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

The relativistic mean-field model of the nucleus is reviewed. It describes the nucleus as a system of Dirac nucleons which interact in a relativistic covariant manner via meson fields. The meson fields are treated as mean fields, i.e. as non-quantal c-number fields. The effect of the Dirac sea of the nucleons is neglected. The model is interpreted as a phenomenological ansatz providing a self-consistent relativistic description of nuclei and nuclear dynamics. It is viewed, so to say, as the relativistic generalisation of the Skyrme-Hartree-Fock ansatz. The capability and the limitations of the model to describe nuclear properties are discussed. Recent applications to spherical and deformed nuclei and to nuclear dynamics are presented.

https://iopscience.iop.org/article/10.1088/0034-4885/52/4/002/pdf

The relativistic mean-field description of nuclei and nuclear dynamics

This paper presents a detailed assessment of the ability of the 240 Skyrme interaction parameter sets in the literature to satisfy a series of criteria derived from macroscopic properties of nuclear matter in the vicinity of nuclear saturation density at zero temperature and their density dependence, derived by the liquid-drop model, in experiments with giant resonances and heavy-ion collisions. The objective is to identify those parametrizations which best satisfy the current understanding of the physics of nuclear matter over a wide range of applications. Out of the 240 models, only 16 are shown to satisfy all these constraints. Additional, more microscopic, constraints on the density dependence of the neutron and proton effective mass β-equilibrium matter, Landau parameters of symmetric and pure neutron nuclear matter, and observational data on high- and low-mass cold neutron stars further reduce this number to 5, a very small group of recommended Skyrme parametrizations to be used in future applications of the Skyrme interaction of nuclear-matter-related observables. Full information on partial fulfillment of individual constraints by all Skyrme models considered is given. The results are discussed in terms of the physical interpretation of the Skyrme interaction and the validity of its use in mean-field models. Future work on application of the Skyrme forces, selected on the basis of variables of nuclear matter, in the Hartree-Fock calculation of properties of finite nuclei, is outlined.

Skyrme interaction and nuclear matter constraints

The formalism for the Dirac-Brueckner approach to the nuclear many-body problem is described including its basis in relativistic two-nucleon scattering. A family of relativistic meson-exchange potentials is constructed which (apart from the usual coupling terms for heavy mesons) apply the pseudovector (gradient) coupling for the interaction of pseudoscalar mesons (\ensuremath{\pi},\ensuremath{\eta}) with nucleons. These potentials describe low-energy two-nucleon scattering and the deuteron data accurately. Using these potentials, the properties of nuclear matter are calculated in the Dirac-Brueckner-Hartree-Fock approximation, in which the empirical nuclear matter saturation is explained quantitatively. The effective two-body interaction in the nuclear matter medium (G matrix) is calculated directly in the nuclear matter rest frame. Thus, cumbersome transformations between the two-nucleon center-of-mass frame and the nuclear matter rest frame are avoided. Size and nature of relativistic effects included in the present approach are examined in detail. The formalism, the potentials, and the results of this paper may also serve as a basis and a realistic starting point for systematic relativistic nuclear structure studies as well as for the investigation of further relativistic many-body corrections and of contributions of higher order.

Relativistic nuclear structure. I. Nuclear matter.

The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. We review each of the three main nuclear EFTs---Chiral, Pionless, Halo/Cluster---highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input.

Nuclear effective field theory: status and perspectives

For any given two-body Hamiltonian, there exists a large class of unitarily equivalent Hamiltonians that lead to the same scattering phase shifts at all energies. The purpose of this paper is to exhibit typical saturation curves for reasonable equivalent potentials. The binding energy per particle changes by several MeV in either direction, and the saturation minimum shifts to higher or lower density as the binding increases or decreases. Softening the potential increases the binding. The separation approximation for the reaction matrix provides qualitative insight into these effects. Our exact calculations start with simple local $s$-wave potentials with either a hard core or a Yukawa core. The binding energy per particle is calculated in the Brueckner approximation with self-consistent single-particle energies below the Fermi level. For our examples we use unitary transformations that differ from the identity by a short-range operator of rank 2 and transformations induced by distortions of the radial scale. The latter class of transformations alters the core radius and produces potential terms that are linear in the square of the momentum.

S. Cohen

Papers

Variation in Nuclear-Matter Binding Energies with Phase-Shift-Equivalent Two-Body Potentials