The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

The role of two particle-two hole excitations in the spin-isospin nuclear response

We investigate the role of the 2p-2h states in the spin-isospin nuclear response function. This is done in the frame of a microscopic approach which includes the meson exchange currents and the nucleon-nucleon correlation. We first test our theory on the transverse response in the inclusive deep inclastic electron scattering, where we achieve a satisfactory agreement with the data for values of the momentum transfer ranging from 1 to 2 fm^?1. We next explore the p-wave pion-nucleus absorptive optical potential. We find that a strong (～3) Lorentz-Lorenz-Ericson-Ericson quenching factor is needed to reproduce in our framework the phenomenological optical potential deduced from π-mesic atom data. We also examine the real photon absorption cross section accounting rather satisfactorily for its behaviour, in particular for the Pauli blocking at small frequencies. Finally, we elucidate the conditions for the existence of a connection between the magnetic photon absorption and the p-wave pion absorption in nuclei.     

Quasifree pion photoproduction on the deuteron in the Δ region

Photo production of pions on the deuteron is studied in the spectator nucleon model. The Born terms of the elementary production amplitude are determined in pseu-dovector πN coupling and supplied with a form factor. The Δ resonance is considered both in the s and the u channel. The parameters of the Δ resonance and the cutoff of the form factors are fixed on the leading photoproduction multipoles. Results for total and differential cross sections are compared with experimental data. Particular attention is paid to the role of Pauli correlations of the final state nucleons in the quasifree case. The results are compared with those for pion photoproduction on the nucleon.     

Dynamics of pion double-charge-exchange reactions

The (π⁺, π^?) reactions leading to the double isobaric analog state are studied at pion energies 50 to 300 MeV, with¹⁴C as an example. Effects of nuclear structure, nuclear recoil, the reaction pathway and off-shell πN interactions are examined in detail. Our study reveals a very strong dependence of calculated cross sections on off-shell πN dynamics. Consequently, use of a self-consistent off-shell πN theory is essential to studying short-range nucleon-nucleon correlations from double-charge-exchange data. The present study further shows that reaction dynamics other than two successive pion single charge exchanges is needed to account for the experimental data.     

Dispersive effects for the nuclear paramagnetic susceptibility

Dispersive effects coming from pionic degrees of freedom (virtual magnetic pion photoproduction) are shown to reproduce the nucleonic magnetic susceptibility and to yield a parallel quenching in nuclei. The relative importance of low lying nuclear vs.Δ-excitations is discussed and the difference of their role for the magnetic and electric polarizability is pointed out.     

Isobar-hole doorway states and π-16O scattering

We describe and apply the isobar-hole approach to intermediate energy pion-nucleus reactions. Pion propagation, nucleon and isobar binding, Pauli restrictions and Δ propagation are calculated explicitly within a shell model framework. Intermediate coupling to multihole channels, for example through pion absorption, is treated phenomenologically through an isobar spreading potential. We find strongly collective Δ-hole states, leading to a reformulation of the approach in an extended schematic model. This entails systematic construction of a Δ-hole doorway state basis within which the Δ-hole propagator is evaluated. We find that this doorway space can be truncated at very low dimensionality while preserving accuracy, thereby simplifying the calculations appreciably. We make a detailed comparison between the theoretical results and recent data for π⁺ — ¹⁶O scattering in the pion energy range 50–340 MeV. Nonresonant πN interactions and the π-nucleus Coulomb interaction are included in the calculations. The data is reproduced quite well both below and in the resonance region, and we discuss in detail the role of various dynamical mechanisms. Above the resonance, the calculations are far less successful. We discuss possible shortcomings, stressing the role of inclusive pion-nucleus reactions for revealing the important dynamics. As a test of the Δ spreading potential used for describing elastic scattering, we calculate the total cross section for pion absorption. The result agrees reasonably well with the available data.     

High-pT pion production in ππ interactions

Charged pion production in high energy π^-π^- interactions is studied in the p_T region of 1–2 GeV/c. The characteristics of pion production in π^-π^- interactions are compared with those in π^-p and pp interactions. The p_T dependence of pion production in these reactions follows a systematic trend which indicates that high-p_T pion production for ππ interactions as well as for πp and pp interactions proceeds via quark-quark scattering as predicted by QCD.     

Near-threshold pion production by protons on nuclei

The p + p → d + π⁺ process is considered in detail along with the p + N → N + N + π process. Such consideration makes it possible to show the difference in the production cross sections for π⁺ and π^? mesons on nuclei. In this case, experimental data can be reproduced both above the pion production threshold at a proton energy of 350 MeV and under the threshold at a proton energy of 180 MeV.     

Chiral symmetry restoration and parity mixing

We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study the modifications in the nuclear medium of the coupling constants of the axial current, namely the pion decay constant and the nucleonic axial one due to the requirements of chiral symmetry. We express the renormalizations in terms of the local scalar pion density. The latter also governs the quark condensate evolution and we discuss the link between this evolution and the renormalizations. In the case of the nucleon axial coupling constant this renormalization corresponds to a new type of pion exchange currents, with two exchanged pions. We give an estimate for the resulting quenching. Although moderate it helps explaining the quenching experimentally observed.     

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

Pionic field and renormalization of the axial coupling constant in nuclei

The renormalization of the axial coupling constant in nuclei is related by PCAC to the exchange effects in the pionic vertex. Using an optical potential as a model for the pion source function, it is shown that in large nuclei the renormalization arises from the short range correlations. The analogy between this problem and that of an electric dipole inside a dielectric medium is pointed out.     

On the role of Δ-resonance in the pion production in collisions of heavy intermediate-energy ions in the hydrodynamic approach

Pion production in heavy-ion collisions is considered within the hydrodynamic approach. It is shown that consideration of pion production as a result of Δ-resonance decay (Δ → N + π) leads to hardening of the high-energy “tails” of subthreshold pions.     

Mesonic wakes in nuclear matter,with application to meson production in nuclear collisions

The process of meson production by a source moving uniformly through infinite nuclear matter is studied in field theoretic models in which a source-meson coupling is assumed, and in which the only effect of the nuclear medium is to modify the propagator of the mesons. If the meson dispersion relation, ω(k), in the medium becomes space-like in some region of k, k > ω(k), there is, for relativistic source velocities, energy loss to the mesonic excitations. Models of the pion propagator in nuclear matter lead to such a space-like region. Rates of pion production are calculated in the lowest order of the pion-source coupling. Consideration of higher order terms leads to an interesting class of problems which we designate as those of “non-Abelian Cherenkov radiation.” Brief consideration is given to the excitation of nuclear collective modes and to the problems of treating meson production in finite nuclei.     

Nuclear relativistic hartree-fock approximation with effective pions

The effect of an interaction between the ??- and ??-meson fields, as well as that of the mixture of pseudoscalar (PS) and pseudovector (PV) couplings for the ??N vertex on the shell structure of finite nuclei are analyzed in the framework of different nonlinear nuclearmodels based on the relativistic Hartree-Fock approximation. For the case of a dominant ??N PV coupling, it is found that if the ??-?? interaction generates an effective pion mass increasing with the nuclear density, the unrealistic effect of pions on the shell structure can be strongly reduced, keeping, roughly, the contribution of pions to the total binding energy. The ??N PS coupling increases slightly the spin-orbit splittings and the binding energy of the single-particle levels.     

Self-consistent QRPA in the theory of nuclear structure

The conventional QRPA is extended to take into account the effect of the Pauli principle and the ground state correlations. The coupling between quasiparticle and phonons is found by minimizing the ground state expectation value of the auxiliary Hamiltonian. The model with pairing plus2-2 interaction is used.     

Pion-nucleus interaction and the range of πN forces

We examine several definitions for the ranges r_πN of the pion-nucleon (πN) forces and conclude that 0.25 ≦ r_πN ≦ 0.5 fm. We investigate two consequences of the finite range of the p-wave πN interaction: the additional spatial extension of the p-wave π-nucleus optical potential and the quenching of the Lorentz-Lorenz effect. For 0.25 ≦ r_πN ≦ 0.5 fm (i) the additional extension of the p-wave optical potential gives negligible contributions to shifts and widths in π-mesic atoms and (ii) the Lorentz-Lorenz effect is largely quenched making nuclear correlations hard to detect by mesic atoms measurements.     

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.     

On the Bosonic Atoms

We investigate the ground state properties of atoms, in which substitute fermions—electrons by bosons, namely, π^?-mesons. We perform some calculations in the frame of modified Hartree–Fock (HF) equation. The modification takes into account symmetry, instead of antisymmetry of the pair identical bosons wavefunction. The modified HF approach thus enhances (doubles) the effect of self-action for the boson case. Therefore, we accordingly modify the HF equations by eliminating the self-action terms “by hand.” The contribution of meson–meson and meson–nucleon non-Coulomb interaction is inessential at least for atoms with low and intermediate nuclear charge, which is our main subject. We found that the binding energy of pion negative ions A_π^-, pion atoms A_π, and the number of extra bound pions ΔN_π increases with the nuclear charge Z. In particular, for Xe ΔN_π = 4. As an example of a simple process with a pion atom, we consider photoionization that differs essentially from that for electron atoms. Namely, it is not monotonic decreasing from the threshold but has instead a prominent maximum above threshold. We study also elastic scattering of pions by pion atoms.