Neutral Pion Condensation Research Articles

Pion condensates. Multiple photon mass generation in presence of heavy ions

It is shown that the charged pion-photon coupling, in the region between two heavy nuclei while colliding, gives rise to a photon mass. Independently of this, when there is a neutral pion condensation (also in the region between the heavy nuclei) as well, a mass arises from a Chern-Simons type term. However, when both these effects are considered together, photons having a multiple mass spectrum are generated. It is thus suggestive that the decay of the “heavy” photons into e +e − could provide an explanation of the anomalous multiple e +e − MeV peaks observed in heavy ion scattering.

Quark matter with neutral pion condensate

The neutral pion condensate in a chirally broken phase of quark matter is studied in the sigma model with quark and meson degrees of freedom. We find that above a critical quark mass of about 200 MeV the pion-condensed phase is the ground state of the system. In this phase the up and down quark Fermi seas are oppositely polarized along the direction of the pion field wave vector. We calculate the net spin density of the up and down Fermi seas and we estimate the magnetization of the system. Astrophysical implications are briefly discussed.

One-fermion-loop contribution to the energy of the neutral pion condensate in the σ-model

The one-fermion loop contribution to the energy of the neutral pion condensate in the Gell-Mann-Lévy σ-model is calculated analytically. Two methods are applied: explicit summation over the Dirac spectrum, and a perturbative method, whose convergence properties are studied quantitatively. Vacuum instability of the theory is found, in agreement with earlier results for solitons in the σ-model.

Equation of state for dense nucleon matter

We report microscopic calculations of the equation of state for dense nuclear and neutron matter. The calculations are performed for five Hamiltonians: the Argonne ${v}_{14}$ and Urbana ${v}_{14}$ two-nucleon potentials, both alone and with the Urbana VII three-nucleon potential, and the density-dependent Urbana ${v}_{14}$ plus three-nucleon interaction model of Lagaris, Friedman, and Pandharipande. The beta-stable equation of state and neutron star structure are also calculated for three of the models. The models with the three-nucleon potential bracket the density-dependent model and are significantly stiffer than those with an unmodified two-nucleon potential only. The Argonne ${v}_{14}$ plus Urbana VII Hamiltonian produces a softening in the neutron matter equation of state localized around twice nuclear matter density which may indicate a neutral pion condensate.

Strangeness and chiral symmetry

A number of difficult problems are encountered in attempts to incorporate the strange quark into hadronic structure by generalizing from two to three flavors because the mass of the strange quark m s ≈ 175 MeV ≈ Λ QCD. This mass is neither small nor large. A question of particular interest is as to the s̄s content of the nucleon. If it is large, it is likely that strangeness condensation will occur at densities ϱ ≈ 3 ϱ o, where ρ o is nuclear matter density. In order to gain insight into the mechanism for strangeness condensation, s-wave neutral pion condensation is first investigated. Then the analogous problem of strangeness condensation, once the SU(3) × SU(3) problem is reduced to an SU(2) × SU(2) one by using V spin, can be simply investigated. The role of the strange quark mass in quark condensates is investigated, employing the Nambu-Jona-Lasinio formalism. In the large N c limit, the quark flavors decouple, but in order 1/N c are strongly mixed by the determinantal interaction between quarks which arises once instantons are integrated out. This suggests a possible mechanism for the strange quark mass to affect the nucleon energy and for the s̄s content of the nucleon to be large.

Extra Neutrino Emissivity of Neutron Stars under the Combined Condensation of Neutral and Charged Pions

Extra neutrino emissivity of neutron stars under the combined condensation of neutral and charged pions (CPC), which we call quasi-particle URCA process, is examined in a realistic approach. Here the isobar L1 (1232) degrees of freedom, baryon-baryon short-range correlations and p-wave form factors are considered consistently in the 7r-baryon and weak interaction vertices. Each role of neutral and charged pion condensate played in this process is clarified and a peculiar role of neutral pion condensate is emphasized. Our results show that quasi-particle URCA process is still dominant over other standard processes, e.g., the modified URCA process, while the emissivity is about one order of magnitude less than the one for the pure charged pion condensed case within a realistic approach.

Stability of the ground state of finite nuclei against neutral pion condensation

The possible occurrence of abnormal nuclear states associated with neutral pion condensation has been studied in /sup 12/C and /sup 16/O within a Jastrow-type variational approach using an effective interaction to simulate ..delta.. mixing into the nucleon states. The role played by short range correlations and ..delta.. excitations in producing ..pi../sup 0/ condensation is discussed.

Variational calculation of nonuniform spin-ordered neutron matter including Δ isobar mixing

A modified two-nucleon interaction describing the effect of Δ (1236) isobar mixing into neutron states has been used in a Jastrow-like variational calculation of nonuniform spin-ordered neutron matter. The results indicate that, at a density larger than normal nuclear density by a factor 3–4, a transition to the inhomogeneous phase, associated with a neutral pion condensate, takes place.

Instability of the nuclear1 S 0 superfluid state for neutral-pion condensation

Instability of the nuclear1 S 0 superfluid state for neutral-pion condensation

Nucleon Superfluidity under Coexistent Condensation of Neutral and Charged Pions in Neutron Matter

Nucleon superfluidity has an important bearing on neutron star phenomena, especially coolingl) and glitches.2) In an ordinary situation the 3 P, superfluid is realized from the Fermi gas state at nucleon density p ~ (1 ~3)po, po being the nuclear density. How this aspect changes when pion condensation develops is not only an interesting problem from the viewpoint of many-body theory but also has an important relevance to the study on the relation between pion condensation and neutron star phenomena. The following two cases were investigated separately in our previous works. First, under neutral pion (7[0) condensation, superfluid becomes of two-dimensional character as a result of the Alternating-Layer-Spin (ALS) structure combined to the 7[0 condensation. ) Second, charged pion (7[C) condensation brings about serious attenuation of the 3 P, superfluidity because the pairing interaction of quasi-neutrons is weakened from the original one in neutron matter:) In this paper, extending these previous works, we study the 3 P2-dominant superfluidity in the phase resulting from pure neutron matter, where both 7[0 and 7[e condensations coexist. Tamiya and one of the present authors (R. T. )5) proposed a model that the 7[0 and 7[c condensations can coexist without interference if the momentum of condensed 7[0 (ko) and that of condensed 7[e (ke) are perpendicular. In this model, nucleons form the ALS structure ) along ko (taken as kocx i) as the source of condensed 7[0 and the 7[e condensation takes place in the layers where nucleons are in the two-dimensional Fermi gas states. By using the 7[-N P-wave interaction, they showed that the energy gains due to two condensations are additive. Since, even for more realistic interactions, the critical density of the7[e condensations7),8) are not so different from that of 7[0 condensation,)O) such coexistent condensation (denoted hereafter by 7[07[e condensation) is expected to possibly occur in neutron star interior.

Stability of nuclear matter against neutral pion condensation

The global stability of the uniform ground state of nuclear matter is tested relative to a π 0-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.

Neutral Pion Condensation and ALS Model Including Isobar Δ (1236)

Neutral Pion Condensation and ALS Model Including Isobar Δ (1236)