Dynamics of pion double-charge-exchange reactions

The (π⁺, π^?) reactions leading to the double isobaric analog state are studied at pion energies 50 to 300 MeV, with¹⁴C as an example. Effects of nuclear structure, nuclear recoil, the reaction pathway and off-shell πN interactions are examined in detail. Our study reveals a very strong dependence of calculated cross sections on off-shell πN dynamics. Consequently, use of a self-consistent off-shell πN theory is essential to studying short-range nucleon-nucleon correlations from double-charge-exchange data. The present study further shows that reaction dynamics other than two successive pion single charge exchanges is needed to account for the experimental data.     

Kaon and antikaon properties in cold nuclear medium

We present results of a self-consistent calculation for the kaon and antikaon spectral functions in cold nuclear matter, using as input the kaon-nucleon and antikaon-nucleon scattering amplitudes of the vacuum. We investigate the effect of in-medium pion dressing on the antikaon-nucleon scattering amplitudes and antikaon spectral function. We find the influence of pion dressing to be minor on the antikaon spectral function and limited on the hyperon resonances causing only a small additional broadening. An exception is the Σ(1690). At nuclear saturation density an attractive mass shift of about 20 MeV and width of about 130 MeV is obtained. The kaon shows a repulsive mass increase of 36 MeV and a small width of the quasiparticle peak at saturation density.     

A phenomenological approach to pion condensation

The threshold of π-condensation in isospin symmetric nuclear matter is studied with a field theoretic model which reproduces the low energy πN data. We find a critical density around normal nuclear matter density. Besides the role of the nucleon-nucleon correlations we investigate the effect of the s-wave πN interaction on- and off-mass-shell. The chiral symmetry breaking Σ-term may impede pion condensation.     

Quenching and hardening in the transverse quasi-elastic peak

We study in the RPA framework the collective response of symmetric, infinite nuclear matter to a spin-isospin sensitive probe with both σ · q and σ × q couplings. The two responses, similar in the low-q region, differ markedly for moderate momenta (?1 fm^?1). Indeed the collective effect manifests itself quite differently in the two responses; whereas the longitudinal one displays a softening and an enhancement (due to the attractive character of the associated particle-hole force), the transverse response is quenched and hardened with respect to the free Fermi gas. The existing experimental data, which we analyze, are compatible with our results. We also explore the total strengths and find that for repulsive forces they are appreciably reduced by the RPA correlations. A large part of this quenching comes from the Δ-excitation (LLEE effect), but some reduction is still present even when the nucleonic degrees of freedom are neglected. This illustrates a violation of strength conservation brought about by the RPA correlations in the spin-isospin channel.     

The spectral function of the rho meson in nuclear matter

We calculate the modification of a rho meson in nuclear matter through its coupling to resonance-hole states. Starting from a recently proposed model, we include all four star resonances up to 1.9 GeV. In contrast to previous works, we include not only resonances that couple to the rho in a relative p-wave, but also those that couple to an s-wave state. In addition, we solve the equation for the rho spectral function self-consistently. We find that s-wave resonances affect the in medium spectral function of the rho strongly. In the transverse channel the rho meson is, especially at non-zero momentum, completely washed out and can in the presence of nuclear matter no longer be viewed as a resonant excitation of the vacuum. Instead, our model shows a continuum of possible excitations with the quantum numbers of a transversely polarized rho. In the longitudinal channel, however, the rho retains its resonant character in our calculation. As a consequence of the self-consistent treatment we also find a strong enhancement of the widths of the included nucleon resonances in medium.     

Pions in isospin asymmetric matter and nuclear Drell-Yan scattering

Using a self-consistent delta-hole model the pion propagation in isospin asymmetric nuclear matter is studied. In neutron-rich matter, corresponding to heavy nuclei, a significant difference in positive and negative pion light-cone distributions is obtained leading to a nuclear enhancement of up antiquark distribution compared to the down antiquark one. This means that the sea-quark asymmetry in the free nucleon cannot be extracted model independently from an experiment on a neutron-rich nucleus.     

Deep-inelastic electron scattering from carbon

We have measured the deep-inelastic electron scattering from carbon up to and including the Δ-region at 36°, 60°, 90° and 145°. The systematic decomposition of the transverse and longitudinal response functions has been obtained by means of a Rosenbluth-type analysis of the data in the momentum transfer interval 200 MeV/c /s |q| /s 600 MeV/c. A comparison with theoretical calculations which extend over the quasielastic and Δ-peak regions is presented. A reduction of the differences between our data and theory seems obtainable through the introduction of meson-exchange currents, resonant and non-resonant meson production, and the use of the shell model. Our experimental Coulomb sum-rule estimates at higher $\text{|}\text{q}\text{|}$ agree with independent particle model predictions. We compare our results in the vicinity of the Δ-peak with the total absorption cross section for real photons.     

Study of the asymmetric nuclear matter with pion dressing

We discuss here a self-consistent method to calculate the properties of the cold asymmetric nuclear matter. The nuclear matter is dressed with s-wave pion pairs. The nucleon-nucleon (N-N) interaction is mediated by these pion pairs, ∞ and ρ mesons. The parameters of these interactions are calculated selfconsistently to obtain the saturation properties like equilibrium binding energy, pressure, compressibility and symmetry energy. The computed equation of state is then used in the Tolman-Oppenheimer-Volkoff (TOV) equation to study the mass and radius of a neutron star containing pure neutron matter.     

Abnormal nuclear matter and pion condensation

The possibility of nuclear matter undergoing a combined phase transition into abnormal matter and a pion condensate is investigated. Various lagrangians for the meson (σ and π_i) fields, based on the σ-models, are used in mean-field approximation, and the entire system (mesons + nucleons) is treated fully relativistically. Equilibrium conditions of nuclear matter are obtained with NN repulsion, parametrized by the excluded volume approximation. It turns out that the formation of abnormal matter depends crucially on the choice of the σ-model lagrangian and considerably less on the additional pion condensate.     

On the longitudinal electromagnetic coupling of the Δ

The relativistic corrections, corresponding to the transverse and longitudinal excitation of the Δ, are included in the original Blomqvist-Laget model. They are calibrated against the pion photoproduction data. The measurement of the transverse-longitudinal interference cross sections of the (e, e′ π⁰) reaction is the most promising way to study the longitudinal coupling of the Δ.     

The (p,π−) reaction and Δ++ components of nuclei

The use of the (p, π^?) reaction as a probe to determine Δ⁺⁺(1232) components of nuclear wave functions is examined within the framework of a model which treats baryon resonances on the same footing as nucleons. Nuclear structure properties which affect the Δ -probability are discussed. Estimates of cross sections, at several energies, are made for the Δ⁺⁺ transfer contribution as well as for the competing processes: proton charge exchange (p, n) followed by an (n, π^?) reaction; emission of a π⁰ followed by pion charge exchange (π^?, π⁰) . Even with Δ-probabilities as small as 0.0001 the Δ-transfer process can compete with ordinary background charge-exchange reactions.     

The role of two particle-two hole excitations in the spin-isospin nuclear response

We investigate the role of the 2p-2h states in the spin-isospin nuclear response function. This is done in the frame of a microscopic approach which includes the meson exchange currents and the nucleon-nucleon correlation. We first test our theory on the transverse response in the inclusive deep inclastic electron scattering, where we achieve a satisfactory agreement with the data for values of the momentum transfer ranging from 1 to 2 fm^?1. We next explore the p-wave pion-nucleus absorptive optical potential. We find that a strong (～3) Lorentz-Lorenz-Ericson-Ericson quenching factor is needed to reproduce in our framework the phenomenological optical potential deduced from π-mesic atom data. We also examine the real photon absorption cross section accounting rather satisfactorily for its behaviour, in particular for the Pauli blocking at small frequencies. Finally, we elucidate the conditions for the existence of a connection between the magnetic photon absorption and the p-wave pion absorption in nuclei.     

The meson propagator in nuclear matter

We present a formal device for calculation of a meson propagator in infinite nuclear matter, through the calculation of the ground state energy of the system in the presence of external, static meson fields, using a pseudo-Hamiltonian simply related to the actual Hamiltonian. This approach is particularly well adapted for dealing with some effects that are not taken into account at all in multiple scattering approaches, for example, the effects of nuclear forces on the intermediate states which are involved in the meson-single-nucleon scattering. A theorem is proved about limiting conditions under which the charged pion propagator is independent of the nuclear forces. These conditions are nearly enough realized in π-nucleus scattering (sufficiently below the energy of the first resonance) so that we can evaluate the corrections perturbatively. The (virtually unknown) two-body force between the 3-3 resonance and nucleons is shown to be of considerable importance in determining the π-meson propagator.     

Sum rule approach to the nuclear response in the isovector spin channel

We study the global features of the response of infinite nuclear matter in the spin-isospin channel through the energy-weighted sum rules S₁ and S_?1. In particular we compare the outcome of the ring approximation with the exact RPA evaluation of the sum rules. We also investigate the influence of the collective character of the response, induced by the particle-hole force for longitudinal and transverse spin couplings. We show that S₁ is insensitive to the collectivity of the response, as long as the Δ-degree of freedom is ignored. The inverse energy-weighted sum rule on the other hand, which is linked to the paramagnetic susceptibility, always reflects the hardening or softening of the nuclear response, due to the repulsive or attractive character of the p-h force. This quantity is well suited to the comparison with the experiments, which we perform for ¹²C and ⁵⁶Fe.     

Pion dispersion relation in hot pion matter

We study the modification of the pion propagation properties when it is embedded in hot pionic matter. We calculate the real part and the imaginary part of the pion self-energy in a scheme, analogous to the Brückner-Hartree-Fock approximation used in nuclear physics, which allows to incorporate in a fully consistent way unitarity and Bose correlations at finite temperature. We discuss the consequences of the medium effects on the pion transverse momentum spectrum measured in ultrarelativistic heavy ion collisions and the so-called soft pion puzzle.     

The πN scattering in nuclear matter

The effect of a nuclear medium on the πN scattering amplitude is discussed in a general formalism. A double-counting problem coming from the usual definition of the density-dependent πN scattering amplitude is resolved in this framework. We study the corrections to the fourth-order Chew-Low amplitude. It is shown that the leading terms of the Pauli correction cancel to this order, when one includes the Pauli effect in all intermediate states. The effect of a nuclear medium at nuclear matter density is found to be a 12 % quenching of the amplitude at threshold.     

A simple model calculation of pion condensation in neutron matter

The charged pion condensed state in pure neutron matter is described analytically in an approximate calculation based on the chirally invariant σ-model. The calculation includes s- and p-wave condensed pion-nucleon interactions, pi-pi interactions, the effect of the N¹ (1236) resonance, and the (Ericson-Ericson Lorentz-Lorentz) effect of nuclear correlations.     

Compound nucleus fission and quasi-fission in reactions of 238U with 16O and 27Al

The thermodynamics of pion-condensed nuclear matter is investigated in a relativistic field theory in the mean field approximation. The conditions of the thermodynamical equilibrium of the system lead to a set of self-consistent equations for the meson field amplitudes and for the wave vector of the pion condensate. It is proved, that in the thermodynamical equilibrium the pressure tensor of isolated, infinite nuclear matter is isotropic at any values of the temperature and chemical potential.     

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.