Cold neutrons trapped in external fields

The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine the binding energies and densities of many neutrons interacting via realistic microscopic interactions and confined in external fields. We perform calculations for different external fields and across several shells to place important constraints on inhomogeneous neutron matter, and hence the large isospin limit of the nuclear energy density functionals that are used to predict properties of heavy nuclei and neutron star crusts. We find important differences between microscopic calculations and current density functionals; in particular, the isovector gradient terms are significantly more repulsive than in traditional models, and the spin-orbit and pairing forces are comparatively weaker.     

The single particle potential in nuclear matter

The energy dependent real part of the optical potential for particles and holes in nuclear matter is calculated from a realistic nuclear hamiltonian that explains the nucleon-nucleon scattering data and equilibrium properties of nuclear matter. The variational method is used with Fermi-hypernetted and single-operator-chain summation techniques. The results are comparable with empirical Woods-Saxon well depths at energies ? 150 MeV. At higher energies the potential has a density dependence suggesting a “wine-bottle” shaped nucleon-nucleus potential.     

Plan for nuclear symmetry energy experiments using the LAMPS system at the RIB facility RAON in Korea

We review the calculation of the equation of state of pure neutron matter using quantum Monte Carlo (QMC) methods. QMC algorithms permit the study of many-body nuclear systems using realistic two- and three-body forces in a non-perturbative framework. We present the results for the equation of state of neutron matter, and focus on the role of three-neutron forces at supranuclear density. We discuss the correlation between the symmetry energy, the neutron star radius and the symmetry energy. We also combine QMC and theoretical models of the three-nucleon interactions, and recent neutron star observations to constrain the value of the symmetry energy and its density dependence.     

Density Dependence of Nuclear Matter Symmetry Energy: VMC Calculations

Physics of Atomic Nuclei - A Variational Monte-Carlo (VMC) method is employed to investigate the density dependence of the symmetry energy of isospin asymmetric nuclear matter. The realistic Urbana...     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.     

Extended Thomas-Fermi theory at finite temperature

We present a generalization of the extended Thomas-Fermi (ETF) theory to finite temperatures T. Starting from the Wigner-Kirkwood expansion of the Bloch density in powers of , we derive the gradient expansion of the free energy and entropy density functionals $\text{F}$[ρ] and σ[ρ] up to fourth order with their correct temperature-dependent coefficients. (Effective mass and spin-orbit contributions are taken into account up to second order.) For a harmonic-oscillator potential we show that both the h-expansion of the free energy and the entropy and the gradient expansion of the functionals [ρ] and σ[ρ] converge very fast and yield the exact quantum-mechanical results for kT ? 3 MeV, where the shell effects are washed out. Finally we discuss the Euler variational equation obtained with the new functionals and use its numerical solutions for semi-infinite symmetric nuclear matter to test the quality of parametrized trial densities. As an application, we present liquid-drop model parameters, calculated with a realistic Skyrme interaction, as functions of the temperature.     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

On energy densities reached in heavy-ion collisions at the CERN SPS

We present a few estimates of energy densities reached in heavy-ion collisions at the CERN SPS. The estimates are based on data and models of proton-nucleus and nucleus-nucleus interactions. In all of these estimates the maximum energy density in central Pb+Pb interactions is larger than the critical energy density GeV/fm³ following from lattice gauge theory computations. In estimates which we consider as realistic the maximum energy density is about . In this way our analysis gives some support to claims that deconfined matter has been produced at the CERN SPS. Any definite statement requires a deeper understanding of formation times of partons and hadrons in nuclear collisions. We also compare our results with implicit energy estimates contained in earlier models of anomalous suppression in nuclear collisions. Received: 3 February 2003 / Revised version: 5 March 2003 / Published online: 5 May 2003     

Nuclear matter and neutron star properties with the extendedNambu-Jona-Lasinio model

An extended Nambu-Jona-Lasinio(eNJL) model with nucleons as the degrees of freedom is used to investigate properties of nuclear matter and neutron stars(NSs),including the binding energy and symmetry energy of the nuclear matter, the core-crust transition density, and mass-radius relation of NSs. The fourth-order symmetry energy at saturation density is also investigated. When the bulk properties of nuclear matter at saturation density are used to determine the model parameters, the double solutions of parameters are obtained for a given nuclear incompressibility. It is shown that the isovector-vector interaction has a significant influence on the nuclear matter and NS properties, and the sign of isovector-vector coupling constant is critical in the determination of the trend of the symmetry energy and equation of state. The effects of the other model parameters and symmetry energy slope at saturation density are discussed.     

Electroweak measurements of neutron densities in CREX and PREX at JLab,USA

We analyze microscopic many-body calculations of the nuclear symmetry energy and its density dependence. The calculations are performed in the framework of the Brueckner-Hartree-Fock and the self-consistent Green’s functions methods. Within Brueckner-Hartree-Fock, the Hellmann-Feynman theorem gives access to the kinetic energy contribution as well as the contributions of the different components of the nucleon-nucleon interaction. The tensor component gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy in a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that neutron matter is less correlated than symmetric nuclear matter. Within the self-consistent Green’s function approach, we compute the momentum distributions and we identify the effects of the high momentum components in the symmetry energy. The results are obtained for the realistic interaction Argonne V18 potential, supplemented by the Urbana IX three-body force in the Brueckner-Hartree-Fock calculations.     

Density content of nuclear symmetry energy from nuclear observables

The nuclear symmetry energy at a given density measures the energy transferred in converting symmetric nuclear matter into the pure neutron matter. The density content of nuclear symmetry energy remains poorly constrained. Our recent results for the density content of the nuclear symmetry energy, around the saturation density, extracted using experimental data for accurately known nuclear masses, giant resonances and neutron-skin thickness in heavy nuclei are summarized.     

Heavy-ion optical potentials at finite temperature calculated using a complex effective interaction derived from a realistic force

Hot density distributions of heavy ions generated by a modified Thomas-Fermi calculation at finite temperature are used to calculate the optical potential using the double-folding method and a complex effective energy and density-dependent interaction deduced from a realistic NN (Reid soft-core) force in nuclear matter. The real and the imaginary part of the optical potential become more attractive when the temperature increases.     

Nuclear matter properties in the relativistic random phase approximation

Nuclear matter properties at zero temperature are studied in terms of the relativistic σ-ω model, including the random phase approximation (RPA) contribution. At normal density, the medium polarization adds about −35 MeV of binding energy to the mean field result. The scalar and vector effective interaction strengths are fitted to the nuclear matter saturation conditions under various approximations for the energy functional including the RPA term. The effective mass and bulk modulus are calculated with these parameters. The relative importance of different contributions to the binding energy is analyzed.     

Correlations in hypernuclear matter

We investigate short-range correlations in nuclear and hypernuclear matter. Self-energies due to short-range correlations and their influence on the nucleon and Λ -hyperon spectral functions are described in an approach accounting for a realistic treatment of mean-field dynamics and a self-consistently derived quasi-particle interaction. Landau-Migdal theory is used to derived the short-range interaction from a phenomenological Skyrme energy density functional, subtracting the long-range pionic contributions to the nucleonic spectral functions. We discuss our results for different hyperon-baryon ratios to show the influence of strangeness on the correlations in hypernuclear matter.     

Study of the Binding Energy of Relativistic Nuclear Matter in the Relativistic σ-ω-π Model

A relativistic σ-ω-π model is proposed to calculate the binding energy of relativistic nuclear matter. We put emphasis on the relativistic particle-hole, delta-hole excitation of pion propagator in nuclear matter. The renormalization of the nucleon self-energy in nuclear matter is made for the pseudo-vector πNN and πNΔ couplings by introducing corresponding form factor and by dispersion relation. We find that the density dependence correction to meson-NN coupling constants is very important to saturate the binding energy of nuclear matter. The density dependence correction to πNN and πNΔ coupling constants has the effect of softening the EOS of nuclear matter.     

Density dependence of nucleon radius and mass in the global color symmetry model of QCD with a sophisticated effective gluon propagator

Making use of the global color symmetry model (GCM) at finite chemical potential and with a sophisticated effective gluon propagator, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given as about 8 times the normal nuclear matter density. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass and the bag constant of the nucleon vanish and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place. Meanwhile, shortening the interaction range among quarks can induce the phase transition to happen easier.     

Equation of state of asymmetric nuclear matter: a VMC study

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.     

Comparison between microscopic and phenomenological nuclear pairing calculations

The isospin and density dependent effective pairing interaction is revisited by fitting the neutron gaps from the microscopic calculations for the neutron matter and the symmetric nuclear matter.The neutron pairing gaps for 1S0 channel for asymmetric nuclear matter are obtained from the BCS gap equation with a realistic bare nucleon-nucleon interaction in the Skyrme mean field.It is shown that the neutron gaps obtained from the new effective pairing interaction for the asymmetric nuclear matter are much imp...