Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force (TBF). It is shown that the potential energy per nucleon in the isospin-singlet T=0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities, the TBF effect on the lsospin-triplet T=1 channel contribution turns out to be much larger than that on the T=0 channel contribution. At low densities around and below the normal nuclear matter density, the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T=1 component is almost independent of isospin asymmetry. As the density increases, the T=1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T=0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.     

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force（TBF） . It is shown that the potential energy per nucleon in the isospinsinglet T = 0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities,the TBF effect on the isospin-triplet T = 1 channel contribution turns out to be much larger than that on the T =0 channel contribution. At low densities around and below the normal nuclear matter density,the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T = 1 component is almost independent of isospin asymmetry. As the density increases,the T = 1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T = 0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.     

Single particle properties in asymmetric nuclear matter and TBF rearrangement effect

We have developed the formula and the numerical code for calculating the rearrangement contribution to the single particle (s.p.) properties in asymmetric nuclear matter induced by three-body forces within the framework of the Brueckner theory extended to include a microscopic three-body force (TBF). We have investigated systematically the TBF-induced rearrangement effect on the s.p. properties and their isospin-behavior in neutron-rich nuclear medium. It is shown that the TBF induces a repulsive rearrangement contribution to the s.p. potential in nuclear medium. The repulsion of the TBF rearrangement contribution increases rapidly as a function of density and nucleon momentum. It reduces largely the attraction of the BHF s.p. potential and enhances strongly the momentum dependence of the s.p. potential at large densities and high-momenta. The TBF rearrangement effect on symmetry potential is to enhances its repulsion (attraction) on neutrons (protons) in dense asymmetric nuclear matter.     

Spin and spin-isospin polarized nuclear matter

Properties of (N = Z) nuclear matter are investigated through a Brueckner method using the Paris potential for two special configurations, one when all spins are pointing in the same direction, the other when neutron spins are pointing upward and proton spins downward. The results of the calculations are used to evaluate the energy of the isoscalar giant spin dipole vibrations and the value of the spin-spin part of the nucleon-nucleus optical-model potential.     

Analytical relations between nuclear symmetry energy and single-nucleon potentials in isospin asymmetric nuclear matter

Using the Hugenholtz-Van Hove theorem, we derive general expressions for the quadratic and quartic symmetry energies in terms of the isoscalar and isovector parts of single-nucleon potentials in isospin asymmetric nuclear matter. These expressions are useful for gaining deeper insights into the microscopic origins of the uncertainties in our knowledge on nuclear symmetry energies especially at supra-saturation densities. As examples, the formalism is applied to two model single-nucleon potentials that are widely used in transport model simulations of heavy-ion reactions.     

Single particle energies of nuclear matter and the reference spectrum method

The single particle energies and the ground state energy of a superfluid system of nuclear matter are investigated. There are two difficulties in calculating these quantitites in the t-matrix approximation: (1) On account of the structure of thet-matrix equation the single particle energy is a very complicated expression, which cannot be evaluated explicitly in general. (2) Due to the superfluidity of nuclear matter, there are singularities in thet-matrix. — To overcome these difficulties we apply the reference spectrum method, recently proposed byBethe, et al. The most important properties of a superfluid medium, the shift of the ground state energy and the gap in the single particle spectrum can then be very well described qualitatively. The quantitative results, however, are not satisfying. Furthermore, the estimation of the single particle potential is very much simplified. However, this is useful only for hole states. For particle statesk>k _F , the single particle energy cannot be calculated with sufficient accuracy on account of new complications coming from the rearrangement energy.     

Zero-sound branches in asymmetric nuclear matter

A polarization operator constructed in the random phase approximation is used to obtain zero-sound excitations in isospin asymmetric nuclear matter (ANM). Two families of the complex solutions ω_sτ(k),τ= p,n are presented. The imaginary part of the solutions corresponds to the damping of the collective mode due to its overlapping with the particle-hole modes and the subsequent emission of a proton (ω_sp(k)) or a neutron (ω_sn(k)). The dependence of the solutions on the asymmetry parameter is studied.     

Vector mesons in asymmetric nuclear matter

The propagation of a vector meson (ϱ and ω) in dense asymmetric nuclear matter (with the number density of protons and neutrons different) is studied. Of particular interest is the density dependence of the vector meson masses, as also their variation with the asymmetry parameter, mass splitting among the ϱ isospin multiplets and the change of the form of the ϱ meson self-energy or the polarization tensor (II_μν) when the p ↔ n symmetry is broken. Contributions of both the Fermi sea and Dirac vacuum have been considered. It is shown that while the density dependent dressing of the vector meson propagator lifts the dispersion characteristics into the region of instability, the Dirac vacuum on the other hand contributes with opposite sign, thereby enhancing the possibility of stable collective modes even for higher values of vector meson momenta. The role of tensor coupling on the dispersion characteristics is also presented.     

Binding energy of asymmetric nuclear matter

The energy per particle of bulk nuclear matter has been calculated in the nuclear matter pair approximation over a wide range of density and symmetry parameter α.     

Variational calculations of asymmetric nuclear matter

We report on variational calculations of the energy E(ρ, β) of asymmetric nuclear matter having ? = ?_n + ?_p = 0.05 to 0.35 fm^?3, and β = (?_n ? ?_p/g9 = 0 to 1. The nuclear h used in this work consists of a realistic two-nucleon interaction, called v₁₄, that fits the available nucleon-nucleon scattering data up to 425 MeV, and a phenomenological three nucleon interaction adjusted to reproduce the empirical properties of symmetric nuclear matter. The variational many-body theory of symmetric nuclear matter is extended to treat matter with neutron excess. Numerical and analytic studies of the β-dependence of various contributions to the nuclear matter energy show that at ? < 0.35 fm^?3 the β⁴ terms are very small, and that the interaction energy EI(ρ, β) defined as E(ρ, β) ? T_F(ρ, β), where T_F is the Fermi-gas energy, is well approximated by EI₀(?) + β²EI₂(ρ). The calculated symmetry energy at equilibrium density is 30 MeV and it increases from 15 to 38 MeV as ? increases from 0.05 to 0.35 fm^?3.     

Skyrme-Hartree-Fock treatment of asymmetric nuclear matter

Asymmetric nuclear matter is studied, within the Hartree-Fock approach, employing the Skyrme force. It is seen that the asymmetry ratio can be considered to be an order parameter for phase transitions between a solid and a fluid phase.     

Droplet formation in cold asymmetric nuclear matter

An extended version of the non-linear Walecka model, with ϱ mesons an electromagnetic field is used to investigate the possibility of phase transitions in cold nuclear matter (T = 0), giving rise to droplet formation. Surface properties of asymmetric nuclear matter as the droplet surface energy and its thickness are discussed. The effects of the Coulomb interaction are investigated.     

Spinodal decomposition of low-density asymmetric nuclear matter

We investigate the dynamical properties of asymmetric nuclear matter at low density. The occurrence of new instabilities, that lead the system to a dynamical fragment formation, is illustrated, discussing in particular the charge symmetry dependence of the structure of the most important unstable modes. We observe that instabilities are reduced by charge asymmetry, leading to larger size and time scales in the fragmentation process. Configurations with less asymmetric fragments surrounded by a more asymmetric gas are favoured. Interesting variances with respect to a pure thermodynamical prediction are revealed, that can be checked experimentally. All these features are deeply related to the structure of the symmetry term in the nuclear Equation of State (EOS) and could be used to extract information on the low density part of the EOS.     

On the properties of asymmetric nuclear matter

The properties of asymmetric nuclear matter withα=(ρ _n-ρ _p)/ρ≦ 0.4 are studied within the framework of the lowest order Brueckner theory, atk _F =1.35fm^?1 (ρ=0.166 fm^?3). TheK-matrix is calculated self-consistently from the Reid soft core nucleon-nucleon interaction. In the case ofρ _n ≠ρ _p theK-matrix contains a term which does not conserve the total isospin of the interacting unlike-nucleon pair. At α=0.4 the relative magnitude of this term is of the order of 1 %. The symmetry energy is found equal to 23.1 MeV.     

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.     

Isospin and density waves in asymmetric nuclear matter

The excitation of small density oscillations (zero sound) and isospin oscillations (isospin sound) in cold asymmetric nuclear matter (in the ground state ?⁰_n> ?⁰_p, ?⁰ = ?⁰_n+?⁰_p = 0.17 nucleons/fm³) is investigated within the framework of the Landau theory of normal Fermi liquids. There is only one undamped mode of excitation, which consists predominantly of isospin oscillations, with some admixture of density oscillations. The phase velocity of this undamped wave depends very weakly on the neutron excess and is close to that of a pure isospin wave (isospin sound) in symmetric nuclear matter of the same density. At the neutron excess corresponding to that existing in heavy nuclei the amplitude of the density oscillations constitutes about 30 % of the amplitude of the neutron excess density oscillations. Calculation with a suitably parametrized charge dependent quasiparticle interaction in asymmetric nuclear matter shows that for (?⁰_n??⁰_p)/?⁰ > 0.63 both zero sound and isospin sound are strongly damped.     

Medium polarization and pairing in asymmetric nuclear matter

The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner–Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of ¹ S ₀ proton–proton and ³ PF ₂ neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (anti-screening) interaction going from pure neutron matter to symmetric nuclear matter is discussed.     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Thermodynamics of a n-p condensate in asymmetric nuclear matter

We study the neutron-proton pairing in nuclear matter as a function of isospin asymmetry at finite temperatures and the empirical saturation density using realistic nuclear forces and Brueckner-renormalized single particle spectra. Our computation of the thermodynamic quantities shows that, while the difference of the entropies of the superconducting and normal phases anomalously changes its sign as a function of temperature for arbitrary asymmetry, the grand canonical potential does not; the superconducting state is found to be stable in the whole temperature-asymmetry plane. The pairing gap completely disappears for density asymmetries exceeding alpha(c) = (rho(n)-rho(p))/rho approximately 0.11.