Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

/pdf/modern-theory-of-nuclear-forces-436h635pm0.pdf

Modern theory of nuclear forces

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

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 present an updated version (Nijm93) of the Nijmegen soft-core potential, which gives a much better description of the np data than the older version (Nijm78). The ${\mathrm{\ensuremath{\chi}}}^{2}$ per datum is 1.87. The configuration-space and momentum-space versions of this potential are exactly equivalent, a unique feature among meson-theoretical potentials. We also present three new NN potential models: a nonlocal Reid-like Nijmegen potential (Nijm I), a local version (Nijm II), and an updated regularized version (Reid 93) of the Reid soft-core potential. These three potentials all have a nearly optimal ${\mathrm{\ensuremath{\chi}}}^{2}$ per datum and can therefore be considered as alternative partial-wave analyses. All potentials contain the proper charge-dependent one-pion-exchange tail.

Construction of high-quality NN potential models

We present a multienergy partial-wave analysis of all NN scattering data below ${\mathit{T}}_{\mathrm{lab}}$=350 MeV, published in a regular physics journal between 1955 and 1992. After careful examination, our final database consists of 1787 pp and 2514 np scattering data. Our fit to these data results in ${\mathrm{\ensuremath{\chi}}}^{2}$/${\mathit{N}}_{\mathrm{df}}$=1.08, with ${\mathit{N}}_{\mathrm{df}}$=3945 the total number of degrees of freedom. All phase shifts and mixing parameters can be determined accurately.

Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV.

As a continuation of our 0--30 MeV analysis we present a multienergy phase shift analysis of all {ital pp} scattering data below {ital T}{sub lab}=350 MeV. In the description of all partial waves we take exactly into account the long-range potential consisting of the improved Coulomb potential (including the magnetic moment interaction), the vacuum polarization potential, and the tail of the one-pion-exchange potential. To describe the short-range interaction in the lower partial waves we use a {ital P}-matrix parametrization. The intermediate partial waves are treated either by optimal mapping techniques or by using the Nijmegen soft-core potential. The latter gives a better description of the data. The final data set comprises 1626 scattering observables. The best fit to this final data set results in {chi}{sup 2}/{ital N}{sub df}=1.117, where {ital N}{sub df}=1576 is the number of degrees of freedom. The {ital pp}{pi}{sup 0} pseudovector coupling constant is determined to be {ital f}{sub 0}{sup 2}=(74.9{plus minus}0.7){times}10{sup {minus}3}. Single-energy phase shifts and errors are also given.

Phase shift analysis of all proton proton scattering data below T(lab) = 350-MeV

A review is given of the various Nijmegen potentials. Special attention is given to some of the newest developments, such as the extended soft-core model, the high-quality potentials, and the Nijmegen optical potentials for NN.

https://arxiv.org/pdf/nucl-th/9509024.pdf

The Nijmegen Potentials

The NN\ensuremath{\pi} coupling constants are extracted in NN partial-wave analyses. The data base contains all pp and np scattering data below ${\mathit{T}}_{\mathrm{lab}}$=350 MeV. Introducing different coupling constants at the different NN\ensuremath{\pi} vertices, at the pion pole we find for the pp${\mathrm{\ensuremath{\pi}}}^{0}$ coupling ${\mathit{f}}_{\mathit{p}}^{2}$=0.0751(6), for the nn${\mathrm{\ensuremath{\pi}}}^{0}$ coupling ${\mathit{f}}_{\mathit{n}}^{2}$=0.075(2), and for the charged-pion coupling ${\mathit{f}}_{\mathit{c}}^{2}$=0.0741(5). These results allow only small charge-independence-breaking effects in the NN\ensuremath{\pi} coupling constants. If we assume charge independence, we find ${\mathit{f}}^{2}$=0.0749(4). The value found for ${\mathit{f}}_{\mathit{c}}^{2}$ is in agreement with the determination in a recent VPI analysis of the \ensuremath{\pi}N scattering data, and with its determination in an analysis of the charge-exchange reaction p\ifmmode\bar\else\textasciimacron\fi{}p\ensuremath{\rightarrow}n\ifmmode\bar\else\textasciimacron\fi{}n.

R. A. M. Klomp

Papers

Construction of high-quality NN potential models

Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV.

Phase shift analysis of all proton proton scattering data below T(lab) = 350-MeV

The Nijmegen Potentials

Determination of the NN pi coupling constants in NN partial-wave analyses.