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The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter. The results, obtained in the framework of the Brueckner-Hartree-Fock approximation with two- and three-body forces, confirm the well-known parabolic dependence on the asymmetry parameter β = (N − Z)/A (β 2law) that is valid in a wide density range. To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction, aside from the mean field approximation, the spin-isospin decomposition of BA is performed. Theoretical indications suggest that the β 2law could be violated at higher densities as a consequence of the three-body forces. This raises the problem that the symmetry energy, calculated according to the β 2law as a difference between BA in pure neutron matter and symmetric nuclear matter, cannot be applied to neutron stars. One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z = N nuclei and pure neutron matter.

The properties of nuclear matter in the presence of a strong magnetic field, including the density-dependent symmetry energy, the chemical composition and spin polarizations, are investigated in the framework of the relativistic mean field models FSU-Gold. The anomalous magnetic moments (AMM) of the particles and the nonlinear isoscalar-isovector coupling are included. It is found that the parabolic isospin-dependence of the energy per nucleon of asymmetric nuclear matter remains valid for values of the magnetic field below $10^{5}B_{c}^{e}$, $B_{c}^{e}=4.414\times10^{13}$G being the electron critical field. Accordingly, the symmetry energy can be obtained by the difference of the energy per nucleon in pure neutron matter and that in symmetric matter. The symmetry energy, which is enhanced by the presence of the magnetic field, significantly affects the chemical composition and the proton polarization. The effects of the AMM of each component on the energy per nucleon, symmetry energy, chemical composition and spin polarization are discussed in detail., Comment: 18 pages, 7 figures, to appear in Nucl. Phys. A

The influence of the core polarization on the effective nuclear interaction of asymmetric nuclear matter is calculated in the framework of the induced interaction theory. The strong isospin dependence of the density and spin density fluctuations is studied along with the interplay between the neutron and proton core polarizations. Moving from symmetric nuclear matter to pure neutron matter the crossover of the induced interaction from attractive to repulsive in the spin singlet state is determined as a function of the isospin imbalance.The density range in which it occurs is also determined. For the spin triplet state the induced interaction turns out to be always repulsive. The implications of the results for the neutron star superfluid phases are shortly discussed., Comment: 6 pages, 4 figures

We investigate the neutron and proton single particle (s.p.) potentials of asymmetric nuclear matter and their isospin dependence in various spin-isospin $ST$ channels within the framework of the Brueckner-Hartree-Fock approach. It is shown that in symmetric nuclear matter, the s.p. potentials in both the isospin-singlet T=0 channel and isospin-triplet T=1 channel are essentially attractive, and the magnitudes in the two different channels are roughly the same. In neutron-rich nuclear matter, the isospin-splitting of the proton and neutron s.p. potentials turns out to be mainly determined by the isospin-singlet T=0 channel contribution which becomes more attractive for proton and more repulsive for neutron at higher asymmetries., 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1310.1192

We have calculated the nucleon effective mass in symmetric nuclear matter within the framework of the Brueckner-Bethe-Goldstone (BBG) theory, which has been extended to include both the contributions from the ground-state correlation effect and the three-body force (TBF) rearrangement effect. The effective mass is predicted by including the ground-state correlation effect and the TBF rearrangement effect, and we discuss the momentum dependence and the density dependence of the effective mass. It is shown that the effect of ground state correlations plays an important role at low densities, while the TBF-induced rearrangement effect becomes predominant at high densities.

Microscopic three-nucleon force consistent with the Bonn B two-nucleon potential is constructed, which includes Δ(1232), Roper, and nucleon-antinucleon excitation contributions. Recent results for the choice of the meson parameters are discussed. The forces are used in Brueckner calculations and the saturation properties of nuclear matter are determined. At the high densities, the nuclear equation of state and the symmetry energy are calculated. The corresponding neutron star mass-radius relations are presented.

Medium polarization effects are studied for 1S0 pairing in nuclear matter within BHF approach. The screening potential is calculated in the RPA limit, suitably renormalized to cure the low density mechanical instability of nuclear matter. The self-energy corrections are consistently included resulting in a strong depletion of the Fermi surface. The self-energy effects always lead to a quenching of the gap, whereas it is almost completely compensated by the anti-screening effect in nuclear matter.

The Fermi surface depletion of beta-stable nuclear matter is calculated to study its effects on several physical properties which determine the neutron star thermal evolution. The neutron and proton Z factors measuring the corresponding Fermi surface depletions, are calculated within the Brueckner-Hartree-Fock approach employing the AV18 two-body force supplemented by a microscopic three body force. Neutrino emissivity, heat capacity and, in particular, neutron 3PF2 superfluidity turn out to be reduced, especially at high baryonic density, to such an extent that the cooling rates of young neutron stars are significantly slowed, Comment: 9 pages, 6 figures, accepted for publication in ApJ

Within the Wigner-Seitz approximation, a self-consistent fully quantum-mechanical calculation of the structure of the inner crust of a neutron star is performed over a wide range of densities with allowance for superfluidity effects. Within the approach used, the Wigner-Seitz cell consists of a nuclear-like cluster surrounded by a nearly uniform neutron gas. An effective energy functional is constructed by matching, at the cluster surface, the realistic phenomenological nuclear functional for the cluster due to S. A. Fayans and his coauthors and the energy functional calculated microscopically for neutron matter. The microscopic component of the functional is calculated within the Brueckner method by using the v18 Argonne interaction.

We try to determine phenomenologically the extent of in-medium modification of σ-meson parameters so that the saturation observables of the nuclear matter equation of state (EOS) are reproduced. To calculate the EOS we have used Brueckner-Bethe-Goldstone formalism with Bonn potential as two-body interaction. We find that it is possible to understand all the saturation observables, namely, saturation density, energy per nucleon and incompressibility, by incorporating in-medium modification of σ-meson-nucleon coupling constant and σ-meson mass by a few per cent.

A self-consistent, completely quantum calculation of the structure of the inner crust of neutron stars is carried out in the Wigner-Seitz approximation with a realistic phenomenological nuclear energy functional, where pair correlations of neutrons and protons are included in the explicit form. It has been shown that the superfluidity of neutrons and protons affects the structure of the ground state of the crust.

A new formalism to calculate the in-medium chiral condensate is presented. At lower densities, this approach leads to a linear expression. If we demand a compatibility with the famous model-independent result, then the pion-nucleon sigma term should be six times the average current mass of light quarks. QCD-like interactions may slow the decreasing behavior of the condensate with increasing densities, compared with the linear extrapolation, if densities are lower than twice the nuclear saturation density. At higher densities, the condensate vanishes inevitably., Comment: contribution to the QCD 2003 conference in Montpellier

The three-body force effects on the equation of state and its iso-spin dependence of asymmetric nuclear matter and on the proton fraction in neutron star matter have been investigated within Brueckner-Hartree-Fock approach by using a microscopic three-body force. 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 is fulfilled in the whole asymmetry range and also up to high density. The three-body force provides a strong enhancement of symmetry energy at high density in agreement with relativistic approaches. It also shows that the three-body force leads to a much more rapid increasing of symmetry energy with density in relatively high density region and to a much lower threshold density for the direct URCA process to occur in a neutron star as compared to the predictions adopting only pure two-body force.

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The 1S0 singlet and the 3S1+3D1 triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E0. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=−8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E0. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E0≥10 MeV.

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f0(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f0(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f0(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.

The pairing gap in semi-infinite nuclear matter has been calculated microscopically by solving the gap equation for a nonlocal interaction with the aid of the method proposed by V.A. Khodel, A.V. Khodel, and J.W. Clark [Nucl. Phys. A 598, 390 (1996)] for the case of infinite nuclear matter. The calculation employs the effective pairing interaction obtained previously for semi-infinite geometry on the basis of the separable 3×3 representation of the Paris nucleon-nucleon potential. The gap found in this way changes sharply in the surface region, where it has a pronounced maximum. The dependence of the surface effect on the chemical potential of nuclear matter has been investigated.

We determine pairing gap and binding energy of symmetric nuclear matter in a combined, self-consistent treatment of BCS gap equation and Brueckner-Hartree-Fock equations. Relative to the uncoupled scheme, we find a reduction of the gap by about 10 percent. The binding energy per nucleon is lowered by up to about 1 MeV.

The nucleon mean free path in nuclear matter is studied within the framework of the Brueckner-Hartree-Fock approximation extended to incorporate ground-state correlations. The ground state particle-hole excitations give rise to a partial opening of the Fermi sphere and to an enhancement of the mean free path above the Fermi surface. A comparison with the classical limit and the mean free path in neutron matter is discussed along with a simple prescription to include the isospin dependence.

Within the framework of Brueckner-Hartree-Fock method, the in-medium nucleon-nucleon (NN) cross section is calculated. We base our investigation on a separable Paris potential for the NN interaction and a continuous choice for the single particle spectrum. It is found that the in-medium cross section is strongly modified by medium effect. In particular, with increasing of nuclear density, the cross sections decrease. This indicates a proper treatment of the density dependence of the in-medium NN cross sections is important.

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iwm2001

We establish a correlation for the symmetry energy at saturation density $S_{0}$, slope parameter $L$ and curvature parameter $K_{\text{sym}}$ based on widely different mean field interactions. With the help of this correlation and available empirical and theoretical information, the density dependent behavior around the saturation density is determined. We compare the results obtained with the present approach with those by other analyses. With this obtained density dependent behavior of the symmetry energy, the neutron skin thickness of $^{208}$Pb and some properties of neutron stars are investigated. In addition, it is found that the expression $S(\rho)=S_{0}(\rho /\rho_{0})^{\gamma}$ or $S(\rho)=12.5(\rho /\rho_{0}) ^{2/3}+C_{p}(\rho /\rho_{0}) ^{\gamma}$ does not reproduce the density dependence of the symmetry energy as predicted by the mean-field approach around nuclear saturation density., Comment: 6 pages, 4 figures

Skyrme-like energy density functionals are built upon new ab initio calculations of nuclear matter which reproduce the empirical saturation properties. These calculations are performed in the framework of the Brueckner-Hartree-Fock approximation with consistent two- and three-body forces. The Skyrme parametrizations are obtained from a simultaneous fit of the spin-isospin components of the potential energy of symmetric nuclear matter and of the experimental energies and charge radii of a number of closed-shell and closed-subshell nuclei. These parametrizations are tested on the energies and charge radii of the Sn isotopic chain and on the ${}^{208}$Pb giant resonances, showing a substantial improvement of the LNS functional obtained in a previous fit. The comparison with standard Skyrme forces can give some hints on how to reconcile nuclear matter and finite nuclei.

We have investigate the nucleon superfluidity in asymmetric nuclear matter and neutron star matter by using the Brueckner‐Hartree‐Fock approach and the BCS theory. We have predicted the isospin‐asymmetry dependence of the nucleon superfluidity in asymmetric nuclear matter and discussed particularly the effect of microscopic three‐body forces. It has been shown that the three‐body force leads to a strong suppression of the proton 1S0 superfluidity in β‐stable neutron star matter. Whereas the microscopic three‐body force is found to enhance remarkably the 3PF2 neutron superfluidity in neutron star matter and neutron stars.

The neutron-proton superfluidity for nuclear matter in the 3 S 1  3 D 1 channel is studied within the BCS formalism. In agreement with previous calculations based on the T -matrix approach, a large energy gap is found if one adopts the bare nucleon-nucleon interaction in the gap equation. The dependence of the results on the single-particle spectrum and on the nucleon-nucleon interaction is analyzed and discussed. The relevance of the results for the structure of neutron stars, nuclear matter saturation and superfluidity in finite nuclei is briefly discussed.

The volume component of the phenomenological optical potential is traced to the microscopic theory of nuclear matter. The latter is based on the Brueckner-Hartree-Fock approach with three-body force, which recently has proved to be able to reproduce the empirical saturation properties of nuclear matter. The self-energy is calculated and its on-shell matrix elements are related to the volume part of the optical potential. A previous investigation, where the real part of the microscopic potential was compared with an empirical one, which is a fit of the experimental nucleon-nucleus elastic scattering, is here extended to the absorptive component. Moreover, the isospin splitting of the optical potential is discussed in connection with the proton and neutron effective masses of isospin asymmetric nuclear systems.

The volume part of the phenomenological optical potential is interpreted in terms of the microscopic theory of nuclear matter. The latter is based on the Brueckner-Hartree-Fock approach with a new version of three-body force, reproducing the empirical saturation properties of nuclear matter. The self-energy is calculated and its on-shell matrix elements are related to the volume part of the optical potential. A comparison is made with a recent parametrization of the optical model potential fitting the experimental nucleon-nucleus elastic scattering. The isospin effects and Coulomb corrections are emphasized.

We investigate the effect of microscopic three-body forces on the {sup 3}P F{sub 2} neutron superfluidity in neutron matter, {beta}-stable neutron star matter, and neutron stars by using the BCS theory and the Brueckner-Hartree-Fock approach. We adopt the Argonne V18 potential supplemented with a microscopic three-body force as the realistic nucleon-nucleon interaction. We have concentrated on studying the three-body force effect on the {sup 3}P F{sub 2} neutron pairing gap. It is found that the three-body force effect considerably enhances the {sup 3}P F{sub 2} neutron superfluidity in neutron star matter and neutron stars.

The transport models, which are employed to describe the central reactions in heavy ion collisions(HIC), are powerful approaches to reproduce the collective observable in HIC and probe the equation of state(EOS) of nuclear matter. Those models, such as the quantum molecular dynamics (QMD) and Boltzmann-UehlingUhlenbeck (BUU) equation as well as their relativistic extensions (RBUU and RQMD), treat the nucleon mean fields and nucleon-nucleon scattering cross sections as the basic input ingredients. Up to now, most caculations of particle producing in nucleus-nucleus reaction are using the free cross sections or the approximations σ∗ NN = 0.8σ free NN , σ ∗ NN/σ free NN = (m ∗/m)2 instead of the in-medium cross sections. Many recent papers have devoted to the in-medium N-N scattering problem within different methods, such as the collectivistic Brueckner approach, and Dirac-Brueckner-Hartree-Fock(DBHF) approach. Here we apply the DBHF approach for its successfully describing the mechanism of the EOS, which meets the empirical region of saturation. However, because of the uncertainty in determining the nucleon self-energy in DBHF approach, Horowitz and Serot have developed a projection technique in which projects the G-matrix onto five covariant amplitudes. This set of five covariant amplitudes is not unique, corresponding to different representations, and we adopt two different representations (pseudo-scalar(ps) and complete pseudo-vector(pv) representations).

We construct microscopic three-nucleon forces consistent with the Bonn and Nijmegen two-nucleon potentials, and including \ensuremath{\Delta}, Roper, and nucleon-antinucleon excitations. Recent results for the choice of the meson parameters are discussed. The forces are used in Brueckner calculations and the saturation properties of nuclear matter are determined.

The single-nucleon potential in hot nuclear matter is investigated in the framework of the Brueckner theory by adopting the realistic Argonne V18 or Nijmegen 93 two-body nucleon-nucleon interaction supplemented by a microscopic three-body force. The rearrangement contribution to the single-particle potential induced by the ground state correlations is calculated in terms of the hole-line expansion of the mass operator and provides a significant repulsive contribution in the low-momentum region around and below the Fermi surface. Increasing temperature leads to a reduction of the effect, while increasing density makes it become stronger. The three-body force suppresses somewhat the ground state correlations due to its strong short-range repulsion, increasing with density. Inclusion of the three-body force contribution results in a quite different temperature dependence of the single-particle potential at high enough densities as compared to that adopting the pure two-body force. The effects of three-body force and ground state correlations on the nucleon effective mass are also discussed., Comment: 14 pages, 5 figures

A separable representation of the Paris interaction is used as input for the investigation of various nuclear matter properties. The faithfulness of the separable representation is checked by comparison with results previously obtained from the original Paris interaction. Calculations are performed for four different values of the Fermi momentum, namely ${\mathit{k}}_{\mathit{F}}$=1.10, 1.36, 1.55, and 1.75 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. One evaluates the contributions to the quasiparticle potential energy that are of first, second, and third order in the reaction matrix. The momentum distribution n(k) in the correlated ground state is calculated up to second order in the reaction matrix. For 0k2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$, it mainly depends upon the ratio k/${\mathit{k}}_{\mathit{F}}$; in the domain 2k4.5 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$, it is accurately reproduced by the expression 1/7${\mathit{k}}_{\mathit{F}}^{5}$${\mathit{e}}^{\mathrm{\ensuremath{-}}1.6\mathit{k}}$, with k and ${\mathit{k}}_{\mathit{F}}$ in units of ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. The quasiparticle strength at the Fermi surface is calculated, as well as the mean-square deviation of the one-body density matrix from that of the unperturbed Fermi sea: This quantity gives an estimate of the minimum value of the norm of the difference between the one-body density matrix of a correlated nucleus and that associated with any Slater determinant. The average kinetic energy per nucleon is evaluated. Various contributions to the average binding energy per nucleon are investigated in the framework of Brueckner's expansion; particular attention is paid to the dependence of the calculated binding energy upon the choice of the ``auxiliary'' potential which is added to and subtracted from the Hamiltonian before performing the expansion. One also evaluates diagrams that are characteristic of the difference between the Green's function and the Brueckner hole-line expansions. The fulfillment of the Hugenholtz--Van Hove theorem is studied.