The Δ-nucleus spin-orbit interaction in π-nucleus scattering

The role of the Δ-nucleus spin-orbit interaction in π-nucleus scattering is studied within the isobar-hole formalism. Due to the peripheral nature of the π-nucleus interaction, elastic scattering is very sensitive to the presence of such an L-S term. We report results for pion scattering on light nuclei in the resonance region. The systematics of the phenomenological Δ-nucleus optical potential are discussed.     

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.     

PION SCATTERING FROM WELL-DIFORMED NUCLEI

In the framework of the eikonal theory and using the first order π-nucleus optical potential, the elastic and inelastic scatterings of π^± from well-deformed nuclei are discussed. The virtual excitations to the low-lying levels are taken into account in the calculations of the elastic scatterings by using the closure approximation. The theoretical results of pion scatterings from ¹⁵²Sm at T_π=180MeV are compared with the data.     

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.     

Isobar dynamics and pion-nucleus elastic scattering

A new formalism is developed for studying pion-nucleus scattering in a model which takes into account the dynamics of the (3, 3) pion-nucleon resonance, or Δ isobar. This treatment is used to calculate π⁺ elastic scattering from ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb at energies from 114 to 240 MeV. Some results for π^? elastic scattering are also given. From fits to π⁺ scattering data it is found that the Δ-nucleus interaction is well described by a spherical local complex potential proportional to the nuclear density. The central strength of this potential depends on energy but not on nuclear mass number. Some difficulties in determining the parameters of this potential from elastic scattering are discussed.     

Quasi-elastic pion scattering on 16O: A comparison between the Δ-hole approach and a standard first-order calculation

We present calculations of quasi-elastic pion scattering on ¹⁶O in both the Δ- hole model and a standard first-order theory. The basic approach is a modified “DWIA”, where the same in-medium πN t-operator is used for the transition and the optical potential generating the distorted pion wave functions. In order to allow a meaningful comparison with the recent SIN data, all technical complications such as background interactions, non-static vertex-corrections, 1/A effects, are taken into account, and the DWIA amplitude is evaluated without further numerical simplification like, e.g., factorization. In contrast to the closure approximation, the Δ-hole model predicts correctly the doubly differential cross sections for (π, π') on ¹⁶O over a wide range of angles and energy-losses.     

Axial polarizability and weak currents in nuclei

The effect of the isobaric excitations on the weak axial coupling constants in nuclei is studied through P.C.A.C. We first establish the Klein-Gordon equation for the virtual pion field in the nucleus; it takes into account pion rescattering. The influence of isobar excitation is contained in the axial polarizability coefficient which is linked to the p-wave π-N scattering volume. The derivation of this equation stresses its analogies with electromagnetism. We give then a basic relation between the axial current and the pionic field. It incorporates the effects of the isobars in the axial polarizability, which leads naturally to an electromagnetic analog. We show that this relation leads in heavy nuclei to a quenching of the axial coupling constant by the Lorentz-Lorenz factor, which may originate from the short range or the Pauli correlations, depending on the range of the π-N forces. Hence this quenching may have a different origin than the existence of short-range correlations and may arise from a Pauli blocking effect. On the other hand, the pseudoscalar coupling constant is found to be strongly suppressed. In finite nuclei, these basic quenchings can be masked by surface effects, the general features of which are studied with the help of a solvable model. This model is further used to obtain the asymptotic pion field which is linked to the effective pion-nucleus coupling constant and can be determined experimentally through π-nucleus dispersion relations. We find that this quantity is quenched, in agreement with recent experimental data.     

Remarks on calculating the pion-nucleus first-order optical potential

It is shown that the factorization approximation should not be used in any serious theoretical effort to calculate the first order optical potential for low energy π-nucleus scattering. In contrast to earlier work, the required off-shell πN t matrix for non-zero total momentum is consistently evaluated using relativistic particle quantum mechanics.     

Momentum-space optical model for K+-nucleus scattering

The momentum-space optical model of K⁺-nucleus scattering is analyzed and comparison with other conventional models is shown. The model is based on the multiple scattering formalism in which the optimal factorization approximation is used. Off-energy-shell extension of the elementary K⁺-nucleon amplitude is neglected which reduces non localities in the optical potential. Predictions of the model are sensitive to the definition of the K⁺-nucleon energy (energy shifts) but they are independent (1–2%) of a particular form of the covariant K⁺-nucleus scattering equation (relativistic Lippmann-Schwinger, Gross, Erkelenz-Holinde). The Coulomb distortion in the total cross section is important for²⁸Si and⁴⁰Ca at low momenta (≈10%). Off-energy-shell effects in the optical potential are discussed too. Results for the total and reaction cross sections are systematically below the data. The reaction cross sections are in a larger disagreement with the data than the total cross sections. This work was supported by grants ASCR A1048703 (P. Bydžovsky) and GACR 202/96/1566 (M. Sotona).     

Pion-nuclear optical potential.s Wave scattering

Difficulties in the theoretical interpretation of thes wave phenomenological parameters of the pion-nuclear optical potential are considered. One-nucleon and two-nucleon parameters of such a potential for slow pion scattering are calculated. Uncertainties in the separation of the dispersive part of the potential into one- and two-nucleon contributions are discussed. It is shown that taking into account off-shell behaviour of the πN amplitude in the calculation of the two-nucleon parameters is important.     

Binding effects in pion-nucleus scattering

The pion nucleus optical potential is evaluated for a pion scattered by a nucleon bound in a potential well. Total cross sections for π-¹⁶O scattering are computed supposing an S-wave separable two body interaction. The comparison with impulse and static approximations shows that they are not justified in a resonance region.     

A three-body calculation of the πd → πnp reaction in the Δ-resonance region

The reaction d(π^±, pπ^±)n at incident pion momentum 340 MeV/c is analyzed based on a relativistic three-body formalism. The contributions of the various reaction mechanisms such as impulse processes, pion multiple scattering and nucleon-nucleon final-state interactions are investigated for several cases of typical kinematics. The impulse term is dominant when the recoil neutron momentum is small. On the other hand, the NN final-state interaction is found to be relatively important when the recoil neutron momentum is large. The effects of dibaryon resonances which have been suggested in πd elastic scattering are estimated using a phenomenological model. Comparisons with other work are also made.