delimited by the thick full line indicates the region where the EOS predicted from the chiral approach of Ref. [41] should be enclosed.