State Of Asymmetric Nuclear Matter Research Articles

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

Probing the nuclear equation-of-state and the symmetry energy with heavy-ion collisions

The present status of studies aimed at constraining the nuclear equation of state with heavy-ion collision dynamics is presented. Multifragmentation phenomena, including their isotopic distributions, charge correlations and emission time-scales, may revel the existence of liquid-gas transitions in the phase diagram. Exploring the isotopic degree of freedom in nuclear dynamics is then required in order to constrain the equation of state of asymmetric nuclear matter which presently represents a major priority due to its relevance to both nuclear physics and astrophysics. Some observables that have successfully constrained the density dependence of the symmetry energy are presented, such as neutron-proton yield ratios and isospin diffusion and drift phenomena. The reported results and status of the art is discussed by also considering some of the present problems and some future perspectives for the heavy-ion collision community.

Angle-dependent gap state in asymmetric nuclear matter

We propose an axisymmetric angle-dependent gap (ADG) state with the broken rotational symmetry in isospin-asymmetric nuclear matter. In this state, the deformed Fermi spheres of neutrons and protons increase the pairing probabilities along the axis of symmetry breaking near the average Fermi surface. We find that the state possesses lower free energy and larger gap value than the angle-averaged gap state at large isospin asymmetries. These properties are mainly caused by the coupling of different m_{j} components of the pairing gap. Furthermore, we find the transition from the ADG state to the normal state is of second order and the ADG state vanishes at the critical isospin asymmetry m_{j} where the angle-averaged gap vanishes.

Simple effective interaction: infinite nuclear matter and finite nuclei

The mean field properties and equation of state for asymmetric nuclear matter are studied using a simple effective interaction, which has a single finite-range Gaussian term. The study of finite nuclei with this effective interaction is done by constructing a quasilocal energy density functional for which the single-particle equations take the form of Skryme–Hartree–Fock equations. The predictions of binding energies and charge radii of spherical nuclei are found to be compatible with the results of successful mean field models, as well as with the experimental data.

Nuclear matter and surface clustering

We demonstrate that the binding energy per nucleon of symmetric nuclear matter (SNM) (with Coulomb interaction switched off and N = Z) in the limit of zero density approaches to its value, uv, at the saturation density, where uv is the volume term of the Weizsäcker mass formula. This phenomenon is a direct result of the clustering of nuclei in the low density region of nuclear matter. We study the implications of this result on the properties of nuclei. We also study the properties of asymmetric nuclear matter. Because of clustering a provocative interpretation of the equation of state of asymmetric nuclear matter emerges which is at considerable variance at low densities with hitherto all the previous calculations. For nuclei, as a framework, an extended version of Thomas-Fermi theory is invoked. Calculations are performed for 2149 nuclei with N, Z ≥ 8. The present scheme leads to a forceful interpretation of the low density asymmetry energy data of Natowitz et al. [1].

Variational study for the equation of state of asymmetric nuclear matter at finite temperatures

An equation of state (EOS) for uniform asymmetric nuclear matter (ANM) is constructed at zero and finite temperatures by the variational method starting from the nuclear Hamiltonian that is composed of the Argonne v18 and Urbana IX potentials. At zero temperature, the two-body energy is calculated with the Jastrow wave function in the two-body cluster approximation which is supplemented by Mayer's condition and the healing-distance condition so as to reproduce the result by Akmal, Pandharipande and Ravenhall. The energy caused by the three-body force is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation conditions. The masses and radii of neutron stars obtained with the EOS are consistent with recent observational data. At finite temperatures, thermodynamic quantities such as free energy, internal energy, entropy, pressure and chemical potentials are calculated with an extension of the method by Schmidt and Pandharipande. The validity of the frozen-correlation approximation employed in this work is confirmed as compared with the result of the fully minimized calculation. The quadratic proton-fraction-dependence of the energy of ANM is confirmed at zero temperature, whereas the free energy of ANM deviates from the quadratic proton-fraction-dependence markedly at finite temperatures. The obtained EOS of ANM will be an important ingredient of a new nuclear EOS for supernova numerical simulations.

R-mode Instability of Neutron Star with Non-Newtonian Gravity

The Chandrasekhar—Friedmann—Schutz (CFS) instabilities of r-modes for canonical neutron stars (1.4 M⊙) with rigid crusts are investigated by using an equation of state of asymmetric nuclear matter with super-soft symmetry energy, where the non-Newtonian gravity proposed in the grand unification theories is also considered. Constrained by the observations of the masses and the spin frequencies for neutron stars, the boundary of the r-mode instability window for a canonical neutron star is obtained, and the results show that the observed neutron stars are all outside the instability window, which is consistent with the theoretical expectation. In addition, an upper limit of the non-Newtonian gravity parameters is also given.

The electric dipole response of exotic nuclei

The electric dipole (E1) response of exotic nuclei, with a focus on the soft E1 excitation of halo nuclei and the pygmy dipole resonance (PDR) of neutron-skin nuclei, is reviewed here from an experimental point of view. Since the discovery of halo nuclei in the late 1980s, the particular dipole response of these loosely bound nuclei located at the neutron-drip line resulting in an extraordinary enhancement of the electric dipole strength at low excitation energies (soft E1 excitation) has been one of the phenomena under intense investigation both in experiments and in nuclear theories. We discuss how such phenomena have been recognized as a unique feature of halo nuclei and how it is applied to probe the halo structure in a quantitative way. Another intriguing feature of the E1 response of neutron-rich nuclei is the PDR in neutron-skin nuclei, which is viewed as a dipole vibration of excess neutrons against a core nucleus and which appears in the low-energy part of the E1 strength function below the giant dipole resonance. The status of the experimental evidence for such a redistribution of dipole strength for neutron-rich nuclei compared to stable ones is reviewed. The relation of the dipole response to the symmetry energy in the equation of state of asymmetric nuclear matter and to the neutron-skin thickness is also briefly discussed. Finally, we outline some perspectives for future experimental investigations toward heavier and more neutron-rich systems. The experimental results reviewed here have been accumulated over the last two decades at fragmentation facilities worldwide at GANIL, GSI, MSU and RIKEN.

Effect of the symmetry energy on the location of the inner edge of the neutron star crust

The symmetry energy effects on the location of the inner edge of neutron star crusts are studied. Three phenomenological models are employed in order to check the accuracy of the well known parabolic approximation of the equation of state for asymmetric nuclear matter in the determination of the transition density ${n}_{t}$ and transition pressure ${P}_{t}$. The results corroborate the statement that the error due to the assumption that a priori the equation of state is parabolic may introduce a large error in the determination of related properties of a neutron star as the crustal fraction of the moment of inertia and the critical frequency of rotating neutron stars.

ELLIPTIC FLOW AND THE SYMMETRY ENERGY AT SUPRA-SATURATION DENSITY

The elliptic flow in collisions of neutron-rich heavy-ion systems at intermediate energies emerges as an observable sensitive to the strength of the symmetry energy at supra-saturation densities. First results obtained by comparing ratios or differences of neutron and hydrogen flows with predictions of transport models favor a moderately soft to linear density dependence, consistent with ab initio nuclear-matter theories. Comprehensive data sets of high accuracy can be expected to improve our knowledge of the equation of state of asymmetric nuclear matter.

Nuclear matter fourth-order symmetry energy in the relativistic mean field models

Within the nonlinear relativistic mean field model, we derive the analytical expression of the nuclear matter fourth-order symmetry energy $E_{sym,4}(\rho)$. Based on two accurately calibrated interactions FSUGold and IU-FSU, our results show that the value of $E_{sym,4}(\rho)$ at normal nuclear matter density $\rho_{0}$ is generally less than 1 MeV, confirming the empirical parabolic approximation to the equation of state for asymmetric nuclear matter at $\rho_{0}$. On the other hand, we find that the $E_{sym,4}(\rho)$ may become nonnegligible at high densities. Furthermore, the analytical form of the $E_{sym,4}(\rho)$ provides the possibility to study the higher-order effects on the isobaric incompressibility of asymmetric nuclear matter, i.e., $K_{sat}(\delta)=K_{0}+K_{sat,2}\delta ^{2}+K_{sat,4}\delta ^{4}+\mathcal{O}(\delta ^{6})$ where $\delta =(\rho_{n}-\rho_{p})/\rho $ is the isospin asymmetry, and we find that the value of $K_{sat,4}$ is generally small compared with that of the $K_{sat,2}$. In addition, we study the effects of the $E_{sym,4}(\rho)$ on the proton fraction $x_{p}$ and the core-crust transition density $\rho_{t}$ and pressure $P_{t}$ in neutron stars. Interestingly, we find that, compared with the results from the empirical parabolic approximation, including the $E_{sym,4}(\rho)$ contribution can significantly enhance the $x_{p}$ at high densities and strongly reduce the $\rho_{t}$ and $P_{t}$ in neutron stars, demonstrating that the widely used empirical parabolic approximation may cause large errors in determining the $x_{p}$ at high densities as well as the $\rho_{t}$ and $P_{t}$ in neutron stars within the nonlinear relativistic mean field model, consistent with previous nonrelativistic calculations.

Studies of the equation of state of asymmetric nuclear matter with R3B at FAIR

The R3B experiment at FAIR will offer unique opportunities worldwide to study the properties of bulk asymmetric nuclear matter, e.g. the phase diagram, equation of state, symmetry energy, transport coefficients and in-medium cross sections. The experiment will take advantage of the intense radioactive beams produced by the SuperFRS with energies up to 2 AGeV. We will outline this physics programme and describe the detector sub-systems of R3B which will enable these measurements. Some detectors are already under construction while others are at the planning/R&D stage.

Isospin and symmetry energy – From the laboratory to compact stars

The equation of state of asymmetric nuclear matter is still controversial, as predictions at subsaturation as well as above-normal density diverge widely. Several experimental observables measured in heavyion collisions in the energy range 0.1-1.500 AGeV are discussed. Estimates of the density dependence of the symmetry energy are derived from comparison of experimental results with those of transport codes with different implementations of the potential part of the symmetry energy are presented.

Nuclear matter properties, phenomenological theory of clustering at the nuclear surface, and symmetry energy

We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy by Natowitz et al., at low densities of nuclear matter and is fully consistent with the static properties of nuclei. In a phenomenological way, clusters of all sizes and shapes along with medium modifications are included. Symmetric nuclear matter properties are discussed in detail. Arguments are given that lead to an equation of state of nuclear matter consistent with clustering in the low-density region. We also discuss properties of asymmetric nuclear matter. Because of clustering, an interesting interpretation of the equation of state of asymmetric nuclear matter emerges. As a framework, an extended version of Thomas-Fermi theory is adopted for nuclei which also contain phenomenological pairing and Wigner contributions. This theory connects the nuclear matter equation of state, which incorporates clustering at low densities, with clustering in nuclei at the nuclear surface. Calculations are performed for various equations of state of nuclear matter. We consider measured binding energies of 2149 nuclei for $N$, $Z$ \ensuremath{\geqslant} 8. The importance of the quartic term in symmetry energy is demonstrated at and below the saturation density of nuclear matter. It is shown that it is largely related to the use of, ab initio, a realistic equation of state of neutron matter, particularly the contribution arising from the three neutron interactions and somewhat to clustering. Reasons for these are discussed. Because of clustering the neutron skin thickness in nuclei is found to reduce significantly. The developed theory predicts situations and regimes to be explored both theoretically and experimentally.

Probing the equation of state of asymmetric nuclear matter with isospin diffusion and stopping in heavy-ion collisions

Results from the study of isospin asymmetric Sn+Sn collisions at E/A=35 MeV and 50 MeV, collected with the LASSA and the Chimera detectors at the NSCL of MSU, respectively, are shown. The diffusion of neutrons and protons between projectiles and targets with different N/Z-asymmetries is studied by means of imbalance ratios measurements. The obtained results and their comparison to transport model simulations provide constraints on the density dependence of the symmetry energy. The systematic study of these phenomena at different impact parameters also allows us to explore isospin transparency and stopping phenomena in more central collisions, with important implications about the attainment of chemical equilibrium in central collisions at 35 MeV/nucleon.

TRANSITION DENSITY AND PRESSURE AT THE INNER EDGE OF NEUTRON STAR CRUSTS

Using the nuclear symmetry energy that has been recently constrained by the isospin diffusion data in intermediate-energy heavy ion collisions, we have studied the transition density and pressure at the inner edge of neutron star crusts, and they are found to be 0.040 fm -3 ≤ ρt ≤ 0.065 fm -3 and 0.01 MeV / fm 3 ≤ Pt ≤ 0.26 MeV / fm 3, respectively, in both the dynamical and thermodynamical approaches. We have also found that the widely used parabolic approximation to the equation of state of asymmetric nuclear matter gives significantly higher values of core-crust transition density and pressure, especially for stiff symmetry energies. With these newly determined transition density and pressure, we have obtained an improved relation between the mass and radius of neutron stars.

Neutron drip line and the equation of state of nuclear matter

We investigate how the neutron drip line is related to the density dependence of the symmetry energy by using a macroscopic nuclear model that allows us to calculate nuclear masses in a way that is dependent on the equation of state of asymmetric nuclear matter. The neutron drip line obtained from these masses is shown to appreciably shift to a neutron-rich side in a nuclear chart as the density derivative of the symmetry energy increases. Such a shift is clearly seen for light nuclei, a feature coming mainly from the surface property of neutron-rich nuclei.

A relativistic approach to the equation of state of asymmetric nuclear matter

The properties of asymmetric nuclear matter for a wide range of densities and asymmetric parameters are investigated within the lowest-order-constrained variational (LOCV) method by employing the relativistic Hamiltonian with a potential which has been fitted relativistically to N-N phase shifts ( $ \tilde{{v}}_{{14}}^{}$ and to the AV14interaction. Like our previous work on symmetric nuclear matter, the boost interaction corrections as well as the relativistic one-body and two-body kinetic corrections are calculated. The various properties of asymmetric nuclear matter such as the symmetry energy, the saturation energy and the validity of the $ \alpha^{2}_{}$ law, etc., are examined. The symmetry energy is reduced by about 7MeV when we use $ \tilde{{v}}_{{14}}^{}$ instead of its non-relativistic version, i.e. the AV14interaction. The results are compared with other many-body calculations.

Equation of state of asymmetric nuclear matter: a VMC study

Abstract A Variational Monte Carlo (VMC) method is employed to investigate the properties of symmetric and asymmetric nuclear matter. The realistic Urbana V 14 twonucleon interaction potential of Lagaris and Pandharipande was used to describe the microscopic interactions. Also, many body interactions are included as a density dependent term in the potential. Total kinetic and potential energies per particle are calculated for asymmetric nuclear matter by VMC method at various densities and isospin asymmetry parameters. The results are compared with data found in literature, and it was observed that the results obtained in this study reasonably agree with the results found in the literature. Also, the symmetry energy and incompressibility factor of the nuclear matter were obtained. The results obtained are in good agreement with those obtained by various authors with different methods and techniques.

Symmetry energy at subnuclear densities deduced from nuclear masses

We examine how nuclear masses are related to the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate nuclear masses in a way dependent on the equation of state of asymmetric nuclear matter. We find by comparison with empirical two-proton separation energies that a smaller symmetry energy at subnuclear densities, corresponding to a larger density symmetry coefficient L, is favored. This tendency, which is clearly seen for nuclei that are neutron-rich, nondeformed, and light, can be understood from the property of the surface symmetry energy in a compressible liquid-drop picture.