Energy of neutron-star matter

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It is generally believed that the interior of some neutron stars is dense enough that the neutron-star matter (NSM) contains not only neutrons, but also protons, electrons, and various hyperons. In the present paper we calculate the effect of some hyperons on the composition and energy of the NSM. We calculate the energy per baryon and the fractions of the various baryons present, as a function of the baryon density, ranging from 0.1 to 2 baryons per fm3, using two slightly different modifications of the Reid-soft-core interaction, one developed by Sawada and Wong, and the other by Campi and Sprung. The interaction energies are based on reaction matrix calculations by the above authors. We consider first a pure neutron gas. However, even at subnuclear densities (<= 0.15 baryons per fm3) it is generally agreed that there are protons present (and also electrons to keep the system neutral.) We calculate the effect of the protons (which constitute less than 10% of the baryons) on the energy. We then study the effect of what, we believe, are the most important hyperons, namely, Σ-, Λ, Δ-, to the composition and energy. The baryon-baryon interaction energies are assumed to be essentially the same as those between nucleons, except that (1) the interaction energy is different between like baryons (ΛΛ or pp) and unlike baryons (ΛΣ- or np); and (2) there is a special factor of 2/3 in the strengths of the long-range attractive part of the hyperon-nucleon interaction, as compared to the nucleon-nucleon interaction. The latter is argued on the basis of a quark model. On the other hand, the short-range repulsive part of the interaction is assumed to be the same between all baryon pairs. Four different models are used. One of our main conclusions is that, in the most realistic of the four models used here, there are relatively few protons and hyperons present (no more than 15% of each species even at the highest density considered) and the energy is only slightly less than for a pure neutron gas (20% and 10%, respectively, for the Sawada-Wong and Campi-Sprung interactions). Finally, we calculate the magnetic susceptibility of NSM treated as a pure neutron gas with Sawada-Wong interaction energies. No evidence of a transition to ferromagnetism is found.

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