We determine the coupling constants of $Sigma$ hyperon with mesons in relativistic mean field (RMF) models using $Sigma^-$ atomic shift data and examine the effects of $Sigma$ on the neutron star maximum mass. We find that we need to reduce the vecto
r-isovector meson coupling with $Sigma$ ($g_{rhoSigma}$) from the value constrained by the SU(3)v symmetry in order to explain the $Sigma^-$ atomic shifts for light symmetric and heavy asymmetric nuclei simultaneously. With the atomic shift fit value of $g_{rhoSigma}$, $Sigma^-$ can emerge in neutron star matter overcoming the repulsive isoscalar potential for $Sigma$ hyperons. Admixture of $Sigma^-$ in neutron stars is found to reduce the neutron star maximum mass slightly.
We systematically investigate the vacuum stability and nuclear properties in the effective chiral model with higher order terms in $sigma$. We evaluate the model parameters by considering the saturation properties of nuclear matter as well as the nor
mal vacuum to be globally stable at zero and finite baryon densities. We can find parameter sets giving moderate equations of state, and apply these models to finite nuclei.
We develop a chiral SU(3) symmetric relativistic mean field (RMF) model with a logarithmic potential of scalar condensates. Experimental and empirical data of symmetric nuclear matter saturation properties, bulk properties of normal nuclei, and separ
ation energies of single- and double-$Lambda$ hypernuclei are well explained. The nuclear matter equation of state (EOS) is found to be softened by $sigmazeta$ mixing which comes from determinant interaction. The neutron star matter EOS is further softened by $Lambda$ hyperons.
We present sets of equation of state (EOS) of nuclear matter including hyperons using an SU_f(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature, and charge fraction for numerical simulations of core collapse
supernovae. Coupling constants of Sigma and Xi hyperons with the sigma meson are determined to fit the hyperon potential depths in nuclear matter, U_Sigma(rho_0) ~ +30 MeV and U_Xi(rho_0) ~ -15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al., in which formation of finite nuclei is included in the Thomas-Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17 M_sun (Ne mu) to 1.63 M_sun (NYe mu) when hyperons are included. In a spherical, adiabatic collapse of a 15$M_odot$ star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T > 40 MeV or rho_B > 0.4 fm^{-3}).
