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Li, B. Nuclear Symmetry Energy. Encyclopedia. Available online: https://encyclopedia.pub/entry/12626 (accessed on 04 December 2023).

Li B. Nuclear Symmetry Energy. Encyclopedia. Available at: https://encyclopedia.pub/entry/12626. Accessed December 04, 2023.

Li, Bao-An. "Nuclear Symmetry Energy" *Encyclopedia*, https://encyclopedia.pub/entry/12626 (accessed December 04, 2023).

Li, B.(2021, July 31). Nuclear Symmetry Energy. In *Encyclopedia*. https://encyclopedia.pub/entry/12626

Li, Bao-An. "Nuclear Symmetry Energy." *Encyclopedia*. Web. 31 July, 2021.

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Nuclear symmetry energy is a measure of the energy cost to make nuclear systems more neutron rich. It depends on the density of the system. Information about the density dependence of nuclear symmetry energy has broad ramifications on the mechanisms of supernova explosions, properties of neutron stars and gravitational waves from their mergers. It is also important for understanding properties of nuclei as well as the dynamics and products of their collisions in laboratory experiments.

equation of state
symmetry energy
neutron stars
Bayesian analysis
quark–hadron phase transition
tidal deformability
GW170817
GW190814
PSR J0740+6620
PSR J0030+0451

The Equation of State (EOS) of uniform neutron-rich nucleonic matter of isospin asymmetry δ = (ρ_{n}− ρ_{p})/ρ and density ρ can be expressed in terms of the energy per nucleon E(ρ, δ) within the parabolic approximation as ^{[1]}^{[2]}^{[3]}^{[4]}.

where E_{s}_{ym}(ρ) ≈ E(ρ, 1) − E(ρ, 0) is the symmetry energy of asymmetric nuclear matter (ANM). It is approximately the energy cost of converting symmetric nuclear matter (SNM, with equal numbers of protons and neutrons) into pure neutron matter (PNM). Many interesting questions including the dynamics of supernova explosions, heavy-ion collisions, structures of neutron stars and rare isotopes, frequencies and strain amplitudes of gravitational waves from both isolated pulsars and collisions involving neutron stars all depend critically on the EOS of neutron-rich nucleonic matter. Thanks to the great eﬀorts of scientists in both nuclear physics and astrophysics over the last four decades, much knowledge about the EOS of SNM, i.e, the E(ρ, 0) term in Eq. (1), has been obtained. In more recent years, significant eﬀorts have been devoted to exploring the poorly known E_{sym}(ρ) using both terrestrial laboratory experiments and astrophysical observations. Theoretically, essentially all available nuclear forces have been used to calculate the E_{sym}(ρ) within various microscopic many-body theories and/or phenomenological models. However, model predictions still vary largely at both sub-saturation and supra-saturation densities although they agree often by construction at the saturation density ρ**_{0}**. Therefore, accurate experimental constraints are imperative for making further progresses in our understanding of the density dependence of nuclear symmetry energy.

Significant progresses have been made in constraining the E_{sym}(ρ) around and below the saturation density ρ**_{0 }**over the last two decades. Comprehensive reviews on the recent progress and remaining challenges in constraining the E

While the symmetry energy at supra-saturation densities remains rather uncertain, some interesting information about its magnitude at twice the saturation density of nuclear matter has been obtained from analyses of neutron star observables since GW170817 as shown in the following figure.

Shown in the following is a comparison of the upper and lower limits of symmetry energy (blue curves) from analyzing neutron star properties with predictions of phenomenological (left window) and microscopic (right window) nuclear many-body theories. Detailed discussions of these predictions and references can be found in Universe 7 (6), 82 (2021).

Combining results from ongoing and planned new laboratory experiments with high energy radioactive beams and astrophysical observations using advanced x-ray observatories and next generation gravitational wave detectors has the great promise of determining more precisely the symmetry energy of dense neutron-rich matter in the near future.

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