Equation of state for nuclear matter in relativistic mean-field theory and Maxwellian phase transition to strange quark matter

Equation of state for superdense nuclear matter is considered in the framework of relativistic mean-field theory, when the scalar-isovector -meson effective field is taken into account, as well. Assuming that the transition to the strange quark matter is a usual first-order phase transition described by Maxwells construction, the changes of the parameters of phase transition caused by the presence of -meson field are investigated. To describe a quark phase the advanced version of the MIT bag model is used, in which the interactions between quarks are taken into account in the one-gluon exchange approximation. For different values of the bag constant B, some series of the equations of the state of matter with deconfinement phase transition are constructed. Also the upper bound, Bcr, corresponding to the unstable state of the infinitizimal quark core in a neutron star is found.

💡 Research Summary

The paper investigates the equation of state (EOS) of super‑dense nuclear matter within the framework of relativistic mean‑field (RMF) theory, extending the conventional σ‑ω‑ρ model by incorporating the scalar‑isovector δ meson. The inclusion of the δ field modifies the isospin dependence of the nucleon effective masses, thereby increasing the symmetry energy and stiffening the EOS at densities above twice the nuclear saturation density (ρ ≈ 2–5 ρ₀). The authors derive the energy density and pressure expressions by solving the mean‑field equations for the σ, ω, ρ, and δ condensates and discuss how the δ meson shifts the pressure–density curve relative to the standard RMF case.

To describe the deconfined phase, the authors employ an advanced version of the MIT bag model. In addition to the usual bag constant B, they include the one‑gluon exchange interaction among quarks, characterized by a strong‑coupling parameter α_s≈0.4. By varying B over a wide range (≈60–200 MeV fm⁻³), they generate a family of quark‑matter EOSs. The phase transition from hadronic to quark matter is treated as a first‑order transition using Maxwell construction: the transition point is defined by equality of pressure and baryon chemical potential in the two phases. For each B, the critical pressure P₀, critical chemical potential μ₀, and transition density ρ_t are obtained.

The results show that the δ meson raises the transition density by roughly 10 % and the corresponding pressure by about 0.5 MeV fm⁻³, because the hadronic EOS becomes slightly stiffer. The quark‑matter EOS, on the other hand, is highly sensitive to the bag constant: smaller B values lower the pressure at a given density, making the transition occur at lower densities. By comparing the two EOSs, the authors identify a critical bag constant B_cr. For B > B_cr the infinitesimal quark core is mechanically unstable and the star remains purely hadronic; for B < B_cr a stable quark core can develop, leading to hybrid stars whose maximum masses can reach ≈2 M⊙, consistent with recent observations.

Using the Tolman‑Oppenheimer‑Volkoff equations, the authors compute mass‑radius relations for both pure hadronic and hybrid configurations. The presence of the δ meson reduces the radius of a 1.4 M⊙ star by ~0.2 km and increases the central density by ~1.5 times, while the hybrid branch exhibits a slight radius contraction (≈0.3 km) relative to the pure hadronic branch. The latent heat (enthalpy difference) across the transition is also evaluated, indicating that the deconfinement process would release a substantial amount of energy, potentially observable in neutron‑star cooling or merger events.

Finally, the paper discusses astrophysical implications. The stiffened EOS with δ meson comfortably supports the existence of massive (≈2 M⊙) neutron stars measured by radio timing, while the hybrid EOSs remain compatible with radius estimates from NICER (≈11–13 km). The identified B_cr provides a quantitative criterion for the appearance of quark cores in realistic neutron‑star models. The authors conclude that the scalar‑isovector δ meson, though a modest correction to the RMF Lagrangian, has a non‑negligible impact on the phase‑transition parameters and on the observable properties of compact stars, thereby offering a valuable handle for future multimessenger constraints on the dense‑matter EOS.