Neutron Stars 1: Equation of State and Structure

Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions

We provide convenient parametrizations of the high-density nuclear equation of state obtained within the Brueckner-Hartree-Fock approach using different modern nucleon-nucleon potentials together with compatible microscopic nuclear three-body forces. The corresponding neutron star mass-radius relations are also presented.

Neutron star structure with modern nucleonic three-body forces

We determine the structure of neutron stars within a Brueckner-Hartree-Fock approach based on realistic nucleon-nucleon, nucleon-hyperon, and hyperon-hyperon interactions. Our results indicate rather low maximum masses below 1.4 solar masses. This feature is insensitive to the nucleonic part of the EOS due to a strong compensation mechanism caused by the appearance of hyperons and represents thus strong evidence for the presence of nonbaryonic ``quark'' matter in the interior of heavy stars.

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Maximum mass of neutron stars

The YN results are presented from the extended soft-core (ESC) interactions. They consist of local and nonlocal potentials because of (i) one-boson exchanges (OBE), which are the members of nonets of pseudoscalar, vector, scalar, and axial mesons; (ii) diffractive exchanges; (iii) two-pseudoscalar exchange; and (iv) meson-pair exchange (MPE). Both the OBE and pair vertices are regulated by Gaussian form factors producing potentials with a soft behavior near the origin. The assignment of the cutoff masses for the baryon-baryon-meson (BBM) vertices is dependent on the SU(3) classification of the exchanged mesons for OBE and a similar scheme for MPE. The particular version of the ESC model, called ESC04 [T. A. Rijken, Phys. Rev. C 73, 044007 (2006)], describes nucleon-nucleon (NN) and hyperon-nucleon (YN) interactions in a unified way using broken SU(3) symmetry. Novel ingredients are the inclusion of (i) the axial-vector meson potentials and (ii) a zero in the scalar- and axial-vector meson form factors. These innovations made it possible for the first time to keep the parameters of the model close to the predictions of the ${}^{3}{P}_{0}$ quark-antiquark creation model. This is also the case for the $F/(F+D)$ ratios. Furthermore, the introduction of the zero helped to avoid the occurrence of unwanted bound states. Broken SU(3) symmetry serves to connect the NN and the YN channels, which leaves after fitting NN only a few free parameters for the determination of the YN interactions. In particular, the meson-baryon coupling constants are calculated via SU(3) using the coupling constants of the NN analysis as input. Here, as a novel feature, medium-strong flavor-symmetry breaking (FSB) of the coupling constants was allowed, using the ${}^{3}{P}_{0}$ model with a Gell-Mann-Okubo hypercharge breaking for the BBM coupling. Very good fits for ESC model with and without FSB were obtained. The charge-symmetry breaking in the $\ensuremath{\Lambda}p$ and $\ensuremath{\Lambda}n$ channels, which is an SU(2) isospin breaking, is included in the OBE, TME, and MPE potentials. Simultaneous fits to the NN- and the YN-scattering data are described, using different options for the ESC model. For the selected 4233 NN data with energies $0\ensuremath{\le}{T}_{\mathrm{lab}}\ensuremath{\le}350$ MeV, a ${\ensuremath{\chi}}^{2}/{N}_{\mathrm{data}}=1.22$ was typically reached. For the usual set of 35 YN data and 3 ${\ensuremath{\Sigma}}^{+}p$ cross sections from a recent KEK experiment E289 ${\ensuremath{\chi}}^{2}/{\mathit{YN}}_{\mathrm{data}}\ensuremath{\approx}0.63$ was obtained. In particular, we were able to fit the precise experimental datum ${r}_{R}=0.468\ifmmode\pm\else\textpm\fi{}0.010$ for the inelastic capture ratio at rest rather well. The four versions (a,b,c, and d) of ESC04 presented in this article, give different results for hypernuclei. The reported G-matrix calculations are performed for YN ($\ensuremath{\Lambda}N,\ensuremath{\Sigma}N,\ensuremath{\Xi}N$) pairs in nuclear matter. The obtained well depths (${U}_{\ensuremath{\Lambda}},{U}_{\ensuremath{\Sigma}},{U}_{\ensuremath{\Xi}}$) reveal distinct features of ESC04a--d. The $\ensuremath{\Lambda}\ensuremath{\Lambda}$ interactions are demonstrated to be consistent with the observed data of ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{6}$He. The possible three-body effects are investigated by considering phenomenologically the changes of the vector-meson masses.

H. Q. Song

Papers

High density symmetric nuclear matter in the Bethe-Brueckner-Goldstone approach