We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the nucleon-nucleon $(NN)$ data below $290\text{\ensuremath{-}}\text{MeV}$ lab energy is comparable to the one of phenomenological high-precision potentials. Since $NN$ potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a $NN$ potential reliable up to $290\phantom{\rule{0.3em}{0ex}}\text{MeV}$. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).

Accurate charge dependent nucleon nucleon potential at fourth order of chiral perturbation theory

Neutron Stars 1: Equation of State and Structure

The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

The shell model as a unified view of 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

We calculate the triton binding energy with a nonlocal {ital NN} potential that fits the world {ital NN} data below 350 MeV with the almost perfect {chi}{sup 2}/datum of 1.03. The nonlocality is derived from relativistic meson field theory. The result obtained in a 34-channel, charge-dependent Faddeev calculation is 8.00 MeV, which is 0.4 MeV above the predictions by local {ital NN} potentials. The increase in binding energy can be clearly attributed to the off-shell behavior of the nonlocal potential. Our result cuts in half the discrepancy between theory and experiment established from local {ital NN} potentials. Implications for other areas of miscroscopic nuclear structure, in which underbinding is a traditional problem, are discussed. {copyright} {ital 1996 The American Physical Society.}

Nonlocal nature of the nuclear force and its impact on nuclear structure.

A new, high-precision, charge-dependent Bonn nucleon-nucleon potential (‘CD-Bonn’) has been constructed that is exactly phase-equivalent to the Nijmegen phase shift analysis and the new high-quality Nijmegen potentials. This non-local CD-Bonn potential predicts 8.0 MeV binding energy for the triton (in a charge-dependent 34-channel Faddeev calculation) which is about 0.4 MeV more than the predictions by the local (phase-equivalent) Nijmegen potential. We pin down origin and size of the nonlocality in the Bonn potential, in analytic and numeric form. The nonlocality is due to the use of the correct relativistic off-shell Feynman amplitude of one-boson-exchange avoiding the commonly used on-shell approximations which yield the local potentials. Adding the relativistic effects from the relativistic nucleon propagators in the Faddeev equations, brings the CD-Bonn result up to 8.2 MeV triton binding. This leaves a difference of only about 0.3 MeV to experiment, which may possibly be explained by refinements in the treatment of relativity and the inclusion of other nonlocalities (e. g., those due to the composite nature of hadrons). Nuclear matter calculations further illustrate our points.

Y. Song

Papers

Nonlocal nature of the nuclear force and its impact on nuclear structure.

Off-Shell NN Potential and Nuclear Binding