A phenomenological approach to pion condensation

The threshold of π-condensation in isospin symmetric nuclear matter is studied with a field theoretic model which reproduces the low energy πN data. We find a critical density around normal nuclear matter density. Besides the role of the nucleon-nucleon correlations we investigate the effect of the s-wave πN interaction on- and off-mass-shell. The chiral symmetry breaking Σ-term may impede pion condensation.     

Pion condensation in neutron star matter: (II). Nuclear forces and stability

This paper presents several stable models of charged-pion condensed neutron star matter. The non-relativistic limit of the chirally symmetric Weinberg Lagrangian is used to describe interactions of the condensed pion field with the nucleons, as well as the pi-pi interactions of the condensed field. In the absence of nucleon-nucleon interactions, matter in this model is unstable, tending to ever-increasing baryon density and condensate wave vector. The connection of this model of condensation with the σ-model is shown.A general framework for including nuclear forces is then laid out. Results are given for a simple model in which the nuclear forces are assumed to produce an interaction energy V(ρ) dependent only on the total baryon density, independent of the degree of pion condensation, and also to produce a constant G-matrix element g in the nucleon-nucleon charge exchange channel. In the absence of condensation the equation of state reduces to that of interacting normal matter. We also consider effects of beta equilibrium and form factors in the p-wave pion-nucleon interaction. The condensed models are stable. Depending on the choice of parameters the models exhibit first- or second-order pion condensation phase transitions, or both.     

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.     

Pion condensation in symmetric nuclear matter

The problem of pion condensation in isospin symmetric nuclear matter is investigated in the framework of the σ-model with a residual nucleon-nucleon interaction (g′σ₁ · σ₂τ₁ · τ₂δ(x)) and Δ-isobars. The equation of state for the pion condensed phase is calculated and applied to a low-energy heavy-ion collision in the TDHF approximation. The effective particle-hole interaction and the response to spin-isospin excitation are used to determine the magnitude of the Landau-Migdal parameter g′. For a reasonable range of g′(0.5 < g′ ≦ in units of g²/4m²_N = 410 MeV · fm³) pion condensation occurs at densities above normal nuclear matter density and leads to an equation of state with no stable density isomer.     

核物质中内介质等效手征Lagrange量和π介子质量

在核物质中从手征等效Lagrange量得到的π介子有效质量是单值的,并且与π介子场的离壳扩展无关,例如PCAC选择.同位旋对称核物质中的有效π介子质量随增加的核密度有些上升,因此有效类时π介子衰变常数和密度相关的夸克凝聚渐渐下降.另外研究了内介质Gell–Mann–Oakes–Renner关系和其它内介质同一性.最后讨论了同位旋对称、各向同性和均匀的核物质中关于介子传播的等效Lagrange量的几个限制.     

Pion condensation in heavy ion collisions

We calculate the pion spectrum in dense nuclear matter for finite temperatures. The critical temperatureT _c(ρ) that marks the beginning of a second order phase transition due to pion condensation is given in a phase diagram. We show that in heavy ion collisions, pion condensation should occur, leading to an enhancement in the formation of nuclear shock waves.     

Effect of nucleon correlations on pion condensation in neutron stars

It is pointed out that nucleon-nucleon correlations, play an important role in the pion condensation problem. Their effect is estimated by a simple analytical method. It is seen that they inhibit condensation by reducing the attraction a pion might otherwise feel in nuclear matter. Further the effect of correlations increases with nucleon density ?, offsetting the corresponding increase in the attraction felt by pions in free neutron matter.     

Behavior of solutions to the pion dispersion equation in the complex frequency plane

Solutions to the pion dispersion equation in the complex plane of the pion frequency ω are obtained for symmetric nuclear matter. Three well-known solution branches—a sound, a pion, and an isobar one—exist on the physical sheet at the medium density below its critical value (ρ<ρ_c). For ρ>ρ_c, the fourth branch ω_c appears on the physical sheet. The condition ω _c ² ≤0 is valid for this branch (in general, Re ω _c ² ≤0). This suggests ground-state instability, possibly associated with pion condensation. The behavior of these solutions is analyzed for various medium densities. The appearance of each solution on the physical sheet of the complex frequency plane and its disappearance are also studied.     

Pion Softening and Pion Condensation

Physics of Atomic Nuclei - In this paper after a historical introduction I discuss ideas of a pion softening and pion condensation in a dense nuclear matter, in particular in neutron stars, and a...     

手征胶子修正夸克平均场模型

这项工作利用考虑π介子与胶子效应的夸克平均场模型研究原子核结构的基本性质。在夸克平均场中,核子由三个束缚在谐振子势场中的组分夸克构成。描述强相互作用的量子色动力学必须满足手征对称性,此外夸克之间也需要通过交换胶子相互作用。因此,在夸克平均场模型中,对利用夸克势获得的核子质量考虑π介子修正与胶子修正。通过少数稳定有限核的结合能与半径实验值确定模型中的未知参数,获得了一组夸克平均场相互作用参数,QMF-NK。利用该组参数计算40Ca和208Pb的电荷密度分布,发现与实验值符合很好。随后获得了与经验值一致的对称核物质的饱和性质。包含π介子修正和胶子修正的夸克平均场模型能够更好地描述有限核和核物质的性质。The basic properties of nuclear structure are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account. In QMF, the nucleon is made up of three constituent quarks confined by a harmonic oscillator potential. The quantum chromodynamics describing the strong interaction must satisfy the chiral symmetry and quarks interact with each other through exchange of gluons. Therefore pion correction and gluon correction are included in the nucleon mass obtained by using quark confinement potential in quark mean field model. We determine the unknown parameters in the model by fitting the experimental data of the binding energies and radii of several stable finite nuclei and obtain a set of parameters of quark mean field interaction, named QMF-NK. The charge density distributions of 40Ca and 208Pb are calculated, which are in good agreement with the experimental data. Later the saturation properties of symmetric nuclear matter which are consistent with the empirical data are obtained. With the pion and gluon corrections, the QMF model could treat finite nuclei and nuclear matter better.     

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.     

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.     

Tensor optimized antisymmetrized molecular dynamics for relativistic nuclear matter

We apply a newly developed many-body theory, tensor optimized antisymmetrized molecular dynamics (TOAMD), to nuclear matter using a relativistic bare nucleon-nucleon interaction in the relativistic framework. It becomes evident that the tensor interaction plays an important role in nuclear many-body system due to the role of the pion in a strongly interacting system. We take the relativistic nuclear matter (RNM) wave function as a basic state and add tensor and short-range correlation operators in the form of pion and omega-meson correlation functions acting on the RNM wave function using the concept of TOAMD. We use the Monte Carlo (Metropolis) method based on the Gaussian integration and the second quantization method for antisymmetrization to calculate all the matrix elements of the many-body Hamiltonian. We write the whole formula of the TOAMD method for numerical calculations of the nuclear binding and saturation properties of nuclear matter using one-boson exchange potential.     

Pion Propagator in the Chiral σ Model of Nuclear Matter

Pion propagator is studied in the chiral σ model at the zero temperature nuclear matter. Due to the tachyon pole of the π and σ tree approximation propagators, only the nucleon polarization insertion loop (explicitly density dependent part and vacuum fluctuation part) can be fully included into the pion propagator. The vacuum fluctuation as a function of nucleon effective mass or pion external momentum (after Wick rotation) is negative for most of the cases. So the variation of nucleon effective mass is restricted to a very limited region where is free of pion condensation (otherwise the nucleon energy density will be complex). The effect of NN short-range correlation is calculated and it is very small for low momentum.     

Abnormal neutron star matter at ultrahigh densities

We consider three models, based on the mean field and sigma models, all of which fit the saturation properties and the symmetry energy of nuclear matter. None of the models yields an abnormal state of neutron star matter at supemuclear density even when pion condensation is taken into account.     

Particle hole state densities

The influence of correlations on the critical temperature and density for the onset of superfluidity in nuclear matter is investigated within the scheme of Nozières and Schmitt-Rink [1]. For symmetric nuclear matter a smooth transition from Bose-Einstein condensation (BEC) of deuteronlike bound states at low densities and low temperatures to Bardeen-Cooper-Schrieffer (BCS) pairing at higher densities is described. Compared with the mean field approach a lowering of the critical temperature is obtained for symmetric nuclear matter as well as for pure neutron matter. The Mott transition in symmetric nuclear matter is discussed. Regions in the temperature-density plane are identified where correlated pairs give the main contribution to the composition of the system, so that approximations beyond the quasi-particle picture are requested.     

Relativistic Particle-Hole and Delta-Hole Excitations for Pion Propagator in Nuclear Matter

The relativistic particle-hole and delta-hole polarization insertions for pion propagator are calculated by using particle-hole-antiparticle representation of nucleon and delta propagators in nuclear matter. The short-range correlations between nucleon-nucleon, nucleon-delta and delta-delta are included via Landau-Migdal parameter g' in the random phase approximation. We calculate the dispersion relations for pions and find out that the damped pion condensation is removed by the short-range correlation and there is a long gap in the dispersion relation.