Pion-induced knock-out reactions

A strong absorption model for pion-induced knock-out reactions is proposed. The distortion of the incoming and outgoing pions has been included by (i) computing the pion wave number in a nuclear medium (dispersive effect) and (ii) excluding the central region of the nucleus where the real pion absorption is dominant (absorption effect). In order to study the dependence of the (π⁺, π⁺p) reaction on the off-shell pion-nucleon t-matrix, different off-shell extrapolations are used. The magnitude of the cross sections seems to be sensitive to the type of off-shell extrapolation; their shapes, however, are similar. The theoretical results are compared with experimental data. The agreement between the theoretical results for separable off-shell extrapolation and the data is good.     

Probing nuclear expansion dynamics with π−/π+-spectra

We study the dynamics of charged pions in the nuclear medium via the ratio of differential π^? - and π⁺-spectra in a coupled-channel BUU (CBUU) approach. The relative energy shift of the charged pions is found to correlate with the pion freeze-out time in nucleus-nucleus collisions as well as with the impact parameter of the heavy-ion reaction. Furthermore, the long-range Coulomb force provides valuable information on the expansion dynamics of the hot nuclear system. Detailed comparisons with experimental data for Au + Au at 1 AGeV and Ni + Ni at 2.0 AGeV are presented.     

A study of single pion production in nucleon-nucleon collisions

A pion exchange model for NN pion production from threshold up to about 6 GeV/c is constructed. In contrast to other models of this type the full information from πN scattering is fed in whereby the πN partial waves on- and off-shell are identified with each other. Detailed comparison with the data for both the channels isospin one and zero, reveals that the shapes of angle and momentum distributions are, in general, well reproduced but the overall magnitude comes out too small for p_L ? 1.5 GeV/c. It is argued that this defect may be due to dibaryon resonances. For reaction cross sections their effects are quantitatively estimated.     

Threshold photoproduction of charged pions on14N

Pion photoproduction processes¹⁴N_gs(γ, π ⁺)¹⁴C and¹⁴N_gs(γ, π ^?)¹⁴O have been studied in the threshold region. These processes provide an excellent tool to study the corrections to soft pion theorems and Kroll-Ruderman limit as applied to nuclear processes. The agreement with the available experimental data for these processes is better with the empirical wave functions while the shell-model wave functions predict a much higher value. Detailed experimental studies of these reactions at threshold, it is shown, are expected to lead to a better understanding of the shell-model inputs and radial distributions in the 1p state.     

Measurement of the reaction π+ p→π+π+ n near threshold

The reaction π⁺ p→π⁺π⁺ n was studied in the vicinity of the reaction threshold at ten incident pion beam momenta from 297 MeV/c to 480 MeV/c. From data angular distributions, invariant mass spectra and integrated cross-sections were deduced. The chiral symmetry breaking parameter as determined by this reaction equals to ξ=1.56±0.26±0.39, where the first error is experimental, while the latter reflects the uncertainty in the ansatz used in the extrapolation to the reaction threshold. A comparison with the other reaction channels of the reaction πp→ππN indicates that a single parameter (ξ) is not sufficient to describe low energy ππ interactions.     

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.     

Pion chemical potentials in heavy-ion collisions: relativistic quantum molecular dynamic analysis

In the framework of relativistic quantum molecular dynamics we analyse pion chemical potentials in the hadron system produced in central heavy-ion collisions at the bombarding energiesE _lab/A=(1–2) GeV/nucl. We find that the equilibrium relations hold for chemical potentials of π^?, of π⁰, of π⁺ and pion energy spectra reach local thermal equilibrium. However, there is no chemical equilibrium. The pion chemical potentials are very large and decrease during the expansion stage.     

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.     

π− Production in16O +27Al at 38, 65 and 93 MeV/u

Negative pion production cross-sections are measured at 38, 65 and 93 MeV per nucleon in O + Al reaction. Rough estimations of the total cross sections are given and compared to previous neutral pion data. Double differential cross sections at 93 and 65 MeV/u show enhancement for pions with velocity close to the beam. At variance no effect is observed at 38 MeV, where π^? and π⁰ distributions are identical. Fewπ ⁺ detected at 38 MeV support this result. This indicates that at the lowest incident energy nearly the whole projectile participates in the production reaction.     

A search for the effects of nuclear matter in backward pion-deuteron quasielastic scattering by 6Li

Results of a kinematically complete experiment on backward π^? d quasielastic scattering by ⁶Li are presented. The experiment was carried out at the ITEP 3-m magnetic spectrometer with pion beams of momenta 0.72, 0.88, and 1.28 GeV/c. The Fermi-motion parameters of a quasideuteron cluster and the effective number of quasideuterons in ⁶Li are determined for the ⁶Li(π^?, π^? d)⁴He reaction. These values agree well with the proton-and electron-beam measurements. The possibility of observation of the effects of deuteron wave-function modification in nuclear matter is discussed for this reaction.     

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.     

The absorptive pion-nucleus optical potential

We calculate s-wave and p-wave absorptive pion-nucleus optical potentials assuming that a pion is absorbed by a pair of nucleons. Employing a model which takes into account both a single nucleon absorption with nucleon-nucleon correlations and rescattering, we obtain simple analytic expressions for Im B₀ sid Im C₀ of the pion-nucleus optical potential. The off-shell effect on the s-wave pion absorption is examined and shown to be strongly modified by short range correlations. The result for the p-wave absorptive part Im C₀ clearly shows the importance of the tensor correlations. The enhanced nn emission after π^? absorption is shown to be related with a large p-wave πN scattering length a₃₃ via the tensor correlations.     

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.     

Neutral pion photoproduction off nucleons revisited

We investigate threshold pion photoproduction in the framework of heavy baryon chiral perturbation theory. We give the expansion of the electric dipole amplitude E ₀₊ to three orders in μ the ratio of the pion to nucleon mass, and show that it is slowly converging. We argue that this observable is not a good testing ground for the chiral dynamics of QCD. In contrast, we exhibit new and fastly converging low-energy theorems in the P-waves which should be used to constrain the data analysis. We also discuss the importance of polarization observables to accurately pin down certain multipoles and give predictions for the reaction γ n → π⁰ n.     

Relativistic study of the reaction pp → dπ: Formalism and comparison with experiment at Tp = 578 MeV

A detailed relativistic calculation of pp → πd is presented. The leading graph is the exchange of a nucleon and a pion. The πN amplitudes, including off-shell information, are input, together with relativistic dpn and πNN vertex functions. The dominant nucleon spectator term is calculated without uncontrolled approximations, and the relativistic pion antiparticle contribution is evaluated. The single nucleon exchange diagram is added. Higher order rescattering is treated by initial and final state distortion factors. All amplitudes and spin observables are calculated and a detailed comparison with the measured data at 578 MeV is made. The remaining observed discrepancies are traced to the pp spin-triplet waves.     

QCD versus recent experimental data on lepton pair production at accelerator energies

New and precise experimental results on Drell-Yan pair production at accelerator energies are now available, both in π^? andp-nucleus interactions. These data are analyzed within the QCD framework including soft gluon resummation. It is shown that a quantitative agreement of the theory with experimental data can be reasonably managed. In particular, the soft gluon resummation is shown to build up nicely the so-calledK-factor. The pion formfactor is deduced from experimental data, but is rather sensitive to the nuclear structure functions we use. Definite nuclear structure functions are needed.     

Study of correlation of production and decay planes in π → 3π diffractive dissociation process on nuclei

A large correlation of production and decay planes of the π^?π⁺π^? system in dissociation of a 40-GeV/c π^? beam on nuclear targets was observed. The dependence of the correlation on atomic number, Feynman variable, and transversal momentum, as well as on invariant mass of the pion triple and neutral pion pair, was investigated. It was shown that the phenomenon has a clear dynamical origin and resembles the single-spin asymmetry behavior.     

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.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.