The Two-Pion Exchange NN-Potential in Nuclear Matter and Nuclear Stability

A meson exchange model of the $\pi\pi$ interaction which fits free $\pi\pi$ scattering data is used to calculate the interactions of pions in nuclear matter as a function of nuclear density. Polarization of the nuclear medium by the pions results in a marked increase in the s-wave $\pi\pi$ attraction at low energy. The influence of this effect on the nucleon-nucleon interaction is a corresponding increase with density of the $NN$ central potential due to the exchange of two correlated pions, resulting in an $NN$ interaction which fails to saturate. A possible mechanism for restoring the theoretical stability of nuclear matter is explored and found to be effective

Nuclear Saturation with in-Medium Meson Exchange Interactions

We show that the assumption of dropping meson masses together with conventional many-body effects, implemented in the relativistic Dirac-Brueckner formalism, explains nuclear saturation. We use a microscopic model for correlated $2\pi$ exchange and include the standard many-body effects on the in-medium pion propagation, which initially increase the attractive nucleon-nucleon ($NN$) potential with density. For the vector meson exchanges in both the $\pi\pi$ and $NN$ sector, we assume Brown-Rho scaling which---in concert with `chiral' $\pi\pi$ contact interactions---reduces the attraction at higher densities.Comment: 5 pages REVTeX, 2 eps-figures included, submitted to Phys. Rev. Let

Two-pion exchange potential and the πN\pi N amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped tar fil

Enhancement of πA→ππA\pi A \to \pi\pi A Threshold Cross Sections by In-Medium ππ\pi\pi Final State Interactions

We address the problem of pion production in low energy $\pi$-nucleus collisions. For the production mechanism we assume a simple model consisting of a coherent sum of single pion exchange and the excitation---followed by the decay into two pions and a nucleon---of the $N^*(1440)$ resonance. The production amplitude is modified by the final state interaction between the pions calculated using the chirally improved J\"ulich meson exchange model including the polarization of the nuclear medium by the pions. The model reproduces well the experimentally observed $\pi A \to \pi\pi A$ cross sections, especially the enhancement with increasing $A$ of the $\pi^+\pi^-$ mass distribution in the threshold region.Comment: 5 pages RevTeX, 3-eps figure

Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry

Within the one-loop approximation of baryon chiral perturbation theory we calculate all one-pion and two-pion exchange contributions to the nucleon-nucleon interaction. In fact we construct the elastic NN-scattering amplitude up to and including third order in small momenta. The phase shifts with orbital angular momentum $L\geq2$ and the mixing angles with $J\geq2$ are given parameterfree and thus allow for a detailed test of chiral symmetry in the two-nucleon system. We find that for the D-waves the $2\pi$-exchange corrections are too large as compared with empirical phase shifts, signaling the increasing importance of shorter range effects in lower partial waves. For higher partial waves, especially for G-waves, the model independent $2\pi$-exchange corrections bring the chiral prediction close to empirical NN phase shifts. We propose to use the chiral NN phase shifts with $L\geq 3$ as input in a future phase shift analysis. Furthermore, we compute the irreducible two-pion exchange NN-potentials in coordinate space. They turn out to be of van-der-Waals type, with exponential screening of two-pion mass range.Comment: 30 pages, TeX,12 figures in ps , submitted to Nucl. Phys.

Medium Modification of The Pion-Pion Interaction at Finite Density

We discuss medium modifications of the unitarized pion-pion interaction in the nuclear medium. We incorporate both the effects of chiral symmetry restoration and the influence of collective nuclear pionic modes originating from the p-wave coupling of the pion to delta-hole configurations. We show in particular that the dropping of the sigma meson mass significantly enhances the low energy structure created by the in-medium collective pionic modes.Comment: 26 pages, 7 figures included, Latex fil

Friedel Oscillations in Relativistic Nuclear Matter

We calculate the low-momentum N-N effective potential obtained in the OBE approximation, inside a nuclear plasma at finite temperature, as described by the relativistic $\sigma$-$\omega$ model. We analyze the screening effects on the attractive part of the potential in the intermediate range as density or temperature increase. In the long range the potential shows Friedel-like oscillations instead of the usual exponential damping. These oscillations arise from the sharp edge of the Fermi surface and should be encountered in any realistic model of nuclear matter.Comment: 11 pages in preprint format, typeset using REVTEX, 3 included figures in tar, compressed, uuencoded forma

Effective Field Theory for Bulk Properties of Nuclei

Recent progress in Lorentz-covariant quantum field theories of the nuclear many-body problem ({\em quantum hadrodynamics}, or QHD) is discussed. The importance of modern perspectives in effective field theory and density functional theory for understanding the successes of QHD is emphasized. The inclusion of hadronic electromagnetic structure and of nonanalytic terms in the energy functional is also considered.Comment: 11 pages, 0 figures, REVTeX 3.0; Invited talk at the 11th Conference on Recent Progress in Many-Body Theories (MB 11), Manchester, UK, July 9--13, 200

Composite vertices that lead to soft form factors

The momentum-space cut-off parameter $\Lambda$ of hadronic vertex functions is studied in this paper. We use a composite model where we can measure the contributions of intermediate particle propagations to $\Lambda$. We show that in many cases a composite vertex function has a much smaller cut-off than its constituent vertices, particularly when light constituents such as pions are present in the intermediate state. This suggests that composite meson-baryon-baryon vertex functions are rather soft, i.e., they have \Lambda considerably less than 1 GeV. We discuss the origin of this softening of form factors as well as the implications of our findings on the modeling of nuclear reactions.Comment: REVTex, 19 pages, 5 figs(to be provided on request