Equation of State of Neutron-Rich Matter in $d$-Dimensions

Abstract

Nuclear systems under constraints, with high degrees of symmetries and/or collectivities may be considered as moving effectively in spaces with reduced spatial dimensions. We first derive analytical expressions for the nucleon specific energy $E_0(\rho )$, pressure $P_0(\rho )$, incompressibility coefficient $K_0(\rho )$ and skewness coefficient $J_0(\rho )$ of symmetric nucleonic matter (SNM), the quadratic symmetry energy $E_{\mathrm{sym}}(\rho )$, its slope parameter $L(\rho )$ and curvature coefficient $K_{\mathrm{sym}}(\rho )$ as well as the fourth-order symmetry energy $E_{\mathrm{sym},4}(\rho )$ of neutron-rich matter in general $d$ spatial dimensions (abbreviated as "$d$D") in terms of the isoscalar and isovector parts of the isospin-dependent single-nucleon potential according to the generalized Hugenholtz-Van Hove (HVH) theorem. The equation of state (EOS) of nuclear matter in $d$D can be linked to that in the conventional 3-dimensional (3D) space by the $\epsilon$-expansion which is a perturbative approach successfully used previously in treating second-order phase transitions and related critical phenomena and more recently in studying the EOS of cold atoms. The $\epsilon$-expansion of nuclear EOS in $d$D based on a reference dimension $d_{\mathrm{f}}=d-\epsilon$ is shown to be effective with $-1\lesssim \epsilon \lesssim 1$ starting from $1\lesssim d_{\mathrm{f}}\lesssim 3$ in comparison with the exact expressions derived using the HVH theorem. Moreover, the EOS of SNM (with/without considering its potential part) is found to be reduced (enhanced) in lower (higher) dimensions, indicating in particular that the many-nucleon system tends to be deeper bounded but saturate at higher densities in spaces with lower dimensions. The links between the EOSs in 3D and $d$D spaces from the $\epsilon$-expansion provide new perspectives to the EOS of neutron-rich matter.

With minor revisions and a new figure. Accepted by Annals of Physics

References in corpus (52)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Neutron Star Observations: Prognosis for Equation of State Constraints
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• Sound velocity bound and neutron stars
• Momentum sharing in imbalanced Fermi systems
• Neutron Stars and the Nuclear Equation of State
• Verification of universal relations in a strongly interacting Fermi gas
• Emergence of a Turbulent Cascade in a Quantum Gas
• New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids
• The Dynamics of Binary Neutron Star Mergers and of GW170817
• Progress in Constraining Nuclear Symmetry Energy Using Neutron Star Observables Since GW170817
• Incompressibility in finite nuclei and nuclear matter
• Quantum Gases in Optical Boxes
• Towards Understanding Astrophysical Effects of Nuclear Symmetry Energy
• Astrophysical Constraints on the Symmetry Energy and the Neutron Skin of ${}^{208}$Pb with Minimal Modeling Assumptions
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Epsilon expansion for a Fermi gas at infinite scattering length
• Chiral Effective Field Theory and the High-Density Nuclear Equation of State
• Modified Structure of Protons and Neutrons in Correlated Pairs
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Symmetry Energy of Nucleonic Matter With Tensor Correlations
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Observation of a non-Hermitian phase transition in an optical quantum gas
• Bayesian Inference of the Symmetry Energy of Super-Dense Neutron-Rich Matter from Future Radius Measurements of Massive Neutron Stars
• Observation of first and second sound in a BKT superfluid
• Momentum Distribution and Contact of the Unitary Fermi gas
• Neutron-proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon-nucleus scattering data within an isospin dependent optical model
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Interdependence of different symmetry energy elements
• Higher-order symmetry energy and neutron star core-crust transition with Gogny forces
• Spin-charge separation in a 1D Fermi gas with tunable interactions
• Contact and sum-rules in a near-uniform Fermi gas at unitarity
• New Results on Short-Range Correlations in Nuclei
• What do we mean by the dimensionality of behavior?
• Laser cooling for quantum gases
• Density-dependent nucleon-nucleon interaction from three-nucleon forces
• Quantum Monte Carlo Study of a Resonant Bose-Fermi Mixture
• Next-to-next-to-leading-order epsilon expansion for a Fermi gas at infinite scattering length
• A two-dimensional Fermi liquid with attractive interactions
• Imprints of high-momentum nucleons in nuclei on hard photons from heavy-ion collisions around the Fermi Energy
• Compressibility and the Equation of State of an Optical Quantum Gas in a Box
• Dark matter component in hadronic models with short-range correlations
• Constraints on Nuclear Saturation Properties from Terrestrial Experiments and Astrophysical Observations of Neutron Stars
• Nuclear matter fourth-order symmetry energy in non-relativistic mean-field models
• Probing proton transition momentum in neutron-rich matter
• Searching for three-nucleon short-range correlations
• Embedding short-range correlations in relativistic density functionals through quasi-deuterons
• Investigating Effects of Relativistic Kinematics, Dimensionality, Interactions, and Short-Range Correlations on the Ratio of Quartic over Quadratic Nuclear Symmetry Energies
• Scattering Hypervolume of Fermions in Two Dimensions
• A search for effects of short range correlations in proton spectra from collisions induced by 47 MeV/u projectiles

Cited by in corpus (6)

• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Recent astrophysical observations reproduced by a short-range correlated van der Waals-type model?
• Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
• High-order isospin-dependent surface tension contribution to the fourth-order symmetry energy of finite nuclei
• Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues
• Effects of short-range correlations at high densities on neutron stars with and without DM content: role of the repulsive self-interaction