Investigating Effects of Relativistic Kinematics, Dimensionality, Interactions, and Short-Range Correlations on the Ratio of Quartic over Quadratic Nuclear Symmetry Energies

Abstract

While ample evidence for the so-called empirical parabolic law of the Equation of State (EOS) of isospin asymmetric nuclear matter (ANM) has been obtained in many studies within both non-relativistic and relativistic nuclear many-body theories using various interactions, it has been unclear if there is any fundamental physics reason for the small quartic symmetry energy compared to the quadratic one even as the ANM approaches pure neutron matter. Within both relativistic and non-relativistic Free Fermi Gas (FFG) models in coordinate spaces of arbitrary dimension $d$ with and without considering Short-Range Correlations (SRC) as well as non-linear Relativistic Mean Field (RMF) models, we study effects of relativistic kinematics, dimensionality, interactions and SRC on the ratio $\Psi (\rho )$ of quartic over quadratic symmetry energies in ANM EOSs. We found that the ratio $\Psi (\rho )$ in the FFG model depends strongly on the dimension $d$. While it is very small already in the normal 3D space, it could be even smaller in spaces with reduced dimensions for sub-systems of particles in heavy-ion reactions and/or whole neutron stars due to constraints, collectivities and/or symmetries. We also found that the ratio $\Psi (\rho )$ could theoretically become very large only at the ultra-relativistic limit far above the density reachable in neutron stars. On the other hand, nuclear interaction directly and/or indirectly through SRC-induced high-momentum nucleons affect significantly the density dependence of $\Psi (\rho )$ compared to the relativistic FFG model prediction. The SRC affects significantly not only the kinetic energy of symmetric nuclear matter but also the ratio $\Psi (\rho )$ while the relativistic corrections are found negligible. The results may help better understand the EOS of dense neutron-rich matter.

A few wording modifications. Phys. Rev. C (2022) in press

References in corpus (26)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Neutron-Rich Nuclei in Heaven and Earth
• Momentum sharing in imbalanced Fermi systems
• Progress in Constraining Nuclear Symmetry Energy Using Neutron Star Observables Since GW170817
• Towards Understanding Astrophysical Effects of Nuclear Symmetry Energy
• Two-dimensional Bose-Einstein condensate in an optical surface trap
• Modified Structure of Protons and Neutrons in Correlated Pairs
• Symmetry Energy of Nucleonic Matter With Tensor Correlations
• Universal Fermi gases in mixed dimensions
• Probing the core of the strong nuclear interaction
• The High-Density Symmetry Energy and Direct Urca
• Higher-order symmetry energy and neutron star core-crust transition with Gogny forces
• Density-dependent nucleon-nucleon interaction from three-nucleon forces
• Quantum Monte Carlo Study of a Resonant Bose-Fermi Mixture
• Effects of short-range correlation reduced kinetic symmetry energy in heavy-ion collisions at intermediate energies
• An numerical approach for finite volume three-body interaction
• The isospin quartic term in the kinetic energy of neutron-rich nucleonic matter
• Imprints of high-momentum nucleons in nuclei on hard photons from heavy-ion collisions around the Fermi Energy
• Short-range correlations effects on the deformability of neutron stars
• Dark matter component in hadronic models with short-range correlations
• The interplay of short-range correlations and nuclear symmetry energy in hard photon productions from heavy-ion reactions at Fermi energies
• Nuclear matter fourth-order symmetry energy in non-relativistic mean-field models
• Probing proton transition momentum in neutron-rich matter
• $d$-dimensional Lüscher's formula and the near-threshold three-body states in a finite volume
• A search for effects of short range correlations in proton spectra from collisions induced by 47 MeV/u projectiles

Cited by in corpus (10)

• Dense Nuclear Matter Equation of State from Heavy-Ion Collisions
• Dark matter effects on tidal deformabilities and moment of inertia in a hadronic model with short-range correlations
• Dark particle mass effects on neutron star properties from a short-range correlated hadronic model
• Novel Scalings of Neutron Star Properties from Analyzing Dimensionless Tolman--Oppenheimer--Volkoff Equations
• Equation of State of Neutron-Rich Matter in $d$-Dimensions
• Impact of quadrupole deformation on intermediate-energy heavy-ion collisions
• 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
• Effects of short-range correlations at high densities on neutron stars with and without DM content: role of the repulsive self-interaction
• Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues