Nuclear matter equation of state from a quark-model nucleon-nucleon interaction

Starting from a realistic constituent quark model for the nucleon-nucleon interaction, we derive the equation of state (EOS) of nuclear matter within the Bethe-Brueckner-Goldstone approach up to the three-hole-line level, without the need to introduce three-nucleon forces. To estimate the uncertainty of the calculations both the gap and the continuous choices for the single-particle potential are considered and compared. The resultant EOS is compatible with the phenomenological analysis of the saturation point, the incompressibility, the symmetry energy at a low density, and its slope at saturation, together with the high-density pressure extracted from flow data on heavy-ion collisions. Although the symmetry energy is appreciably higher in the gap choice in the high-density region, the maximum neutron star masses derived from the continuous-choice EOS and the gap-choice EOS are similar and close to two solar masses, which is again compatible with recent observational data. A comparison with other microscopic equations of state is presented and discussed.

Figure 1

Phase shifts of the energy-independent Gaussian fss2 potential up to the energy $T_{\text{lab}}\le 350$ MeV (solid black curves) compared with the results for the Argonne V18 [52] [long-dashed (red) curves)] and CD-Bonn [53] [short-dashed (blue) curves] potentials. Symbols show results from the Nijmegen multienergy phase shift analysis [54, 55] and Arndt's $np$ phase shift analyses [56, 57, 58, 59].

Figure 2

Deuteron wave functions $u\left(r\right)=u_{0\alpha }\left(r\right)$ and $w\left(r\right)=u_{2\alpha }\left(r\right)$ predicted by the energy-independent Gaussian potential based on fss2 (solid black curve) compared with CD-Bonn [dashed (blue) curve] [53].

Figure 3

Same as Fig. 2, but for deuteron wave functions in momentum space $qu\left(q\right)=q{f}_{0\alpha }\left(q\right)$ and $qw\left(q\right)=q{f}_{2\alpha }\left(q\right)$.

Figure 4

Goldstone diagrams contributing to the nuclear matter EOS. Diagrams (a) and (b) correspond to the BHF calculation. The sum of the other diagrams gives the three-hole-line contribution. For details, please see the text.

Figure 5

The energy per particle of SNM (top) and PNM (bottom) for several EOSs as a function of the baryon density. Curves FSS2 (CC) and FSS2 (GC) show the calculated fss2 EOS with the continuous and gap choice, respectively. Curve $A{v}_{18}+\mathrm{UIX}$ refers to the BHF calculation using Argonne V18 plus Urbana IX TBFs from Refs. [8] and [9], curve APR is the variational calculation from Ref. [2], curve $A{v}_{18}+\mathrm{micro}$ TBF is the BHF calculation from Refs. [10] and [11], and curve DBHF is the relativistic DBHF calculation from Ref. [3].

Figure 6

Pressure of symmetric matter for several EOSs. The larger shaded (yellow) and smaller shaded (violet) bands represent the phenomenological constraints from experimental data. See text for details.

Figure 7

Symmetry energy for several EOSs.

Figure 8

Symmetry energy at a low density. The shaded (yellow) band represents recent constraints [81] and the solid (brown) line shows the region restricted by the neutron skin data, whereas the different curves are the results of the microscopic many-body methods.

Figure 9

${L=3\rho (\partial S/\partial \rho )|}_{\rho ={\rho }_0}$ versus symmetry energy at saturation $S_0$, predicted by several EOSs. See text for details of the experimental constraints.

Figure 10

(a) Proton fraction $x_p$, (b) pressure $P$, and (c) speed of sound (in units of $c$) of $\beta$-stable nuclear matter for several EOSs as a function of the baryon density $\rho$.

Figure 11

Neutron star mass as a function (a) of the radius or (b) of the central baryon density for several EOSs. Thin lines indicate results obtained with purely nucleonic EOSs, whereas thick lines show results for several EOSs including hyperons. See text for details.