State Of Asymmetric Nuclear Matter Research Articles

Nuclear Matter Equation of State in the Brueckner–Hartree–Fock Approach and Standard Skyrme Energy Density Functionals

The equation of state of asymmetric nuclear matter as well as the neutron and proton effective masses and their partial-wave and spin–isospin decomposition are analyzed within the Brueckner–Hartree–Fock approach. Theoretical uncertainties for all these quantities are estimated by using several phase-shift-equivalent nucleon–nucleon forces together with two types of three-nucleon forces, phenomenological and microscopic. It is shown that the choice of the three-nucleon force plays an important role above saturation density, leading to different density dependencies of the energy per particle. These results are compared to the standard form of the Skyrme energy density functional, and we find that it is not possible to reproduce the BHF predictions in the (S,T) channels in symmetric and neutron matter above saturation density, already at the level of the two-body interaction, and even more including the three-body interaction.

Properties of Pb208 predicted from the relativistic equation of state in the full Dirac space

Relativistic Brueckner-Hartree-Fock (RBHF) theory in the full Dirac space allows one to determine uniquely the momentum dependence of scalar and vector components of the single-particle potentials. In order to extend this new method from nuclear matter to finite nuclei, as a first step, properties of $^{208}\mathrm{Pb}$ are explored by using the microscopic equation of state for asymmetric nuclear matter and a liquid droplet model. The neutron and proton density distributions, the binding energies, the neutron and proton radii, and the neutron skin thickness in $^{208}\mathrm{Pb}$ are calculated. In order to further compare the charge densities predicted from the RBHF theory in the full Dirac space with the experimental charge densities, the differential cross sections and the electric charge form factors in the elastic electron-nucleus scattering are obtained by using the phase-shift analysis method. The results from the RBHF theory are in good agreement with the experimental data. In addition, the uncertainty arising from variations of the surface term parameter ${f}_{0}$ in the liquid droplet model is also discussed.

Nuclear Equation of State for Arbitrary Proton Fraction and Temperature Based on Chiral Effective Field Theory and a Gaussian Process Emulator.

We calculate the equation of state of asymmetric nuclear matter at finite temperature based on chiral effective field theory interactions to next-to-next-to-next-to-leading order. Our results assess the theoretical uncertainties from the many-body calculation and the chiral expansion. Using a Gaussian process emulator for the free energy, we derive the thermodynamic properties of matter through consistent derivatives and use the Gaussian process to access arbitrary proton fraction and temperature. This enables a first nonparametric calculation of the equation of state in beta equilibrium, and of the speed of sound and the symmetry energy at finite temperature. Moreover, our results show that the thermal part of the pressure decreases with increasing densities.

Accuracy versus predictive power in nuclear mass tabulations

The nuclear mass evaluations have been brought into quite an accurate level with the advent of machine learning, while their extrapolations are in great debate as manifested by the large discrepancies between themselves. Here, we present a possible way to heal these existing differences and raise the predictive ability of mass formulas through performing the multi-objective optimization aimed at both the binding energy and the $\ensuremath{\alpha}$ decay energy. As exemplified by the microscopically inspired Dulfo-Zuker model, the Pareto optimal solutions are found to guarantee the robust mass predictions especially towards the extreme neutron-rich nuclei plus the coherent statistical analysis. Besides effectively avoiding the overfitting problem, our results shed new light on narrowing the window of symmetry energy in nuclear mass formulas serving not only the reliable nuclear dripline but also the stringent equation of state in asymmetric nuclear matter.

Van der Waals equation of state for asymmetric nuclear matter

The application of the van der Waals equation of state to the asymmetric nuclear matter is considered in a critical state region. The corrections to the van der Waals pressure and free energy due to the Fermi statistics are obtained starting from the Thomas - Fermi entropy expression which ensures the fulfilment of the Nernst theorem. The derived corrections account for the effective nucleon mass and neutron-proton isotopic asymmetry. The parameters of the van der Waals equation of state are deduced by taking the experimental value of critical temperature for symmetric nuclear matter and testing the model of van der Waals with statistics corrections included against the theory of Skyrme energy density functional. A critical line in pressure-temperature-composition space is considered. The incompressibility coefficient is determined along the critical line as a function of nuclear matter composition. A jump in the value of specific heat upon crossing a critical line is discussed.

Equation of state of asymmetric nuclear matter and the tidal deformability of neutron star

Neutron star (NS) is a unique astronomical compact object where the four fundamental interactions have been revealed from the observation and studied in different ways. While the macroscopic properties of NS like mass and radius can be determined within the General Relativity using a realistic equation of state (EOS) of NS matter, such an EOS is usually generated by a nuclear structure model like, e.g., the nuclear mean-field approach to asymmetric nuclear matter. Given the radius of NS extended to above 10 km and its mass up to twice the solar mass, NS is expected to be tidally deformed when it is embedded in a strong tidal field. Such a tidal effect was confirmed unambiguously in the gravitation wave signals detected recently by the LIGO and Virgo laser interferometers from GW170817, the first ever direct observation of a binary NS merger. A nonrelativistic mean-field study is carried out in the present work within the Hartree-Fock formalism to construct the EOS of NS matter, which is then used to determine the tidal deformability, gravitational mass, and radius of NS. The mean-field results are compared with the constraints imposed for these quantities by the global analysis of the observed GW170817 data, and a strong impact by the incompressibility of nuclear matter on the hydrostatic configuration of NS is shown.

Asymmetric nuclear matter and realistic potentials

The equation of state for asymmetric nuclear matter is presented within the Brueckner–Hartree–Fock (BHF) approach by using recent high-quality soft nucleon–nucleon potentials from next-to-leading order (NLO) up to fifth order (N4LO) of the chiral expansion for the wide range of densities and asymmetry parameter, which are very interesting these days in the heavy-ion collisions and neutron stars. For comparison purposes, the same calculations are performed for Brueckner–Hartree–Fock approach plus two-body density-dependent Skyrme potential which is equivalent to three-body forces. Also the results are compared with the other theoretical models, especially the Brueckner–Hartree–Fock plus three-body forces and the Dirac–Brueckner–Hartree–Fock approaches. Our equation-of-state models are able to reproduce the empirical symmetry energy $$\hbox {E}_\mathrm{{sym}}$$ and its slope parameter L at the empirical saturation density $$\rho _{0}$$ and are compatible with experimental data from collisions between heavy nuclei. The symmetry energy of about 30 MeV is obtained at the saturation nuclear matter density. There is very good agreement between the experimental symmetry energy value and those calculated in the Brueckner–Hartree–Fock approach.

Isospin-sensitive observables as a probe of proton transition momentum in the HMT * * Partially supported by the National Natural Science Foundation of China (11875152, 11675066, U1867207, 11505085)

Based on the IBUU transport model, the effect of proton transition momentum on collective flows is studied in 40Ca + 40Ca,112Sn + 112Sn, and 197Au + 197Au collisions at an incident beam energy of 400 MeV/A with impact parameter . It is found that in a neutron rich system, the difference between neutron and proton elliptic flow is largely affected by the proton transition momentum. At beam energies around (and particularly below) the pion production threshold, the ratio is greatly sensitive to proton transition momentum in asymmetric nuclear matter. This study may help us to understand the nucleon momentum distribution in nuclei, which is important for the equation of state of asymmetric nuclear matter, such as neutron stars.

Topics on the equation of state of asymmetric nuclear matter

Topics on the equation of state of asymmetric nuclear matter

Nuclear Symmetry Energy and the Breaking of the Isospin Symmetry: How Do They Reconcile with Each Other?

We analyze and propose a solution to the apparent inconsistency between our current knowledge of the equation of state of asymmetric nuclear matter, the energy of the isobaric analog state (IAS) in a heavy nucleus such as ^{208}Pb, and the isospin symmetry breaking forces in the nuclear medium. This is achieved by performing state-of-the-art Hartree-Fock plus random phase approximation calculations of the IAS that include all isospin symmetry breaking contributions. To this aim, we propose a new effective interaction that is successful in reproducing the IAS excitation energy without compromising other properties of finite nuclei.

Equation of state of asymmetric nuclear matter using re-projected nucleon–nucleon potentials

In this paper, we have calculated the equation of state of asymmetric nuclear matter using the lowest order constrained variational approach and Argonne family potentials with and without three-nucleon interaction (TNI) contribution. In particular, we have used the AV18 potential and the re-projected potentials, AV8′, and AV6′. We have also calculated the saturation properties of symmetric nuclear matter, and the nuclear symmetry energy using AV18+TNI, AV8′+TNI and AV6′+TNI potentials. The inclusion of TNI has modified the agreement with experiment. We have also made a comparison between our results and those of other many-body calculations.

The nuclear symmetry energy and the breaking of the isospin symmetry: how do they reconcile with each other?

Our current knowledge of the Equation of State of asymmetric nuclear matter around saturation density and of the energy of the Isobaric Analog State in a heavy nucleus such as 208Pb seem to be in contradiction. In Ref. [1], the problem has been highlighted and a solution has been proposed. In the present contribution, we overview the aforementioned work by giving some new details not previously published.

The role of three-body forces in nuclear symmetry energy and symmetry free energy

Within the framework of lowest-order constrained variational (LOCV) method using AV18 two-body interaction supplemented by UIX three-body force, equation of state of asymmetric nuclear matter at both zero and finite temperature is studied. Density dependence of the nuclear symmetry energy as well as its partial wave decomposition is also investigated. It is shown that all saturation properties of the cold symmetric nuclear matter, including the symmetry energy and its slope, can be correctly reproduced if the three-body force is used in the LOCV formalism. Furthermore, density and temperature dependence of the symmetry energy and symmetry free energy in hot neutron rich matter is studied. An opposite temperature dependence for the symmetry energy and symmetry free energy is found.

Warm unstable asymmetric nuclear matter: Critical properties and the density dependence of the symmetry energy

The spinodal instabilities in hot asymmetric nuclear matter and some important critical parameters derived thereof are studied using six different families of relativistic mean-field (RMF) models. The slopes of the symmetry energy coefficient vary over a wide range within each family. The critical densities and proton fractions are more sensitive to the symmetry energy slope parameter at temperatures much below its critical value ($T_c\sim$14-16 MeV). The spread in the critical proton fraction at a given symmetry energy slope parameter is noticeably larger near $T_c$, indicating that the warm equation of state of asymmetric nuclear matter at sub-saturation densities is not sufficiently constrained. The distillation effects are sensitive to the density dependence of the symmetry energy at low temperatures which tend to wash out with increasing temperature.

Extended Skyrme interactions for nuclear matter, finite nuclei, and neutron stars

Recent progress in theory, experiment and observation challenges the mean field models using the conventional Skyrme interaction, suggesting that the extension of the conventional Skyrme interaction is necessary. In this work, by fitting the experimental data of a number of finite nuclei together with a few additional constraints on nuclear matter using the simulated annealing method, we construct three Skyrme interaction parameter sets, namely, eMSL07, eMSL08 and eMSL09, based on an extended Skyrme interaction which includes additional momentum and density dependent two-body forces to effectively simulate the momentum dependence of the three-body force. The three new interactions can reasonably describe the ground-state properties and the isoscalar giant monopole resonance energies of various spherical nuclei used in the fit as well as the ground-state properties of many other spherical nuclei, nicely conform to the current knowledge on the equation of state of asymmetric nuclear matter, eliminate the notorious unphysical instabilities of symmetric nuclear matter and pure neutron matter up to a very high density of $1.2$ fm$^{-3}$, and simultaneously support heavier neutron stars with mass larger than two times solar mass. One important difference of the three new interactions is about the prediction of the symmetry energy at supra-saturation densities, and these new interactions are thus potentially useful for the determination of the largely uncertain high-density symmetry energy in future. In addition, a comparison is made for the predictions of nuclear matter, finite nuclei and neutron stars with the three new interactions versus those with three typical interactions BSk22, BSk24 and BSk26 from Brussels group.

Extended Skyrme equation of state in asymmetric nuclear matter

We present a new equation of state for infinite systems (symmetric, asymmetric and neutron matter) based on an extended Skyrme functional constrained by microscopic Brueckner-Bethe-Goldstone results. The resulting equation of state reproduces with very good accuracy the main features of microscopic calculations and it is compatible with recent measurements of two times Solar-mass neutron stars. We provide all necessary analytical expressions to facilitate a quick numerical implementation of quantities of astrophysical interest.

From the lightest nuclei to the equation of state of asymmetric nuclear matter with realistic nuclear interactions

We present microscopic calculations of light and medium mass nuclei and the equation of state of symmetric and asymmetric nuclear matter using different nucleon-nucleon forces, including a new Argonne version that has the same spin/isospin structure as local chiral forces at next-to-next-to-leading order (N2LO). The calculations are performed using Auxiliary Field Diffusion Monte Carlo (AFDMC) combined with an improved variational wave function. We show that the AFDMC method can now be used to successfully calculate the energies of very light to medium mass nuclei as well as the energy of isospin-asymmetric nuclear matter, demonstrating microscopically the quadratic dependence of the energy on the symmetry energy.

Isospin effects and symmetry energy studies with INDRA

The equation of state of asymmetric nuclear matter is still controversial, as predictions at subsaturation as well as above normal density widely diverge. We discuss several experimental results measured in heavy-ion collisions with the INDRA array in the incident energy range 5-80 MeV/nucleon. In particular an estimate of the density dependence of the symmetry energy is derived from isospin diffusion results compared with a transport code: the potential part of the symmetry energy linearly increases with the density. We demonstrate that isospin equilibrium is reached in mid-central collisions for the two reactions Ni+Au at 52 MeV/nucleon and Xe+Sn at 32 MeV/nucleon. New possible variables and an improved modelization to investigate symmetry energy are discussed.

Flow probe of symmetry energy in relativistic heavy-ion reactions

Flow observables in heavy-ion reactions at incident energies up to about 1 GeV per nucleon have been shown to be very useful for investigating the reaction dynamics and for determining the parameters of reaction models based on transport theory. In particular, the elliptic flow in collisions of neutron-rich heavy-ion systems emerges as an observable sensitive to the strength of the symmetry energy at supra-saturation densities. The comparison of ratios or differences of neutron and proton flows or neutron and hydrogen flows with predictions of transport models favors an approximately linear density dependence, consistent with ab-initio nuclear-matter theories. Extensive parameter searches have shown that the model dependence is comparable to the uncertainties of existing experimental data. Comprehensive new flow data of high accuracy, partly also through providing stronger constraints on model parameters, can thus be expected to improve our knowledge of the equation of state of asymmetric nuclear matter.

Gamow-Teller strength in deformed nuclei within self-consistent pnQRPA with the Gogny force

In recent years fully consistent quasiparticle random-phase approximation (QRPA) calculations using finite range Gogny force have been performed to study elec- tromagnetic excitations of several axially-symmetric deformed nuclei up to the 238 U. Here we present the extension of this approach to the charge-exchange nuclear excitations (pn- QRPA). In particular we focus on the Gamow-Teller (GT) excitations. A comparison of the predicted GT strength distribution with existing experimental data is presented. The role of nuclear deformation is shown. Special attention is paid toβ-decay half-lives calculations for which experimental data exist. Spin-isospin nuclear excitations, in particular the Gamow-Teller (GT) resonances, play nowadays a crucial role in several fields of physics. First, in nuclear physics since they can provide informations on the nuclear interaction, on the equation of state of asymmetric nuclear matter and on the nuclear skin thickness. Second, in astrophysics, since they influence stellar evolution and nucleosynthesis by governing the electroweak processes. Finally, in particle physics in connection with the neutrino physics beyond the standard model and the evaluation of the Vud element of the Cabibbo-Kobayashi- Maskawa quark-mixing matrix. Experimentally the spin-isospin nuclear excitations are studied via charge-exchange reactions, such as (p, n), (n, p), (d, 2 He), ( 3 He, t) or (t, 3 He) andβ-decay measurements. In spite of the great efforts and interest, the whole nuclear chart cannot be experimentally studied. To study the nuclei ex- perimentally inacessible one can rely on theoretical models. In this context one of the most employed models is the so called proton-neutron quasiparticle random-phase approximation (pnQRPA). To treat consistently isotopic chains from drip line to drip line two main features of the theoretical model are in order: the possibility to deal with deformed nuclei and the use of an unique effective nuclear force. The term unique has here two meanings. First of all, it means that the interaction is the same for all the nuclei; second, that the nuclear interaction used to describe the ground state and the excited states is the same (this is the so-called self-consistency of the calculation). In spite of the relatively large number of pnQRPA calculations, only a very few of those include both features. Furthermore, even in such self-consistent calculations, it remains at least one coupling constant, typically in the particle-particle channel, which should be considered as a free parameter usually fitted to half-lives or to the experimental position of the GT excitation energy. Here we present the fully consistent axially-symmetric-deformed pnQRPA calculation based on the finite range Gogny force. The originality of the present work consists in the use of the Gogny