Δ-isobar dynamics in finite nuclei: Pion elastic scattering

Pion elastic scattering from finite nuclei in the 3,3 resonance region is described in terms of the coupling of a pion wave to correlated isobar-hole states. This is first carried out in an optical potential picture and then treated as a many-body response problem within the framework of RPA. Results are presented for the example of pion scattering from ⁴He; they show appreciable effects of isobar self-energy interactions and isobar-hole correlations other than one-pion exchange.     

Pion multiplicity in nuclear collisions

Data on the mean multiplicity of ^- produced in minimum bias proton-proton, proton-neutron and proton-nucleus interactions as well as central nucleus-nucleus collisions at momenta of 1.4–400 GeV/c per nucleon have been compiled and studied. The results for neutron-neutron and nucleon-nucleon interactions were then constructed. The dependence of the mean pion multiplicity in proton-nucleus interactions and central collisions of identical nuclei are studied as a function of the collision energy and the nucleus mass number. The number of produced pions per participant nucleon in central collisions of identical nuclei is found to be independent of the number of participants at a fixed incident momentum per nucleon. The mean multiplicity of negatively charged hadrons per participant nucleon for central nucleus-nucleus collisions is lower by about 0.12 than the corresponding multiplicity for nucleon-nucleon interactions atp _LAB 15 A·GeV/c, whereas the result at 200 A·GeV/c is above the corresponding nucleon-nucleon multiplicity. This may indicate change of the collision dynamics at high energy.     

Pion suppression in nuclear collisions

The pion multiplicity per participating nucleon in central nucleus–nucleus collisions at the energies 2–15 AGeV is significantly smaller than in nucleon–nucleon interactions at the same collision energy. This effect of pion suppression is argued to appear due to the evolution of the system produced at the early stage of heavy–ion collisions towards a local thermodynamic equilibrium and further isentropic expansion. Received: 21 July 1997 / Revised version: 12 November 1997 / Published online: 26 February 1998     

Pion production in nuclear collisions

The production of pions in nuclear collisions is analyzed in terms of a microscopic reaction model, where the free energy of the entrance channel is transferred to the final channel through the coupling of the relative motion to the internal excitation of N^*-resonances. Such a model allows quite naturally for a consistent analysis of the exclusive and the inclusive production of pions. It turns out that the pionic fusion cross section is determined predominantly by the spectroscopic parentage between the initial target projectile combination and the final nucleus, whereas the inclusive part is dominated by the energy dependence of the phase space factor, i.e. by the number of the degrees of freedom which are relevant in a given kinematical situation. This model is applied to the analysis of available experimental data from threshold to the (1232)-region. A consistent analysis of both the inclusive and the exclusive part of the pion spectrum is presented.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Pion superfluidity in nuclear matter

We utilize analogies with theories and properties of both liquid He⁴ and electrons in solids and liquids in constructing a model of nuclear matter in which the presence of stabilized pions is assumed. This model is then used to predict relationships between various thermodynamic parameters of a nuclear matter system, such as that between its “free” pion density and the characteristic transition temperature at which a Bose-Einstein condensation will commence.     

Pion Compton scattering in perturbative QCD

Pion Campton scattering is studied in perturbative QCD for real and space-like initial photons. Different methods for the convolution of the hard amplitude with the pion wave-functions, which have in the past led to conflicting results, are compared.     

Pion fluctuation in deep inelastic scattering

The forward neutron production in the ep collisions at 300GeV measured by H1 and ZEUS Collaborations at DESY has been used to estimate the total probability for proton fluctuation into nπ⁺ and pπ⁰. The probability found is on the order of 30%. This number is compared with the numbers obtained for the probability of quark fluctuation into π⁺ from several alternative DIS processes (Gottfried sum rule, polarized structure function) and the axial-vector coupling constant, where the pion fluctuation is believed to play an important role.     

Pion condensation in symmetric nuclear matter

The problem of pion condensation in isospin symmetric nuclear matter is investigated in the framework of the σ-model with a residual nucleon-nucleon interaction (g′σ₁ · σ₂τ₁ · τ₂δ(x)) and Δ-isobars. The equation of state for the pion condensed phase is calculated and applied to a low-energy heavy-ion collision in the TDHF approximation. The effective particle-hole interaction and the response to spin-isospin excitation are used to determine the magnitude of the Landau-Migdal parameter g′. For a reasonable range of g′(0.5 < g′ ≦ in units of g²/4m²_N = 410 MeV · fm³) pion condensation occurs at densities above normal nuclear matter density and leads to an equation of state with no stable density isomer.     

Pion condensation in symmetric nuclear matter

Using a model which is based essentially on the chiral SU(2)×SU(2) symmetry of the pion-nucleon interaction, we examine the possibility of pion condensation in symmetric nucleon matter. We find that the pion condensation is not likely to occur in symmetric nuclear matter for any finite value of the nuclear density. Consequently, no critical opalescence phenomenom is expected to be seen in the pion-nucleus interaction.     

Pion condensation and dynamics of neutron stars

When the central density of a neutron star reaches the critical value for pion condensation a catastrophic transformation of the star is triggered. In a short time the radius of the superdense core becomes comparable with the stellar radius and performs damped oscillations near the new equilibrium position. Due to the enormous release of energy during this process the envelop may be blown off.     

Pion effects on nuclear magnetic moment and transitions

The present evidence for pion contributions to magnetic moments, transitions and form factors is selectively reviewed with emphasis on the crucial evidence for specific effects. The theoretical basis will be discussed with special emphasis on the physical picture which emerges in the long wavelength limit.     

Pion production and the higher resonances in pion-nucleon scattering

The reaction π + N → 2π + N has been studied in the vicinity of the higher resonances in the pion-nucleon cross section. The Low equation for the production amplitude is transformed into an integral equation by isolating the true one-meson intermediate states and discarding higher order contributions. The only part kept in the inhomogeneous term corresponds to the collision of a pion in the nucleon cloud with the incident pion in the resonant T = J = 1 state, which is simulated by an unstable vector Boson. Crossed terms are neglected and the 2π-N state is described by the static model. The terms kept in the sum over states describe the rescattering (off the nucleon) of one of the outgoing pions. The required off-the-energy-shell elastic scattering amplitude is approximated by the 3-3 resonance formula of Chew and Low. With these simplifications the Low equation for the production amplitude reduces to an easily soluble linear integral equation. The rescattering amplitude, which dominates the inhomogeneous term in the resonance region, is proportional to the 3-3 scattering amplitude of one of the outgoing pions. Although the result provides some support for the conventional isobar model, it is important to note that the largeness of the rescattering term arises from scattering far off the energy shell, rather than by “real” excitation as in the phenomenological isobar model. Quantitative calculations for the $\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ channel leading to a p-wave ($\text{J =}\text{3}\text{2}$) and an s-wave pion produce a maximum in the cross section near 600 Mev incident pion lab energy. For a π-π resonance energy squared S = 10, agreement with experiment is obtained with a width about one third that suggested by nucleon electromagnetic structure. In our approximation, the well known 600 Mev $\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ isospin $\text{1}\text{2}$ resonance occurs at the same energy as the 800 Mev $\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ isospin $\text{3}\text{2}$ resonance. It is assumed, but not proved, that the neglected terms are responsible for the splitting of the resonance energies. When this splitting is taken into account, the predicted charge state ratios near the second resonance agree well with existing data. The “third” resonance occurs for the state having two p-wave pions, according to the present theory, although no numerical calculations were made for this case. This point of view suggests that the $\text{F}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, and $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ incident channels contribute to the third resonance.     

Pion mean free path in nuclear matter

The mean free paths for true absorption and inelastic scattering-as well as true absorption alone-of pions in symmetric nuclear matter are deduced from two sets of optical model parameters.     

Pion exchange currents in elastic electron deuteron scattering

The effects of pion-exchange pari and recoil currents on the electromagnetic form factors of the deuteron are calculated. Both exchange currents give significant contributions to the charge form factor and, despite some cancellation, their net effect is appreciable for q² ? 10 fm^?2.     

Pion bremsstrahlung and critical phenomena in relativistic nuclear collisions

We investigate the dependence of pion bremsstrahlung on the deceleration of the nuclei in relativistic heavy ion collisions. The vicinity of an abnormal phase in nuclear matter can lead - owing to critical N-N scattering - to faster deceleration or decreasing transparency of the nuclei. This would result in a threshold enhancement of the pion bremsstrahlung cross section, which in turn can be used to search for abnormal nuclear states experimentally.     

Pion interaction in nuclear matter and chiral symmetry restoration

This paper is devoted to the interplay between p-wave, s-wave pion-nucleon/nucleus interaction and in-medium pion-pion interaction with special emphasis on the role of the nuclear pionic scalar density driving a large amount of chiral symmetry restoration. In particular we show that the πNN coupling constant and the Goldberger-Treiman relation are preserved in the nuclear medium under certain conditions. We also discuss the related problem of the in-medium pion-pion strength function.     

Pion electroproduction in parity violating elastic ep scattering experiment

This study has been developed for electron-proton scattering experiments when only the scattered electrons are detected. Pion electroproduction on the proton including the cascade π⁰→ 2γ decay and the QED radiative corrections to elastic ep scattering are investigated. Our results are shown in the kinematical configuration of the parity violating electron scattering experiment planned at the Mainz Microtron (MAMI). Received: 20 April 1999 / Revised version: 4 June 1999