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.     

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.     

Ring diagrams,Landau parameters,pion condensation and the binding energy of nuclear matter

We calculate all direct π-exchange ring diagrams to arbitrary orders in nuclear matter. Our model incorporates intermediate Δ(1236) resonances, correlations, ρ- as well as π-meson exchange and mesonic form factors. We find that the convergence of the diagram summation is governed by two quantities which have an immediate physical interpretation: the Landau parameter G'₀ and the threshold for pion condensation. The contribution to the energy of nuclear matter from terms of third and higher order is 2 MeV/particle (repulsion) at normal density, with a strong density dependence.     

Criteria for pion condensation thresholds in neutron star matter

The criteria for the appearance of pion condensation in neutron star matter are developed in terms of the pion Green's function in the normal state.     

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.     

Charge-constrained coherent pion states produced in nuclear matter

In a recent article, Bloss, Hone and Scalapino have used a simplified model Hamiltonian and Keldysh field theoretic methods to approximately calculate the power radiated as Cherenkov charged pions whose emission is triggered when a fast nucleon traverses nuclear matter. The model used by these authors conserves charge by flipping the isospin state of the fast nucleon alone for each charged pion emitted. Since it is the nuclear matter excited by the fast nucleon which should be largely reponsible for emitting the Cherenkov charged pions, we investigate an alternate model that allows all the disturbed nuclear matter to change its charge state when a charged pion is emitted—as an idealization, the emitting matter is assumed to have an infinite number of charge states, in contrast to the two of the fast nucleon. This modified model is shown to be exactly solvable in terms of charge-constrained coherent pion states; the power radiated as charged pions is found to be approximately twice that calculated by Bloss et al. from their model.     

Pion condensation in symmetric nuclear matter

Using a model which is based essentially on the chiral SU(2)×SU(2) symmetry of the pion-nucleon interaction, we examine the possibility of pion condensation in symmetric nucleon matter. We find that the pion condensation is not likely to occur in symmetric nuclear matter for any finite value of the nuclear density. Consequently, no critical opalescence phenomenom is expected to be seen in the pion-nucleus interaction.     

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.     

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.     

Update on pion weak decay constants in nuclear matter

The QCD sum rule calculation of the in-medium pion decay constants using pseudoscalar–axial-vector correlation function,

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is revisited. In particular, we argue that the dimension 5 condensate, , which is crucial for splitting the time (f_t) and space (f_s) components of the decay constant, is not necessarily restricted to be positive. Its positive value is found to yield a tachyonic pion mass. Using the in-medium pion mass as an input, we fix the dimension 5 condensate to be around −0.025 GeV²−0.019 GeV². The role of the N and Δ intermediate states in the correlation function is also investigated. The N intermediate state is found not to contribute to the sum rules. For the Δ intermediate state, we either treat it as a part of the continuum or propose a way to subtract explicitly from the sum rules. With (and without) explicit Δ subtraction while allowing the in-medium pion mass to vary within 139 MeVm_π^*159 MeV, we obtain f_s/f_π=0.370.78 and f_t/f_π=0.630.79.     

Comment on pion condensation

A criterion for pion condensation in nucleon matter can be concisely formulated when the pion Green function is given by the sum of poles, and is simply that two poles on the opposite side of the real axis come together. This criterion gives identical instability conditions as found by Sawyer using a different method.     

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.     

Pion condensation in electrically neutral cold matter with finite baryon density

In contrast to theoretical expectations, experimental results at GeV for the reaction γp → π⁰X show no evidence for odderon exchange. The upper limit on the cross section is an order of magnitude smaller than the theoretical estimate. It is argued that chiral symmetry leads to a large suppression, taking the theoretical estimates well below the data. Two additional arguments are presented which may decrease the theoretical estimate further. The calculations are more sensitive to the assumptions made in evaluating the hadronic scattering amplitude than in the processes considered previously and lattice gauge calculations indicate that the odderon intercept may be appreciably lower than usually assumed. These two latter effects are particularly relevant for the reactions γp → and γp → for which the data upper limits are also below the theoretical predictions, but not so dramatically as for γp → π⁰X.     

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.     

Fluctuational signals for pion Bose-Einstein condensation

We consider the Bose-Einstein condensation (BEC) in a relativistic pion gas. At high collision energy, in the samples of events with a fixed number of all pions, N, the pion system may approach the conditions of the BEC. An anomalous increase of the scaled variances of neutral and charged pion number fluctuations then appears. The size of this increase is restricted by the finite size of the pion system which should increase with the collision energy.     

On pion condensation in finite nuclei

The critical pionic state leading to pion condensation is investigated for finite nuclear systems. The threshold density for light nuclei, including⁴He, is found to be close to that of nuclear matter. For¹⁶O and⁴⁰Ca, the angular momenta of the most critical states areL=0 andL=2.     

Surface pion condensation in finite nuclei

We discuss here the possible occurrence of surface pion condensation in finite nuclei. We show the argument for this possibility by the recent findings in few-body calculations and the spin-flip experiments. We show the calculated results on various N = Z nuclei using the relativistic mean-field theory with a pion.Received: 30 September 2002, Published online: 22 October 2003PACS: 21.60.-n Nuclear-structure models and methods     

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.