ar X iv : 1 60 2 . 08 10 6 v 1 [ nu cl - t h ] 2 5 Fe b 20 16 Equation of state for neutron stars with hyperons by the variational method

We investigate the effects of the odd-state part of bare ΛΛ interactions on the structure of neutron stars (NSs) by constructing equations of state (EOSs) for uniform nuclear matter containing Λ and Σ hyperons with use of the cluster variational method. The isoscalar part of the Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are employed as the interactions between nucleons, whereas, as the bare ΛN and even-state ΛΛ interactions, two-body central potentials that are determined so as to reproduce the experimental data on singleand double-Λ hypernuclei are adopted. In addition, the ΣN interaction is constructed so as to reproduce the empirical single-particle potential of Σ in symmetric nuclear matter. Since the odd-state part of the ΛΛ interaction is not known owing to lack of experimental data, we construct four EOSs of hyperonic nuclear matter, each with a different odd-state part of the ΛΛ interaction. The EOS obtained for NS matter becomes stiffer as the odd-state ΛΛ interaction becomes more repulsive, and correspondingly the maximum mass of NSs increases. It is interesting that the onset density of Σ depends strongly on the repulsion of the odd-state ΛΛ interaction. Furthermore, we take into account the three-baryon repulsive force to obtain results that are consistent with observational data on heavy NSs.