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.

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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

Neutron Stars 1: Equation of State and Structure

Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions

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

The authors present a new high-quality nucleon-nucleon potential with explicit charge dependence and charge asymmetry, which they designate Argonne {upsilon}{sub 18}. The model has a charge-independent part with fourteen operator components that is an updated version of the Argonne {upsilon}{sub 14} potential. Three additional charge-dependent and one charge-asymmetric operators are added, along with a complete electromagnetic interaction. The potential has been fit directly to the Nijmegen pp and np scattering data base, low-energy nn scattering parameters, and deuteron binding energy. With 40 adjustable parameters it gives a {chi}{sup 2} per datum of 1.09 for 4,301 pp and np data in the range 0--350 MeV.

https://arxiv.org/pdf/nucl-th/9408016.pdf

Accurate nucleon-nucleon potential with charge-independence breaking

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

Triton calculations with the new Nijmegen potentials

The Faddeev equations for the hypertriton are solved precisely using the Nijmegen hyperon-nucleon and realistic NN interactions The hypertriton turns out to be bound at the experimental value Thereby the \ensuremath{\Lambda}-\ensuremath{\Sigma} conversion is crucial States of the \ensuremath{\Lambda}(\ensuremath{\Sigma})NN system with quantum numbers (T,J) different from (0,1/2) are not bound We visualized properties of the hypertriton wave function in various ways

Properties of the bound Λ(Σ)NN system and hyperon-nucleon interactions

Pion-meson-exchange nucleon-nucleon potentials are derived for two nucleons in the intermediate states. The mesons we include are (i) pseudoscalar mesons \ensuremath{\pi},\ensuremath{\eta}, and ${\mathrm{\ensuremath{\eta}}}^{\ensuremath{'}}$, (ii) vector mesons \ensuremath{\rho}, \ensuremath{\omega}, and \ensuremath{\varphi}, (iii) scalar mesons ${\mathit{a}}_{0}$(980), \ensuremath{\varepsilon}(760), and ${\mathit{f}}_{0}$(975), and (iv) the J=0 contribution from the Pomeron. Strong dynamical pair suppression is assumed, and at the nucleon-nucleon-meson vertices Gaussian form factors are incorporated into the relativistic two-body framework using a dispersion representation for the pion- and meson-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators. The potentials are first calculated in the adiabatic approximation to all planar and crossed three-dimensional momentum-space \ensuremath{\pi}-meson diagrams. Next, we calculate the 1/M corrections. \textcopyright{} 1996 The American Physical Society.

https://arxiv.org/pdf/nucl-th/9509029.pdf

V. G. J. Stoks

Papers

Accurate nucleon-nucleon potential with charge-independence breaking

Construction of high-quality NN potential models

Triton calculations with the new Nijmegen potentials

Properties of the bound Λ(Σ)NN system and hyperon-nucleon interactions

Soft two-meson-exchange nucleon-nucleon potentials. I. Planar and crossed-box diagrams