Abnormal nuclear matter and pion condensation

The possibility of nuclear matter undergoing a combined phase transition into abnormal matter and a pion condensate is investigated. Various lagrangians for the meson (σ and π_i) fields, based on the σ-models, are used in mean-field approximation, and the entire system (mesons + nucleons) is treated fully relativistically. Equilibrium conditions of nuclear matter are obtained with NN repulsion, parametrized by the excluded volume approximation. It turns out that the formation of abnormal matter depends crucially on the choice of the σ-model lagrangian and considerably less on the additional pion condensate.     

Stability of nuclear matter against neutral pion condensation

The global stability of the uniform ground state of nuclear matter is tested relative to a π⁰-condensed state characterized by static spin-(isospin-) waves. Strong nuclear correlations are introduced into the trial wave functions for each phase, thereby permitting models of the realistic two-nucleon force to be employed. In low cluster-order comparison, the uniform phases of symmetrical nuclear matter and neutron matter are emphatically favored over the entire density range considered.     

Landau parameters for nuclear matter using the Skyrme interaction

Landau parameters for nuclear matter are calculated for several Skyrme interactions. Resulting values of G_o and G′_o are in disgreement with empirical values and lead to instability against spin collapse in several cases. A suitable generalization of the interaction is suggested to overcome these difficulties.     

Quasi-stationary nonlinear waves in nuclear matter close to pion condensation

The nuclear hydrodynamic model is extended to include the fluctuating spin-isospin density and its interaction with the nuclear matter density. Using the TDHF equations, it is shown that the dynamics of these densities interacting with the pion field can be expressed in terms of the generalized pressures derivable from the generalized nuclear matter equation of state. A phenomenological Skyrme interaction model is used to obtain these pressures. A theory of pion-like spin-isospin quasi-stationary nonlinear waves is formulated from the generalized hydroequations describing the dynamics of a coupled pion nuclear matter system. In the lowest order of nonlinearity, it is proved that the amplitude of the spin-isospin sound wave satisfies a nonlinear Schrödinger equation. The solution of these equations is the amplitude modulated pion-like solitary waves in nuclear matter. When this matter is near the pion condensate, the speed of these nonlinear waves is much smaller than that of the ordinary sound waves. An implication of the solitary waves excited in such nuclear matter produced in heavy ion collisions is discussed. The characteristic signature of breaking of such waves, produced in a heavy ion central collision, is the emission of a delayed component of correlated nucleons (possibly also with a pion) peaked in the forward direction. It may be that the lighter nuclei³He and³H are produced through such a mechanism.     

Role of the effective nucleon mass for pion condensation in nuclear matter

The dependence of the threshold for pion condensation in symmetric nuclear matter on the effective nucleon mass $\text{M}{}^1$ is investigated, using extrapolations of $\text{M}{}^1\text{(?)}$ to high densities ?, based on boson exchange mechanisms. It is found that if $\text{M}{}^1\text{(?)}$ decreases below the standard value $\text{M}{}^1\text{=0.8M}$ as the density increases beyond the nuclear matter density ?₀, the critical density is raised considerably beyond ?₀ once short-range repulsive correlations are included.     

On the contribution of anomalous diagrams to the ground-state energy of nuclear matter

It is shown that spin-orbit two-nucleon interaction does not lead to anomalous contributions to the Brueckner-Goldstone perturbation series in the second approximation.In conclusion, the author thanks Prof. I. Úlehla for pointing out this problem and J. Kvasnica C.Sc. for valuable remarks regarding the paper.     

Study of the asymmetric nuclear matter with pion dressing

We discuss here a self-consistent method to calculate the properties of the cold asymmetric nuclear matter. The nuclear matter is dressed with s-wave pion pairs. The nucleon-nucleon (N-N) interaction is mediated by these pion pairs, ∞ and ρ mesons. The parameters of these interactions are calculated selfconsistently to obtain the saturation properties like equilibrium binding energy, pressure, compressibility and symmetry energy. The computed equation of state is then used in the Tolman-Oppenheimer-Volkoff (TOV) equation to study the mass and radius of a neutron star containing pure neutron matter.     

A simple model calculation of pion condensation in neutron matter

The charged pion condensed state in pure neutron matter is described analytically in an approximate calculation based on the chirally invariant σ-model. The calculation includes s- and p-wave condensed pion-nucleon interactions, pi-pi interactions, the effect of the N¹ (1236) resonance, and the (Ericson-Ericson Lorentz-Lorentz) effect of nuclear correlations.     

Landau parameters and pairing-on the shores of the nuclear Fermi sea

We present a systematic scheme for calculating the ground-state energy, single-particle energies and the effective mass, Fermi-liquid parameters, and pairing matrix elements for nuclear and neutron matter with realistic state-dependent interactions. The method retains much of the clarity of more conventional treatments while permitting reliable numerical calculations. Deficiencies in the central Jastrow correlation operator ansatz are largely overcome by low-order perturbation theory in the correlated basis generated by the Jastrow operator. Calculations of these quantities are presented for the Reid and Bethe-Johnson interactions. An analysis of the results emphasizes the importance of state-dependent correlations arising directly from the interaction or indirectly through many-body effects. The numerical results provide insight into the actual structure of the self-energy operator in nuclear and neutron matter and into the usefulness of sum rules for the quasiparticle interaction and the Landau parameters.     

On relativistic approaches to the pion self-energy in nuclear matter

We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon-hole and delta-isobar-nucleon-hole contributions to the pion self-energy incorporates the s-wave scattering, whose magnitude within the RPA is in conflict with the near-threshold behavior imposed by chiral symmetry. As a result, a relativistic approach to the pion self-energy in isospin-symmetric nuclear matter, containing only these diagrams, does not satisfy the known experimental results on the near-threshold behavior of the -nucleon (forward) scattering amplitude.Received: 12 December 2003, Revised: 16 March 2004, Published online: 26 May 2004PACS: 24.10.Cn Many-body theory - 13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) - 21.65. + f Nuclear matter - 25.70.-z Low and intermediate energy heavy-ion reactions     

Delta and pion abundances in hot dense nuclear matter and the nuclear equation of state

Delta and pion abundances in hot dense nuclear matter are calculated self-consistently within a relativistic mean-field model for different equations of state. The density of deltas turns out to be much more sensitive to the effective masses of the baryons than to the stiffness of the equation of state. The results are compared to experimental pion yields from intermediate-energy nucleus-nucleus collisions. The influence of deviations from thermal momentum distributions for the baryons is estimated.     

Nuclear binding energy and symmetry energy of nuclear matter with modern nucleon–nucleon potentials

The binding energy of nuclear matter at zero temperature in the Brueckner–Hartree–Fock approximation with modern nucleon–nucleon potentials is studied. Both the standard and continuous choices of single particle energies are used. These modern nucleon–nucleon potentials fit the deuteron properties and are phase shifts equivalent. Comparison with other calculations is made. In addition we present results for the symmetry energy obtained with different potentials, which is of great importance in astrophysical calculation.     

Self-consistent inclusion of pion polarisation in the relativistic Dirac-Brueckner approach to nuclear matter

We investigate the influence of pion polarisation effects in the Dirac-Brueckner approach. The pion polarisation is included preserving the self-consistency of the DB approach. Results for single-particle properties, equation of state, and total effective cross sections in symmetric nuclear matter are presented. Also, we calculated the pion condensation threshold.     

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling (“BR scaling”) and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand, it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau–Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However, these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the Landau–Migdal approach.     

On the effect of ΛΣ conversion on the Λ particle binding energy in nuclear matter

The Λ particle binding energy in nuclear matter is calculated with a phenomenological separable ΛN-ΣN potential matrix and with a separable NN potential. The calculation includes the three-body ΛNN cluster energy and the rearrangement energy, both of which give only relatively small contributions to the calculated substantial Σ suppression.     

On the determination of the nuclear matter equation of state from pion yield data

Attempts to derive the nuclear matter equation of state from pion yield data have shown that the data can be reproduced by quite different parametrisations of the equation of state. We investigate this ambiguity within the one-dimensional shock wave model by deriving equations of statenot restricted to a predefined functional form. The results show that while in principle the dependence of the pion yields on energy can be reproduced by widely differing equations of state, some of these equations of state do not allow for sufficiently high bombarding energies. Others may violate causality inside the experimentally studied energy range, so that the admissible range of equations of state may be narrowed down considerably. Suggestions for further improvement are made.     

Symmetry energies of nuclear matter and the spin and isospin dependence of the nuclear single-particle potential in the Landau theory

The spin and spin-isospin symmetry energies of nuclear matter and the spin and isospin dependent terms of the nuclear single-particle potential at the Fermi surface are calculated within the frame of the Landau theory of the normal Fermi liquid from the existing sets of the Landau parameters. The possibility of the relation of these parameters to the experimental energies of certain collective nuclear excited states is pointed out. The results are also applied to the calculation of the symmetry and the spin-spin terms in the low energy nuclear optical model potential.     

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.