Is s-wave pion absorption by nuclei sensitive to off-shell properties of pion-nucleon scattering?

The absorptive part of the pion-nucleus optical potential for pionic atoms is calculated in the independent pair approximation, using the rescattering mechanism. Off-shell pion-nucleon effects are found important and an experiment is proposed to test these effects more directly.     

On mesonic interference phenomena in deep inelastic scattering

Possible effects of a π′ contribution to lepton deep-inelastic scattering (DIS) are analyzed. The exchange of the first radial excitation of the pion (π′(0^?)) has been advocated recently to solve the notorious problem of hard vertex form factors innucleon-nucleon scattering. The π′-meson exchange contribution is calculated in addition to the well known pionic (Sullivan) contribution. Interference between π and π′ contributions and their possible influence on the cut-off mass parameter of the πNN form factor extracted from DIS on the nucleon are examined. It is shown that the orthogonality relation between the π and π′ wave functions, in conjunction with number and momentum sum rules, put strong restrictions on the size of the interference effect. The interference effect between π and π′ is found to be negligible for the nucleon quark distributions and to modify only higher moments of the quark distributions. The interference effects of a pionic contribution with other mesons are discussed.     

Pion-deutron and pion-nucleus scattering — a review

We review recent developments in the microscopic theory of pion-nucleus elastic scattering. Particular emphasis is placed on the connection which has developed between the sophisticated studies of the three-body πNN system, and the less rigorous (but equally sophisticated) treatments of the pion-nucleus many-body problem. Complete sections are devoted to an examination of the underlying pion-nucleon interaction, and also to the difficult question of the effect of absorption on elastic scattering. Our discussion leads very naturally to a comparison with recent data - both for elastic scattering and reactions.     

Scattering of low energy pions by 12C, 40Ca, 58,60,64Ni and the anomaly in pionic atoms

Several cases of anomalously small level shifts and widths are known in pionic atoms. These lead to pion-nucleus potentials which are different from those describing all other “normal” pionic atoms. Data on the elastic scattering of 19.5 MeV π^± by ¹²C and ⁴⁰Ca and 30 MeV π^± by ^58,60,64Ni is in very good agreement with predictions made with normal potentials and clearly rule-out potentials obtained from the “anomalous” cases.     

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.     

In-medium isovector piN amplitude from low-energy pion scattering

Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni, and Zr have been measured as part of a study of the pion-nucleus potential across the threshold. The "anomalous" repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.     

Off-shell sensitivity,repulsive correlations and the pion-nucleus optical potential

Repulsive nucleon-nucleon correlations tend to reduce the dependence of pion-nucleus elastic scattering upon the off-shell pion-nucleon dynamics. However, optical potential calculations can in practice be quite sensitive to the particular choice of off-shell model parameters. It is argued that this sensitivity results from the nature of the optical potential as a one-body operator which introduces extra off-shell dependence not found in the physical many-body process itself. Thus, one must be very careful in any attempt to extract correlation or off-shell information, or to predict pion-nucleus phase shifts, by means of an optical potential theory. Results of model calculations are presented for purposes of illustration.     

Strong interaction effects in the 2p-1s transition in pionic neon

We present experimental results for the 2p-1s transition energy and the natural line-width of the 1s state in pionic neon. The line width ifΓ=14.5 ± 3.0 keV is in substantial agreement with semiphenomenological low-energy pion-nucleus interaction theories in the region A ≈ 20.     

Microscopic description of the A(p, π)A + 1 reaction

We have developed a flexible and thoroughly tested computer program for microscopic calculations of proton-induced pion production in nuclei at bombarding energies up to 500 MeV. The model used includes explicitly both the one-nucleon (pionic stripping) mechanism and the resonant p-wave rescattering part of the two-nucleon mechanism. Initial and final state interactions are included through proton-nucleus and pion-nucleus optical model distortions, with careful consideration of the multiple scattering series. The intermediate delta in the two-nucleon mechanism is treated as static with possible inclusion of a local density approximation for the delta-nucleus interaction. We explain the philosophy of the model, detail the parametrization of the microscopic dynamics, and give the formalism for the calculation of experimental observables. We also describe the testing of the computer program and present preliminary results for the ³He(p, π⁺)⁴He reaction.     

Many-body effects in resonant pion-nucleus scattering

The many-body approach of Barshay et al. for resonant pion-nucleus scattering is extended to non-uniform density distribution s and compared with recent total cross section data for ¹²C, ³²S, ¹²⁰Sn and ²⁰⁸Pb. For light nuclei the shapes and magnitudes are very well reproduced and represents an improvement over fits not using many-body corrections. A recent modification suggested by linearing the Low equation is seen to be not very significant for these calculations.     

Pionic x-rays and the neutron radius of 44Ca

Differences between strong interaction level shifts and widths for 2p states in pionic atoms of ^44,40Ca have been measured. Analysis in terms of an effective pion-nucleus potential leads to a difference in neutron rms radii of r_n(44)?r_n(40) = 0.05 ± 0.05 fm.     

On contributions to the pion-nucleus optical potential non-linear in nuclear density: The Ericson-Ericson Lorentz-Lorentz correction

A well-defined set of higher order corrections to the lowest order pion-nucleus optical potential is examined within the framework of many-body theory for an infinite nuclear medium. The connection between the pion self-energy operators and multiple scattering formalisms is thereby indicated and a deriviation of the EELL effect given.     

The reactive two-body part of the pion-nucleus optical potential

We calculate the reactive component of the two-body contribution to the pion-nucleus optical potential from a two-nucleon pion absorption mechanism that predicts the total cross section and angular distributions for π⁺d → pp very well. At threshold the calculated absorptive parts explain most of the values obtained from pionic atom level widths, whereas the dispersive parts, which are very sensitive to wave function correlations are considerably more attractive than what the conventional phenomenological parameters would suggest.     

π介子与原子核相互作用的某些进展

本文介绍了近年来π—核相互作用方面的进展,讨论了π-核相互作用对认识原子核所起的作用,着重讨论了π引起的各种反应。     

The absorptive P-wave pion-nucleus optical potential

We derive the absorptive part of the P-wave pion-nucleus optical potential from a two-body model for the absorption mechanism which involves rescattering of a pion and ?-meson through a Δ₃₃ resonant state. The model gives an adequate explanation for the fundamental π⁺d → pp reaction cross section and leads to values for the optical potential parameter which are in fair agreement with those obtained from pionic atom level widths.     

The pion optical potential and its application to reaction processes

The gross features of the pion-nucleus interaction are studied within the framework of an optical potential approach. The optical potential is determined by a systematic analysis of the data on pionic atoms and elastic scattering. It is then decomposed into quasi-free and absorption terms through theoretical consideration of the reactive content. A method of calculating the absorption cross section using the optical potential with the above decomposition is proposed. It takes into account not only direct absorption from the elastic channel but also the absorption after the quasi-free processes. The calculated absorption cross sections are in reasonable agreement with the observed ones. The cross sections for inelastic, single-charge-exchange and double-charge-exchange processes are calculated as an extended application of the method. The results are consistent with the available data. Inclusive spectra of pions and protons are also considered in this approach. An application to the (γ, π) reaction is briefly discussed.     

Nuclear structure effects in light π- mesoatoms

Performing the angle transformation from pion-nucleon to pion-nucleus CMS frame the first order pion-nucleus optical potential receives also a contribution due to nucleonic Fermi motion. The corresponding term is always repulsive and reflects the nuclear spin-orbital interaction playing an important role particularly for nuclei with half-filled valence shells. We demonstrate the effects due to this term yielding a contribution to the level shifts and widths of pionic atoms. Such ideas allow one to explain theA-dependence of 2p-level energy shifts for most of the s-d shell-mesoatoms.Dedicated by the co-authors to the memory of M. Gmitro.Two authors (A. C. and R. M.) are grateful to Prof. H. J. Leisi, Prof. M. P. Locher and Dr. P. F. A. Goudsmit for stimulating discussions and hospitality extended to them during their stay at Paul Scherrer Institute.     

Many-body dipole-induced dipole model for electrorheological fluids

Theoretical investigations on electrorheological (ER) fluids usually rely on computer simulations. An initial approach for these studies would be the point-dipole (PD) approximation, which is known to err considerably when the particles approach and finally touch each other due to many-body and multipolar interactions. Thus various works have attempted to go beyond the PD model. Being beyond the PD model, previous attempts have been restricted to either local-field effects only or multipolar effects only, but not both. For instance, we recently proposed a dipole-induced-dipole (DID) model which is shown to be both more accurate than the PD model and easy to use. This work is necessary because the many-body (local-field) effect is included to put forth the many-body DID model. The results show that the multipolar interactions can indeed be dominant over the dipole interaction, while the local-field effect may yield a correction.     

Description of Chiral Doublet Bands in Odd-Odd Cs Isotopes

Properties of the chair doublet bands of the odd-odd Cs isotopes built on the π h_11/2 \otimes ν h_11/2 configuration are investigated systematicallywithin the supersymmetry scheme including many-body interactions andpossessing the SO(5)(or SU(5)) symmetry on the rotational symmetry.Quantitatively good results of the energy spectra, the energy staggering parameter as a function of the spin are obtained. The calculation shows that the stronger competition between the pairing and anti-pairing effects and the SU(3) symmetry broking more seriously exist in the stable chiral structure.