Relativistic mean-field description of collective motion in nuclei: the pion field

The influence of the pion field on isovector dipole and spin-dipole collective oscillations is investigated in a time-dependent model based on relativistic mean field theory. We find that the inclusion of the long range pion-nucleon interaction provides an additional strong damping mechanism for the isovector dipole vibrations. The inclusion of the pion field has also a strong effect on the dynamics of spin-dipole vibrations, and in particular on the splitting of excitation energies of theJ ^π (0^?,1^?,2^?) components of the isovector spin-dipole resonance.     

Inclusive radiative pion capture in nuclei

The problem of inclusive radiative pion capture is reanalyzed from a many-body point of view which allows to investigate effects like the Pauli blocking and the polarization of the medium by the spin-isospin interaction in a systematic way. Standard approximations are improved by means of this method, which is however much simpler technically than other available methods and very transparent. Results are presented for a variety of nuclei and the branching ratios for the capture rates are in overall agreement with experiment. The energy distribution of the photons is narrower than experiment and several mechanisms to solve these discrepancies are examined.     

On pion condensation in finite nuclei

The critical pionic state leading to pion condensation is investigated for finite nuclear systems. The threshold density for light nuclei, including⁴He, is found to be close to that of nuclear matter. For¹⁶O and⁴⁰Ca, the angular momenta of the most critical states areL=0 andL=2.     

Surface pion condensation in finite nuclei

We discuss here the possible occurrence of surface pion condensation in finite nuclei. We show the argument for this possibility by the recent findings in few-body calculations and the spin-flip experiments. We show the calculated results on various N = Z nuclei using the relativistic mean-field theory with a pion.Received: 30 September 2002, Published online: 22 October 2003PACS: 21.60.-n Nuclear-structure models and methods     

The pion mass difference in threshold pion reactions on light nuclei

We investigate the effect of the pion mass difference in scattering and photoproduction of pions on light nuclei near threshold. The effect is found to be most easily described in a nuclear K-matrix formalism where the nuclear K-matrix elements are shown to be independent of the mass difference.     

Weak pion production from nuclei

The charged current pion production induced by neutrinos in¹²C,¹⁶O and⁵⁶Fe nuclei has been studied. The calculations have been done for the coherent as well as the incoherent processes assuming Δ dominance and takes into account the effect of Pauli blocking, Fermi motion and the renormalization of Δ in the nuclear medium. The pion absorption effects have also been taken into account     

A model for pion absorption in nuclei

To describe pion absorption in nuclei, we introduce a model which assumes that incident pion is absorbed by the row of target nucleons along the beam direction. The momentum distribution of these nucleons after absorbing the pion is assumed to be determined by the phase space. The experimental data on the inclusive proton cross section are well reproduced.     

Investigation of the pion condensation threshold in finite nuclei

The threshold condition for pionic instabilities in finite nuclei is investigated by evaluating the response function for pion-like nuclear excitations (i.e. isovectorJ ^π =0^?, 1⁺, 2^?, ... excitations). The onset of pion condensation is then defined as the point where the response function for givenJ ^π becomes infinite at frequencyω=0. Using a momentum space representation for the response function which allows to establish clear connections to the nuclear matter case, we find that for angular momentaJ smaller than a maximum value which depends on the size of the nucleus, the threshold condition is almost the same as for infinite matter. We also study the systematics of this phenomenon as a function of nuclear mass number.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Unnatural parity states in nuclei and pion condensation

This is a systematic study to assess a lower limit on the threshold density for pion condensation on the basis of empirical nuclear data. It turns out that the isovector unnatural parity states in ⁴He, ¹⁶O and ⁴⁰Ca, and quantities related to them are best suited for a quantitative test. Assuming for the interactions parameters in the nucleon-hole and Δ-isobar-hole channels g′: = g′_NN = g′_NΔ = g′_ΔΔ, a value g′ = 0.7±0.1 is obtained from the measured energy shifts of unnatural parity states. Taking also into account results by Oset and Rho who obtain g′_ΔΔ = 0.6?0.7 from the observed quenching of Gamov-Teller matrix elements of (A±1) nuclei around ¹⁶O and ⁴⁰Ca, one finds the onset of pion condensation in nuclear matter at densities considerably larger than twice normal nuclear density, if at all. We discuss the work of Migdal et al. who prefer the assumption g′_NΔ = g′_ΔΔ = 0 and obtain lower critical densities. Also the question of (pre)critical behaviour in finite nuclei is investigated in terms of a quantitative example. It is found that a genuine signal for proximity to pion condensation would be the appearance of a strongly collective spin-isospin mode which has, however, not been observed experimentally so far.     

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.     

Experimental investigation of pion reactions with the lightest nuclei

The dynamics of the N-system in the lightest nuclei, its effects, and properties are reviewed and discussed.Invited talk to the symposium Mesons and Light Nuclei IV, Bechyn, Czechoslovakia, September 5–10, 1988.     

Charged pion electroproduction on light nuclei near the threshold

The experimental data for charged pion electroproduction on ¹²C and ¹⁶O measured at Mainz and Sendai are analyzed in a modified equivalent photon approximation. For the Sendai experiment we use distorted waves for the pion, while for the Mainz experiment we adopt a closure sum with a finite Fermi-gas model. We can roughly reproduce both sets of experimental data.     

Pauli principle and renormalization of the pion nucleon interaction in nuclei

We show that the exclusion principle provides an alternative mechanism to the Lorentz-Lorenz effect for the renormalization of the pion-nucleon coupling constant in nuclei. This mechanism proves to be less sensitive to the range of the π - N forces. The implications for pion-nucleus scattering are discussed.     

A survey of pion charge-exchange reactions with nuclei

A survey study of the elastic charge-exchange reactions is presented. The charge-exchange cross sections are evaluated in a coupled-channel framework with optical potentials obtained from the Kisslinger and Laplacian models for the pi-nucleon off-shell scattering amplitude. Considerable differences between these two modles are obtained for pion kinetic energies below the pi-nucleon (3, 3) resonance. The effect of two-nucleon correlations is included by calculating the second-order pi-nucleus optical potential. We find that this effect dominates the charge-exchange reactions at energies of about 100 MeV.     

Three pion production on nuclei at 200 GeV

We have carried out a systematic study of the coherent dissociation of pions into 3 pions using nuclear targets. The experiment was performed at Fermilab using a high resolution forward spectrometer. Data were taken with carbon, copper and lead targets at an incident momentum of 202.5 GeV/c. Results are presented on momentum transfers, 3-pion masses, and on the nuclearA-dependence of the production cross section.