Effective YN and YY interactions and hyperon-mixing in neutron star matter -: Y ≡ Λ case

Effective LambdaN and Lambda Lambda 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 Lambda in neutron star matter and the equation of state are analyzed. The Lambda -mixed phase is shown to appear in neutron star cores with a baryon number density rho greater than or similar to rho (t)(Lambda) similar or equal to (3 - 5) rho (0), where rho (l)(Lambda) is the threshold density for the Lambda -mixing and rho (0) is the normal nuclear matter density. The density rho (t)(Lambda) depends not only on the LambdaN but also on the NN interactions. The three-body force introduced in the NN interaction to reproduce the proper nuclear saturation properties enhances the Lambda -mixing and drastically softens the equation of state. The resulting equation of state is not consistent with the observed neutron star mass M-obs = 1.44 M.. It is found that this crucial problem can be resolved by the introduction of a three-body repulsion also for the LambdaN and Lambda Lambda interactions. The finite-temperature effect on the Lambda -mixing is found to be large, especially at lower densities and is expected to affect the properties of neutron stars at birth.