Analytical expressions for the saturation density of asymmetric nuclear matter as well as its binding energy and incompressibility at saturation density are given up to fourth order in the isospin asymmetry δ = (ρ n − ρ p )/ρ using 11 characteristic parameters defined by the density derivatives of the binding energy per nucleon of symmetric nuclear matter, the symmetry energy E sym (ρ), and the fourth-order symmetry energy E sym,4 (ρ) at normal nuclear density ρ 0 . Using an isospin-and momentum-dependent modified Gogny interaction (MDI) and the Skyrme-Hartree-Fock (SHF) approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibilityat saturation density. Our results show that the magnitude of the higher order K sat,4 parameter is generally small compared to that of the K sat,2 parameter. The latter essentially characterizes the isospin dependence of the incompressibility at saturation density and can be expressed asL, where L and K sym represent, respectively, the slope and curvature parameters of the symmetry energy at ρ 0 and J 0 is the third-order derivative parameter of symmetric nuclear matter at ρ 0 . Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model that can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the higher order J 0 contribution to K sat,2 generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between K sym and L as well as between J 0 /K 0 and K 0 . These correlations together with the empirical constraints on K 0 , L, E sym (ρ 0 ), and the nucleon effective mass lead to an estimate of K sat,2 = −370 ± 120 MeV.

The critical densities and impact of forming ∆(1232) resonances in neutron stars are investigated within an extended nonlinear relativistic mean-field (RMF) model. The critical densities for the formation of four different charge states of ∆(1232) are found to depend differently on the separate kinetic and potential parts of nuclear symmetry energy, the first example of a microphysical property of neutron stars to do so. Moreover, they are sensitive to the in-medium Delta mass m∆ and the completely unknown ∆-ρ coupling strength gρ∆. In the universal baryon-meson coupling scheme where the respective ∆-meson and nucleon-meson coupling constants are assumed to be the same, the critical density for the first ∆ − (1232) to appear is found to be ρ crit ∆ − =(2.08 ± 0.02)ρ0 using RMF model parameters consistent with current constraints on all seven macroscopic parameters usually used to characterize the equation of state (EoS) of isospin-asymmetric nuclear matter (ANM) at saturation density ρ0. Moreover, the composition and the mass-radius relation of neutron stars are found to depend significantly on the values of the gρ∆ and m∆.

Various kinds of isovector nucleon effective masses are used in the literature to characterize the momentum/energy dependence of the nucleon symmetry potential or self-energy due to the space/time non-locality of the underlying isovector strong interaction in neutron-rich nucleonic matter. The multifaceted studies on nucleon isovector effective masses are multi-disciplinary in nature. Besides structures, masses and low-lying excited states of nuclei as well as nuclear reactions, studies of the isospin dependence of short-range correlations in nuclei from scatterings of high-energy electrons and protons on heavy nuclei also help understand nucleon effective masses especially the so-called E-mass in neutron-rich matter. A thorough understanding of all kinds of nucleon effective masses has multiple impacts on many interesting issues in both nuclear physics and astrophysics. Indeed, essentially all microscopic many-body theories and phenomenological models with various nuclear forces available in the literature have been used to calculate single-nucleon potentials and the associated nucleon effective masses in neutron-rich matter. There are also fundamental principles connecting different aspects and impacts of isovector strong interactions. In particular, the Hugenholtz-Van Hove theorem connects analytically nuclear symmetry energy with both isoscalar and isovector nucleon effective masses as well as their own momentum dependences. It also reveals how the isospin-quartic term in the equation of state of neutron-rich matter depends on the high-order momentum-derivatives of both isoscalar and isovector nucleon potentials. The Migdal-Luttinger theorem facilitates the extraction of nucleon E-mass and its isospin dependence from experimentally constrained single-nucleon momentum distributions. The momentum/energy dependence of the symmetry potential and the corresponding neutron-proton effective mass splitting also affect transport properties and the liquid-gas phase transition in neutron-rich matter. Moreover, they influence the dynamics and isospin-sensitive observables of heavy-ion collisions through both the Vlasov term and the collision integrals of the Boltzmann-Uehling-Uhlenbeck transport equation. We review here some of the significant progresses made in recent years by the nuclear physics community in resolving some of the hotly debated and longstanding issues regarding nucleon effective masses especially in dense neutron-rich matter. We also point out some of the remaining key issues requiring further investigations in the era of high precision experiments using advanced rare isotope beams. Nucleon effective masses in non-relativistic modelsWe focus on non-relativistic nucleon effective masses or the ones derived from the Schrödinger equivalent singleparticle potential in relativistic models. The k-mass M * ,k J and E-mass M * ,E J of a nucleon J = n/p can be obtained from the momentum and energy dependence of the single-nucleon potential U J (ρ, δ, k, E) in nucleonic matter of density ρ and isospin asymmetry δ...

The nuclear symmetry energy $E_{sym}(\rho)$ and its density slope $L(\rho)$ can be decomposed analytically in terms of the single-nucleon potential in isospin asymmetric nuclear matter. Using three popular nuclear effective interaction models which have been extensively used in nuclear structure and reaction studies, namely, the isospin and momentum dependent MDI interaction model, the Skyrme Hartree-Fock approach and the Gogny Hartree-Fock approach, we analyze the contribution of different terms in the single-nucleon potential to the $E_{sym}(\rho)$ and $L(\rho)$. Our results show that the observed different density behaviors of $E_{sym}(\rho)$ for different interactions are essentially due to the variation of the symmetry potential $U_{sym,1}(\rho,k)$. Furthermore, we find that the contribution of the second-order symmetry potential $U_{sym,2}(\rho,k)$ to the $L(\rho)$ generally cannot be neglected. Moreover, our results demonstrate that the magnitude of the $U_{sym,2}(\rho,k)$ is generally comparable with that of $U_{sym,1}(\rho,k)$, indicating the second-order symmetry potential $U_{sym,2}(\rho,k)$ may have significant corrections to the widely used Lane approximation to the single-nucleon potential in extremely neutron(proton)-rich nuclear matter.Comment: 16 pages, 13 figures, 1 big table. Results of BSk14-17, Rsigma-fit, and Gsigma-fit in the big table updated, typos fixed. Published version in PR

The density dependence of nuclear symmetry energy is among the most uncertain parts of the Equation of State (EOS) of dense neutron-rich nuclear matter. It is currently poorly known especially at suprasaturation densities partially because of our poor knowledge about isovector nuclear interactions at short distances. Because of its broad impacts on many interesting issues, pinning down the density dependence of nuclear symmetry energy has been a longstanding and shared goal of both astrophysics and nuclear physics. New observational data of neutron stars including their masses, radii, and tidal deformations since GW170817 have helped improve our knowledge about nuclear symmetry energy, especially at high densities. Based on various model analyses of these new data by many people in the nuclear astrophysics community, while our brief review might be incomplete and biased unintentionally, we learned in particular the following: (1) The slope parameter L of nuclear symmetry energy at saturation density ρ0 of nuclear matter from 24 new analyses of neutron star observables was about L≈57.7±19 MeV at a 68% confidence level, consistent with its fiducial value from surveys of over 50 earlier analyses of both terrestrial and astrophysical data within error bars. (2) The curvature Ksym of nuclear symmetry energy at ρ0 from 16 new analyses of neutron star observables was about Ksym≈−107±88 MeV at a 68% confidence level, in very good agreement with the systematics of earlier analyses. (3) The magnitude of nuclear symmetry energy at 2ρ0, i.e., Esym(2ρ0)≈51±13 MeV at a 68% confidence level, was extracted from nine new analyses of neutron star observables, consistent with the results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories. (4) While the available data from canonical neutron stars did not provide tight constraints on nuclear symmetry energy at densities above about 2ρ0, the lower radius boundary R2.01=12.2 km from NICER’s very recent observation of PSR J0740+6620 of mass 2.08±0.07M⊙ and radius R=12.2–16.3 km at a 68% confidence level set a tight lower limit for nuclear symmetry energy at densities above 2ρ0. (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron–quark phase transition from observables of canonical neutron stars indicated that the phase transition shifted appreciably both L and Ksym to higher values, but with larger uncertainties compared to analyses assuming no such phase transition. (6) The high-density behavior of nuclear symmetry energy significantly affected the minimum frequency necessary to rotationally support GW190814’s secondary component of mass (2.50–2.67) M⊙ as the fastest and most massive pulsar discovered so far. Overall, thanks to the hard work of many people in the astrophysics and nuclear physics community, new data of neutron star observations since the discovery of GW170817 have significantly enriched our knowledge about the symmetry energy of dense neutron-rich nuclear matter.

The energy of a free gas of neutrons and protons is well known to be approximately isospin parabolic with a negligibly small quartic term of only 0.45 MeV at the saturation density of nuclear matter ρ0 = 0.16 fm −3 . Using an isospin-dependent single-nucleon momentum distribution including a high (low) momentum tail (depletion) with its shape parameters constrained by recent high-energy electron scattering and medium-energy nuclear photodisintegration experiments as well as the stateof-the-art calculations of the deuteron wave function and the equation of state of pure neutron matter near the unitary limit within several modern microscopic many-body theories, we show for the first time that the kinetic energy of interacting nucleons in neutron-rich nucleonic matter has a significant quartic term of 7.18 ± 2.52 MeV. Such a large quartic term has broad ramifications in determining the equation of state of neutron-rich nucleonic matter using observables of nuclear reactions and neutron stars.

Flexible manipulation of the fate of cancer cells through exogenous stimulation-induced metabolic reprogramming could handle the cellular plasticity-derived therapies resistance, which provides an effective paradigm for the treatment of refractory and relapsing tumors in clinical settings. Herein, we demonstrated that moderate heat (45 °C) could significantly regress the expression of antioxidants and trigger specific lipid metabolic reprogramming in cancer cells synergized with iron oxide nanoparticles (Fe 3 O 4 NPs). This metabolic control behavior destroyed the tumor redox homeostasis and produced overwhelming lipid peroxides, consequently sensitizing the tumor to ferroptosis. Based on these findings, a heat-triggered tumor-specific ferroptosis strategy was proposed by the rational design of a polypeptide-modified and 1H-perfluoropentane (1H-PFP)-encapsulated Fe 3 O 4 -containing nanoformulation (GBP@Fe 3 O 4 ). When irradiated by an 808 nm laser, the phase transition of 1H-PFP was triggered by localized moderate heat (45 °C), leading to burst release of Fe 3 O 4 in situ to produce potent reactive oxygen species through the Fenton reaction in the tumor microenvironment. Together with the antioxidant inhibition response and distinctive lipid metabolic reprogramming by heat stress, this oxidative damage was amplified to induce tumor ferroptosis and achieve sufficient antitumor effects. Importantly, we confirmed that ACSBG1, an acyl-CoA synthetase, was the key pro-ferroptotic factor in this heat-induced ferroptosis process. Moreover, knockout of this gene could realize cancer cell death fate conversion from ferroptosis to non-ferroptotic death. This work provides mechanistic insights and practical strategies for heat-triggered ferroptosis in situ to reduce the potential side effects of direct ferroptosis inducers and highlights the key factor in regulating cell fate under heat stress.

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy Esym,4(ρ). Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of Esym,4(ρ) at normal nuclear matter density ρ0 is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at ρ0. On the other hand, we find that the Esym,4(ρ) may become nonnegligible at high densities. Furthermore, the analytical form of the Esym,4(ρ) provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., Ksat(δ) = K0 + Ksat,2δ 2 + Ksat,4δ 4 + O(δ 6 ) where δ = (ρn − ρp)/ρ is the isospin asymmetry, and we find that the value of Ksat,4 is generally small compared with that of the Ksat,2. In addition, we study the effects of the Esym,4(ρ) on the proton fraction xp and the core-crust transition density ρt and pressure Pt in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the Esym,4(ρ) contribution can significantly enhance the xp at high densities and strongly reduce the ρt and Pt in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the xp at high densities as well as the ρt and Pt in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.the well-known empirical parabolic law.