Equation of State of Dense Matter: Pauli Degeneracy, Pairing Correlations, and Implications for Neutron Stars

Abstract

We develop a unified description of dense fermionic matter that consistently incorporates Pauli degeneracy, interaction effects, and pairing correlations. The condition that the temperature is much smaller than the Fermi energy leads to a natural separation among the Sommerfeld, Fermi-liquid, and pairing regimes. We show how these contributions enter the equation of state. The resulting EOS is applied to the Tolman-Oppenheimer-Volkoff equations to analyze neutron-star structure. We demonstrate that Pauli degeneracy provides the dominant pressure, interactions determine the stiffness of the EOS, and pairing correlations produce subleading but potentially significant corrections, especially in quark matter. Implications for mass-radius constraints and modern observations are discussed. The quasiparticle interaction in the normal Fermi-liquid phase is parameterized by the isotropic Landau parameter F_0^s and linked explicitly to the compressibility and sound speed. The theoretical mass-radius curves are compared with four recent NICER measurements.

Comments: 13 pages, 5 figures, 2 tables. Proceedings of the XXIV Ukrainian Scientific and Practical Conference "Theoretical and Applied Problems of Physics, Mathematics and Informatics" (Kyiv, May 13--16, 2026)