The Bonn Meson Exchange Model for the Nucleon Nucleon Interaction

The infrared divergence phenomena and high-energy processes

Nowadays it has become customary in nuclear physics to denote by “tradition” the approach that considers nucleons and mesons as the relevant degrees of freedom. It is the purpose of this chapter to review this “traditional” approach in the area of nuclear forces and their applications to nuclear structure.

The Meson Theory of Nuclear Forces and Nuclear Structure

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.

Chiral effective field theory and nuclear forces

A nucleon-nucleon potential consistent with experiment and the boson exchange theory of nuclear forces

A formulation is presented for the derivation of a Schr\"odinger-equation potential from a field-theoretical model. The relativistic two-body equation of Bethe and Salpeter is reduced using a generalization of the Blankenbecler-Sugar method. The resulting equation is shown to be identical with the nonrelativistic Lippmann-Schwinger equation upon a unitarity-preserving identification of the amplitudes. An equivalent potential is thereby defined and expressed as a solution of an integral equation. The second- and fourth-order potentials are calculated, and their energy dependence and nonlocality are studied. An approximation scheme is developed for expanding the configuration-space potentials in the powers of the momentum operator. Terms up to and including the first power are retained, giving rise to a potential composed of central, spin-orbit, tensor, and spin-spin parts. The contributions of the meson resonances $\ensuremath{\eta}$, $\ensuremath{\rho}$, and $\ensuremath{\omega}$ are included to second order. The complete potential is numerically calculated using masses and coupling parameters taken from meson experiments; no parameter of the potential is searched upon. The resulting potential is remarkably similar to that of Hamada and Johnston (outside half a pion Compton wavelength), particularly for the parts that are relatively well determined by nucleon-nucleon scattering data. Further extensions of the program, including the treatment of the nucleon resonances and pair suppression, are discussed, and an outline of such extensions is given.

Field-Theoretical Nucleon-Nucleon Potential

The extended Gari-Krumpelmann (GK) model of nucleon electromagnetic form factors, in which the $\rho$, $\rho'$, $\omega$, $\omega'$ and $\phi$ vector meson pole contributions evolve at high momentum transfer to conform to the predictions of perturbative QCD (pQCD), was recently shown to provide a very good overall fit to all the nucleon electromagnetic form factor (emff) data, including the preliminary $R_p$ and $R_n$ polarization data available in 2002, but excluding the older $G_{Ep}$ and $G_{En}$ differential cross section data that was inconsistent with the $R_p$ and $R_n$ data. The recently published final version of the polarization data of the electric to magnetic ratio $R_p$ differs little from the preliminary values for the former, but the new values of $R_n$ are midway between the preliminary values and those inferred from the differential cross section data and the Rosenbluth separation. A new fit of the parameters of the same model has been made with the final $R_p$ and $R_n$ data replacing the preliminary values and the addition of some new $R_n$ and $G_{Mn}$ data. Again there is a good fit to all the data when excluding the differentialcross section data that is inconsistent with the polarization data. This includes a very good fit of the $R_p$ data, which was not possible when the differential cross section $G_(En)$ data was used in place of the polarization $R_n$ data. Thus the change between the preliminary and final $R_n$ data, while substantial, has not impeded the good simultaneous fit to the neutron and proton data. The parameters, fit to the data and predictions of the new model are compared to those of the previous models. Low momentum structures that appear in some data analyses are partially reproduced by the model.

Effect of recent R(p) and R(n) measurements on extended Gari-Krumpelmann model fits to nucleon electromagnetic form-factors

The boundary condition model of strong interactions

Nucleon electromagnetic form factor data (including recent data) is fitted with models that respect the confinement and asymptotic freedom properties of QCD. Gari-Kr\"umpelmann (GK) type models, which include the major vector meson pole contributions and at high momentum transfer conform to the predictions of perturbative QCD, are combined with H\"ohler-Pietarinen (HP) models, which also include the width of the $\ensuremath{\rho}$ meson and the addition of higher mass vector meson exchanges, but do not evolve into the explicit form of PQCD at high momentum transfer. Different parametrizations of the GK model's hadronic form factors, the effect of including the width of the $\ensuremath{\rho}$ meson, and the addition of the next (in mass) isospin 1 vector meson are considered. The quality of fit and the consistency of the parameters select three of the combined HP/GK type models. Projections are made to the higher momentum transfers which are relevant to electron-deuteron experiments. The projections vary little for the preferred models, removing much of the ambiguity in electron-nucleus scattering predictions.

Earle L. Lomon

Papers

A nucleon-nucleon potential consistent with experiment and the boson exchange theory of nuclear forces

Field-Theoretical Nucleon-Nucleon Potential

Effect of recent R(p) and R(n) measurements on extended Gari-Krumpelmann model fits to nucleon electromagnetic form-factors

The boundary condition model of strong interactions

Extended Gari-Krümpelmann model fits to nucleon electromagnetic form factors