Effective YN and YY Interactions and Hyperon-Mixing in Neutron Star Matter: Y Case

Abstract

Effective ΛN and ΛΛ interactions in dense hyperonic nuclear matter are constructed on the basis of the G-matrix calculation with Nijmegen hard-core potentials. With these effective interactions, the mixing of Λ in neutron star matter and the equation of state are analyzed. The Λ-mixed phase is shown to appear in neutron star cores with a baryon number density ρ≳ρ_t(Λ)≃(3–5)ρ₀, where ρ_t(Λ) is the threshold density for the Λ-mixing and ρ₀ is the normal nuclear matter density. The density ρ_t(Λ) depends not only on the ΛN but also on the NN interactions. The three-body force introduced in the NN interaction to reproduce the proper nuclear saturation properties enhances the Λ-mixing and drastically softens the equation of state. The resulting equation of state is not consistent with the observed neutron star mass M_obs=1.44M_⊙. It is found that this crucial problem can be resolved by the introduction of a three-body repulsion also for the ΛN and ΛΛ interactions. The finite-temperature effect on the Λ-mixing is found to be large, especially at lower densities and is expected to affect the properties of neutron stars at birth.