In the framework of the Brueckner-Bethe-Goldstone theory, we determine a fully microscopic equation of state for asymmetric and $\beta$-stable nuclear matter containing $\sim$ and $\la$ hyperons. We use the Paris and the new Argonne $Av_{18}$ two-body nucleon interaction, whereas the nucleon-hyperon interaction is described by the Njimegen soft-core model. We stress the role played by the three-body nucleon interaction, which produces a strong repulsion at high densities. This enhances enormously the hyperon population, and produces a strong softening of the equation of state, which turns out almost independent on the nucleon-nucleon interaction. We use the new equation of state in order to calculate the structure of static neutron stars. We obtain a maximum mass configuration with $M_{\rm max}$ = 1.26 (1.22) when the Paris ($Av_{18}$) nucleon potential is adopted. Central densities are about 10 times normal nuclear matter density. Stellar rotations, treated within a perturbative approach, increase the value of the limiting mass by about 12%.Comment: 16 pages, latex, 10 figures, submitted to Phys. Rev.

We study the hadron-quark phase transition in the interior of neutron stars (NS's). We calculate the equation of state (EOS) of hadronic matter using the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by using the indications coming from the recent experimental results obtained at the CERN SPS on the formation of a quark-gluon plasma. We find necessary to introduce a density dependent bag parameter, and the corresponding consistent thermodynamical formalism. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, 1.4 M ⊙ ≤ M max ≤ 1.7 M ⊙ . The precise value of the maximum mass turns out to be only weakly correlated with the value of the energy density at the assumed transition point in nearly symmetric nuclear matter.

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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. PACS number(s): 26.60. Kp, 21.45.Ff, 21.65.Mn, 24.10.Cn Introduction. The theoretical investigation of dense stellar objects like neutron stars and supernovae requires the knowledge of the nucleonic equation of state (EOS) up to densities of about ten times normal nuclear density ρ 0 = 0.17 fm −3 . At these densities nucleonic three-body forces (TBF) contribute an important or even dominant part to the effective in-medium nucleon-nucleon interaction that is used within the different theoretical approaches like Brueckner-Hartree-Fock (BHF)Consequently for reliable predictions theoretically wellcontrolled and consistent TBF are required. At present the theoretical status of microscopically derived TBF is still quite rudimentary: In most approaches semi-phenomenological TBF are used that involve several free parameters which are just fitted to the relevant data [4][5][6][7][8]. An important theoretical constraint is the consistency with a given two-body force, i.e., both two-body and three-body forces should be based on the same theoretical footing and use the same microscopical parameters in their construction.We present in this report new results obtained within this framework, namely using meson-exchange TBF that employ the same meson-exchange parameters as an underlying nucleon-nucleon potential. In particular we show results based on the Argonne V 18 (V18) [9], the Bonn B (BOB) [10], and the Nijmegen 93 (N93) [11] potentials. For completeness we compare with results obtained with the widely used phenomenological Urbana-type (UIX) TBF [6,8] (in combination with the V 18 potential).Our theoretical approach for calculating the EOS based on these interactions is the BHF formalism, for which the inclusion of TBF has been shown to be the dominant missing many-body effect [12][13][14], while three-hole line corrections are known to be small [15].This Brief Report is based on Ref. [14], where detailed information on the construction of the microscopic TBF is given, and extends Ref. [16], where previous results obtained with the V 18 were presented. We begin with a short overview of the necessary formalism.Formalism. At the present state of the art of the BHF approach, in order to avoid the very difficult problem of solving the relevant Faddeev equations as for the threehole-line corrections, the TBF is reduced to an effective, density-dependent, two-body force by averaging over the third nucleon in the medium, the average being weighted by the BHF

We analyze the different possibilities for the hadron-quark phase transition occurring in beta-stable matter including hyperons in neutron stars. We use a Brueckner-Hartree-Fock approach including hyperons for the hadronic equation of state and a generalized MIT bag model for the quark part. We then point out in detail the differences between Maxwell and Gibbs phase transition constructions including the effects of surface tension and electromagnetic screening. We find only a small influence on the maximum neutron star mass, whereas the radius of the star and in particular its internal structure are more affected.

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. The only way to obtain information on the structure and properties of baryonic matter at extreme densities of several times normal nuclear matter density ρ 0 ≈ 0.17 fm −3 seems to be the theoretical modelling of neutron stars, the unique environment where such densities are actually reached in nature, and the subsequent confrontation with observational data. Any given equation of state (EOS) of baryonic matter determines uniquely the mass-radius relation of neutron star sequences and in particular the maximum mass a neutron star can achieve before collapsing into a black hole.Most theoretical investigations performed so far point to an important feature of high-density β-stable matter, namely that hyperons will appear at densities of about 2, . . . , 3 ρ 0 and strongly soften the EOS. The main consequence is a substantial reduction of the maximum mass [1]. This seems to be an inevitable feature of any approach taking into account the hyperons, caused simply by the availability of additional degrees of freedom of the matter at high density. Any theoretical study of neutron stars without allowing for the presence of hyperons is therefore unrealistic.Evidently it is then important to carry out microscopic calculations as precisely as possible in order to make reliable predictions for the maximum mass of a neutron star composed of baryonic matter and the eventual confrontation with observational data. In this work we report on recent results following this motivation. We try to present strong evidence that the maximum mass of baryonic neutron stars is very low and that therefore neutron stars with larger masses (above ca. 1.5 solar masses) must necessarily contain quark matter.Our theoretical framework is the nonrelativistic BruecknerHartree-Fock (BHF) approach based on microscopic nucleonnucleon (NN), nucleon-hyperon (NY), and hyperon-hyperon (YY) potentials that are fitted to scattering phase shifts, where possible. Nucleonic three-body forces (TBF) are included in order to (slighty) shift the saturation point of purely nucleonic matter to the empirical value.It has been demonstrated that the theoretical basis of the BHF method, the hole-line expansion, is well founded: the nuclear EOS can be calculated with good accuracy in the BHF two hole-line approximation with the continuous choice for the single-particle potential, since the results in this scheme are quite close to the full convergent calculations which include also the three hole-line contribution [2]. Due to these facts, combined with the absence of adjustable parameter...

We perform Brueckner-Hartree-Fock calculations of hypernuclear matter employing the recent Nijmegen ESC08 hyperon-nucleon potentials, provide useful parametrizations of the numerical results, and compute the structure of hyperon (neutron) stars within this approach. Very low maximum masses below 1.4 solar masses are found.