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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 single- and double-$Λ$ hypernuclei are adopted. In addition, the $Σ^- N$ 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.