Relativistic effects are investigated in nuclear matter calculations employing renormalized low-momentum nucleon-nucleon ($NN$) interactions. It is demonstrated that the relativistic effects cure a problem of non-relativistic low-momentum interactions, which fail to reproduce saturation of nuclear matter. Including relativistic effects, one already obtains saturation in a Hartree-Fock calculation. Brueckner-Hartree-Fock calculations lead to a further improvement of the saturation properties. The results are rather insensitive to the realistic $NN$ interaction on which they are based.
A study of the correlation between nuclear temperatures and symmetry energy is presented for heavy-ion collisions at intermediate energies via the isospin-dependent quantum molecular-dynamics model. It is found that different symmetry energy parameters will change the density and kinetic energy distribution of the hot nuclei. More importantly, nuclear temperatures that are based on kinetic energy properties can be used to study symmetry energy information.
The nuclear saturation mechanism is discussed in terms of two-nucleon and three-nucleon interactions in chiral effective field theory (Ch-EFT), using the framework of lowest-order Brueckner theory. After the Coester band, which is observed in calculating saturation points with various nucleon-nucleon (NN) forces, is revisited using modern NN potentials and their low-momentum equivalent interactions, detailed account of the saturation curve of the Ch-EFT interaction is presented. The three-nucleon force (3NF) is treated by reducing it to an effective two-body interaction by folding the third nu…
Yoichiro Nambu put a great foot print in nuclear physics in the era of its fundamental developments including his pioneering insight into essential ingredients of repulsive core of nuclear force and its relation to the saturation of nuclear matter. The present review article focuses onto recent developments of the interaction models between colliding nuclei in terms of Brueckner's G-matrix theory staring from realistic nuclear forces and the saturation property of symmetric nuclear matter as well as neutron-star matter. A recently proposed unique scenario of extracting the saturation property …
We derive the empirical formulas for the neutron star mass and gravitational redshift as a function of the central density and specific combination of the nuclear saturation parameters, which are applicable to the stellar models constructed with the central density up to threefold nuclear saturation density. Combining the both empirical formulas, one also estimates the neutron star radius. In practice, we find that the neutron star mass (radius) can be estimated within $\sim 10\%$ (a few percent) accuracy by comparing the mass and radius evaluated with our empirical formulas to those determine…
The ancient problem of the saturation of symmetric nuclear matter is reviewed with an update on the status of the crises that were identified at an early stage by John Clark. We discuss how the initial problem with variational calculations providing more binding than the two hole-line contribution for the same interaction was overcome by calculations including three hole-line contributions without however reproducing the empirical nuclear saturation properties. It is argued that this remaining problem is still open because many solutions have been proposed or ad hoc adjustments implemented wit…
Background: Nuclear radius is one of the most important and basic properties of atomic nuclei and its evolution is closely related to the saturation of the nuclear density in the internal region but the systematics of the nuclear radii for the neutron-rich unstable nuclei is not well known. Purpose: Motivated by the recent interaction cross section measurement which indicates the 48Ca core swelling in the neutron-rich Ca isotopes, we explore the mechanism of the enhancement of the neutron and proton radii for spherical nuclei. Methods: Microscopic Hartree-Fock calculations with three sets of S…
Only one third of the nucleons in $^{208}$Pb occupy the saturation density area. Consequently nuclear observables related to average properties of nuclei, such as masses or radii, constrain the equation of state (EOS) not at saturation density but rather around the so-called crossing density, localised close to the mean value of the density of nuclei: $ρ\simeq$0.11 fm$^{-3}$. This provides an explanation for the empirical fact that several EOS quantities calculated with various functionals cross at a density significantly lower than the saturation one. The third derivative M of the energy at t…
Using FOPI data on elliptic flow in Au+Au collisions between 0.4 and 1.5A GeV we extract constraints for the equation of state (EOS) of compressed symmetric nuclear matter using the transport code IQMD by introducing an observable describing the evolution of the size of the elliptic flow as a function of rapidity. This observable is sensitive to the nuclear EOS and a robust tool to constrain the compressibility of nuclear matter up to 2 $ρ_0$.
Different saturation properties of cold symmetric nuclear matter in the strong magnetic field have been considered. We have seen that for magnetic fields about $B> 3 \times 10 ^ {17}\ G$, {for both cases with and without nucleon anomalous magnetic moments}, the saturation density and saturation energy grow by increasing the magnetic field. It is indicated that the magnetic susceptibility of symmetric nuclear matter becomes negative showing the diamagnetic response especially at $B< 3 \times 10 ^ {17}\ G$. We have found that for the nuclear matter, the magnitude of orbital magnetization reaches…
It is very difficult for any nuclear model to pin down the saturation property and high-density equation of state (EOS) simultaneously because of high nonlinearity of the nuclear many-body problem. In this work, we propose, for the first time, to use the special property of light kaonic nuclei to characterize the relation between saturation property and high-density EOS. With a series of relativistic mean-field models, this special property is found to be the level inversion between orbitals $2S_{1/2}$ and $1D_{5/2}$ in light kaonic nuclei. This level inversion can serve as a theoretical labor…
We show that gluon saturation gives rise to a strong modification of the scaling in both the nuclear mass number $A$ and the virtuality $Q^2$ of the vector meson production cross-section in exclusive deep-inelastic scattering off nuclei. We present qualitative analytic expressions for how the scaling exponents are modified as well as quantitative predictions that can be tested at an Electron-Ion Collider.
Low-mass neutron stars are directly associated with the nuclear saturation parameters because their central density is definitely low. We have already found a suitable combination of nuclear saturation parameters for expressing the neutron star mass and gravitational redshift, i.e., $η\equiv (K_0L^2)^{1/3}$ with the incompressibility for symmetric nuclear matter, $K_0$, and the density-dependent nuclear symmetry energy, $L$. In this study, we newly find another suitable combination given by $η_τ\equiv (-K_τL^5)^{1/6}$ with the isospin dependence of incompressibility for asymmetric nuclear matt…
The saturation density of nuclear matter $ρ_0$ is a fundamental nuclear physics property that is difficult to predict from fundamental principles. The saturation density is closely related to the interior density of a heavy nucleus, such as $^{208}$Pb. We use parity violating electron scattering to determine the average interior weak charge and baryon densities in $^{208}$Pb. This requires not only measuring the weak radius $R_{\rm wk}$ but also determining the surface thickness of the weak charge density $a$. We obtain $ρ_0=0.150\pm0.010$ fm$^{-3}$, where the 7\% error has contributions form …
In order to systematically examine the possible maximum mass of neutron stars, which is one of the important properties characterizing the physics in high-density region, I construct neutron star models by adopting phenomenological equations of state with various values of nuclear saturation parameters for low-density region, which are connected to the equation of state for high-density region characterized by the possible maximum sound velocity in medium. I derive an empirical formula for the possible maximum mass of neutron star. If massive neutron stars are observed, it could be possible to…
From general Fermi liquid theory arguments, we derive correlations among the symmetry energy (J), its slope parameter (L), and curvature (K_sym) at nuclear matter saturation density. We argue that certain properties of these correlations do not depend on details of the nuclear forces used in the calculation. We derive as well a global parametrization of the density dependence of the symmetry energy that we show is more reliable, especially at low densities, than the usual Taylor series expansion around saturation density. We then benchmark these predictions against explicit results from chiral…
Taking into account the terrestrial experiments and the recent astrophysical observations of neutron stars and gravitational-wave signals, we impose restrictions on the equation of state (EoS) for isospin-asymmetric nuclear matter. Using the relativistic mean-field model with SU(3) flavor symmetry, we investigate the impacts of effective nucleon mass, nuclear incompressibility, and slope parameter of nuclear symmetry energy on the nuclear and neutron-star properties. It is found that the astrophysical information of massive neutron stars and tidal deformabilities as well as the nuclear experim…
Experimental giant monopole resonance energies are now known to constrain nuclear incompressibility of symmetric nuclear matter $K$ and its density slope $M$ at a particular value of sub-saturation density, the crossing density $ρ_c$. Consistent with these constraints, we propose a reasonable way to construct a plausible equation of state of symmetric nuclear matter in a broad density region around the saturation density $ρ_0$. Help of two additional empirical inputs, the value of $ρ_0$ and that of the energy per nucleon $e(ρ_0)$ are needed. The value of $K(ρ_0)$ comes out to be $211.9\pm 24.5…
饱和密度下同位旋非对称核物质的不可压缩性$K_sat(δ)$。我们的结果表明，在$K_sat(δ)$的幂的同位旋不对称$δ$，即，$K_sat(δ)$ = K_{0} + K_{sat,2} δ^{2}+ K_{sat,4} δ^{4}+O（δ^{6}）$, the magnitude of the 4th-order K_{sat,4} parameter is generally small. The 2nd-order K_{sat,2} parameter thus essentially characterizes the isospin dependence of the incompressibility of asymmetric nuclear matter at saturation density. Furthermore, the K_{sat,2} can be expressed as K_{sat,2}=K_{sym}-6L-J_{0}/{K_{0}L in terms of the slope parameter $ L $ and the curvature parameter $ K_{ \mathrm{sym} } $ of the symmetry energy and the third-order derivative parameter…
