coupling constants; For neutron star matter consisting of a neutral mixture of baryons and leptons, the β - equilibrium conditions without trapped neutrinos are given by The scalar coupling constants are chosen to give reasonable hyperon potentials. We de- note the potential depth of the hyperon species i in the matter of the baryon species j by U ( j ) i . It is estimated from the experimental data of single-Λ hypernuclei that the potential depth of a Λ in saturated nuclear matter should be around U ( N ) Λ ≃ − 30 MeV [47]. For Σ hyperons, the analysis of Σ atomic experimental data suggests that Σ-nucleus potentials have a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption. In recent theoretical works, the Σ potential in saturated nuclear mat- ter is considered to be repulsive with a strength of about 30 MeV [18, 47]. Some recent developments in hypernuclear physics suggest that Ξ hyperons in saturated nuclear matter have an attraction of around 15 MeV [18, 48]. In this article, we adopt U ( N ) Λ = − 30 MeV, U ( N ) Σ = +30 MeV, and U ( N ) Ξ = − 15 MeV to determine the scalar coupling constants. We obtain, for the TM1 (NL3) parameter set, g$_{σ}$$_{Λ}$ = 6 . 228 (6.323), g$_{σ}$$_{Σ}$ = 4 . 472 (4.709), and g$_{σ}$$_{Ξ}$ = 3 . 114 (3.161), respectively. The hyperon couplings to the hidden-strangeness meson σ ∗ are restricted by the relation U (Ξ) Ξ ≈ U (Ξ) Λ ≈ 2 U (Λ) Ξ ≈ 2 U (Λ) Λ obtained in Ref. [49]. The weak Y Y interaction implied by the Nagara event suggests U (Λ) Λ ≃ − 5 MeV, and hence we obtain g$_{σ}$ ∗ Λ = 5 . 499 (5.678) and g$_{σ}$ ∗ Ξ = 11 . 655 (11.899) for the TM1 (NL3) parameter set. We assume g$_{σ}$ ∗ Σ = g$_{σ}$ ∗ Λ and take m$_{σ}$ ∗ = 980 MeV and m$_{φ}$ = 1020 MeV in this article. where µ$_{i}$ is the chemical potential of species i . At zero temperature, the chemical potentials µ$_{p}$ = µ$_{Σ}$ + = µ$_{n}$ − µ$_{e}$, (8) µ$_{Λ}$ = µ$_{Σ}$ 0 = µ$_{Ξ}$ 0 = µ$_{n}$, (9) µ$_{Σ}$ − = µ$_{Ξ}$ − = µ$_{n}$ + µ$_{e}$, (10) µ$_{µ}$ = µ$_{e}$, (11) 7 1 3 g$_{ωN}$ = 1 2 g$_{ω}$$_{Λ}$ = 1 2 g$_{ω}$$_{Σ}$ = g$_{ω}$$_{Ξ}$, g$_{ρN}$ = 1 2 g$_{ρ}$$_{Σ}$ = g$_{ρ}$$_{Ξ}$, g$_{ρ}$$_{Λ}$ = 0 , 2 g$_{φ}$$_{Λ}$ = 2 g$_{φ}$$_{Σ}$ = g$_{φ}$$_{Ξ}$ = − $_{2}$√$_{2}$ 3 g$_{ωN}$, g$_{φN}$ = 0 . (7)