Based on a systematic Hartree-Fock+BCS calculation, new perturbation scheme is proposed to modify the existing Skyrme-type effective nuclear force. Much attention is paid to have a better description of fission property of heavy nuclei. In terms of incorporating the nuclear medium effects on the fission barrier height more correctly, two typical Skyrme parameter sets (SkM* and SLy4) are modified. In conclusion, according to the comparison to experiments, the calculated fission barrier heights are improved by almost 90$\%$.
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.
During the past two decades, chiral effective field theory has become a popular tool to derive nuclear forces from first principles. Two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory and three-nucleon forces up to fifth order. Applications of some of these forces have been conducted in nuclear few- and many-body systems---with a certain degree of success. But in spite of these achievements, we are still faced with great challenges. Among them is the issue of a proper uncertainty quantification of predictions obtained when applying these forces in {\i…
I review the recent progress in our understanding of nuclear forces in terms of an effective field theory (EFT) for low-energy QCD and put this progress into historical perspective. This is followed by an assessment of the current status of EFT based nuclear potentials. In concluding, I will summarize some unresolved issues.
We review the impact of nuclear forces on matter at neutron-rich extremes. Recent results have shown that neutron-rich nuclei become increasingly sensitive to three-nucleon forces, which are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. This includes the formation of shell structure, the spectroscopy of exotic nuclei, and the location of the neutron dripline. Nuclear forces also constrain the properties of neutron-rich matter, including the neutron skin, the symmetry energy, and the structure of neutron stars. We first review our unde…
How does nature hold together protons and neutrons to form the wide variety of complex nuclei in the universe? Describing many-nucleon systems from the fundamental theory of quantum chromodynamics has been the greatest challenge in answering this question. The chiral effective field theory description of the nuclear force now makes this possible but requires certain parameters that are not uniquely determined. Defining the nuclear force needs identification of observables sensitive to the different parametrizations. From a measurement of proton elastic scattering on $^{10}$C at TRIUMF and ab i…
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.
I will review recent progress in our understanding of the nuclear force. In the course of the 1990's, so-called high-precision, charge-dependent nucleon-nucleon potentials have been constructed which are, essentially, phenomenological models. These potentials are now commonly used as input for exact few-body calculations and microscopic nuclear many-body theory. I will critically analyses those models and point out their strenghts and weaknesses. Particular emphasis will be on charge dependence. Other recent research was conducted on a more basic level: understanding the nuclear force in terms…
Nowadays, the Gogny force is a referent in the theoretical description of nuclear structure phenomena. Its phenomenological character manifests in a simple analytical form that allows for implementations of techniques both at the mean field and beyond all over the nuclide chart. Over the years, multiple applications of the standard many-body techniques in an assorted set of nuclear structure applications have produced results which are in a rather good agreement with experimental data. The agreement allows for a simple interpretation of those intriguing phenomena in simple terms and gives conf…
Novel simple properties of the monopole component of the effective nucleon-nucleon interaction are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of $N$ and $Z$ consistently with experiments. Some key cases of this shell evolution are discussed, clarifying the effects of central and tensor forces. The validity of the present tensor force is examined in terms of the low-momentum interaction V$_{low k}$ and the Q$_{box}$ formalism.
A linear correlation is shown quantitatively between the magnitude of the EMC effect measured in electron deep inelastic scattering (DIS) and the nuclear residual strong interaction energy (RSIE) obtained from nuclear binding energy subtracting the Coulomb energy contribution. This phenomenological relationship is used to extract the size of in-medium correction (IMC) effect on deuteron and to predict the EMC slopes $|dR_{EMC}/dx|$ of various nuclei. We further investigate the correlations between RSIE and other quantities which are related to the EMC effect. The observed correlations among RS…
We review our research work on the single-particle properties and the equation of state (EOS) of isospin asymmetric nuclear matter within the framework of the Brueckner-Hartree-Fock (BHF) approach extended by including a microscopic three-body force (TBF). The TBF is shown to affect significantly the nuclear matter EOS and the density dependence of nuclear symmetry energy at high densities above the normal nuclear matter density, and it is necessary for reproducing the empirical saturation property of symmetric nuclear matter in a nonrelativistic microscopic framework. The TBF-induced rearrang…
An attempt is made to interpret, in the framework of QCD, the likeness between the shapes of the neutron-neutron strong and electrostatic interactions at the distances $\sim 1÷3$ fm.
We first define a series of NN interaction models ranging from very simple to fully realistic. We then present Green's function Monte Carlo calculations of light nuclei to show how nuclear spectra evolve as the nuclear forces are made increasingly sophisticated. We find that the absence of stable five- and eight-body nuclei depends crucially on the spin, isospin, and tensor components of the nuclear force.
This paper deals with the possible motion of nucleons in the nucleus, which is due to realistic inter-nucleonic forces. This approach provides new or more substantiated conclusions about the nuclear structure than those based on the effective interaction of nucleons, while the shell model of the nucleus may lead to questionable conclusions regarding the nuclear structure and nuclear reaction mechanisms.
These are personal recollections of how Gerry Brown's work and thinking influenced the development of the chiral effective Lagrangian based theory of nuclear forces.
Quantitative information on the tensor force induced isospin-dependence of short-range nucleon-nucleon correlation (SRC) extracted from recent J-Lab experiments was used in constraining the high-momentum tails of single nucleon momentum distributions in both symmetric nuclear matter (SNM) and pure neutron matter (PNM). Its effects on the Equations of State of SNM and PNM as well as the nuclear symmetry energy are investigated. It is found that the tensor force induced isospin-dependence of SRC softens significantly the nuclear symmetry energy especially at supra-saturation densities.
We calculate the equation of state of nuclear matter in the self-consistent T-matrix scheme including three-body nuclear interactions. We study the effect of the three-body force on the self-energies and spectral functions of nucleons in medium.
Nuclear forces and the nuclear many-body problem have been some of Gerry Brown's main topics in his so productive life as a theoretical physicist. In this talk, I outline how Gerry's work laid the foundations of the modern theory of nuclear forces and ab initio calculations of atomic nuclei. I also present some recent developments obtained in the framework of nuclear lattice simulations.
In spite of the great progress we have seen in recent years in the derivation of nuclear forces from chiral effective field theory (EFT), some important issues are still unresolved. In this contribution, we discuss the open problems which have particular relevance for microscopic nuclear structure, namely, the proper renormalization of chiral nuclear potentials and sub-leading many-body forces.
We review the main achievements of the research programme for the study of nuclear forces in the framework of chiral symmetry and discuss some problems which are still open.
We review a new generation of nuclear forces derived in chiral effective field theory using the recently proposed semilocal regularization method. We outline the conceptual foundations of nuclear chiral effective field theory, discuss all steps needed to compute nuclear observables starting from the effective chiral Lagrangian and consider selected applications in the two- and few-nucleon sectors. We highlight key challenges in developing high-precision tree-body forces, such as the need to maintain consistency between two- and many-body interactions and constraints placed by the chiral and ga…
After a historical review, I present the progress in the field of realistic NN potentials that we have seen in recent years. A new generation of very quantitative (high-quality/high-precision) NN potentials has emerged. These potentials will serve as reliable input for microscopic nuclear structure calculations and will allow for a systematic investigation of off-shell effects. The issue of three-nucleon forces is also discussed.
The present note summarizes the discourse on power counting issues of chiral nuclear forces, with an emphasis on renormalization-group invariance. Given its introductory nature, I will lean toward narrating a coherent point of view on the concepts, rather than covering comprehensively the development of chiral nuclear forces in different approaches.
We review the nuclear forces currently in use, i.e., the high-precision NN potentials of the 1990's and the nuclear two- and many-body forces based upon chiral effective field theory (EFT). We argue that the EFT approach is superior to any of the older schemes. Since accurate chiral forces are available now, the stage is set for microscopic nuclear structure to move into a new exciting era.
In these proceedings, we discuss the current status of nuclear bound state predictions based on chiral nuclear interactions. Results of ordinary $s$- and $p$-shell nuclei and light hypernuclei are shown.
Using the Hellmann--Feynman theorem we analyze the contribution of the different terms of the nucleon-nucleon interaction to the nuclear symmetry energy $E_{sym}$ and the slope parameter $L$. The analysis is performed within the microscopic Brueckner--Hartree--Fock approach using the Argonne V18 potential plus the Urbana IX three-body force. We find that the main contribution to $E_{sym}$ and $L$ is due to the tensor component of the nuclear force.
The theory of nuclear forces has made great progress since the turn of the millenium using the framework of chiral effective field theory (ChEFT). The advantage of this approach, which was originally proposed by Weinberg, is that it has a firm basis in quantum-chromodynamics and allows for quantitative calculations. Moreover, this theory generates two-nucleon forces (2NF) and many-body forces on an equal footing and provides an explanation for the empirically known fact that 2NF >> 3NF >> 4NF. I will present the recent advances in more detail and put them into historical context. In addition, …
We propose new effective inter-nucleon forces with a finite-range three-body operator. The proposed forces are suitable for describing the nuclear structure properties over a wide mass number region, including the saturation point of nuclear matter. The forces are applied to microscopic calculations of $Z=N$ ($A\le 40$) nuclei and O isotopes with a method of antisymmetrized molecular dynamics. We present the characteristics of the forces and discuss the importance of the finite-range three-body term.
After a brief review on the status of few--nucleon studies based on conventional nuclear forces, we sketch the concepts of the effective field theory approach constrained by chiral symmetry and its application to nuclear forces. Then first results for few--nucleon observables are discussed.
This paper is a write-up of introductory lectures on the modern approach to the nuclear force problem based on chiral effective field theory given at the 2009 Joliot-Curie School, Lacanau, France, 27 September - 3 October 2009.
A relation between nuclear forces derived using a phenomenological approach and nuclear effective field theory (NEFT) is proposed from a renormalization group point of view. A phenomenological nuclear force (V_ph) and an NEFT-based NN-potential (V_EFT) are satisfactorily related to each other through the Wilsonian renormalization group (WRG) method. It is clearly shown that use of the simple contact interactions in NEFT is adequate to simulate small scale phenomena, and that an NEFT-based NN-potential (V_EFT) is free from dependence on the model used to describe small scale phenomena. We study…
Effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of Quantum Chromodynamics. We review the foundations of this approach and discuss its application for light nuclei at various resolution scales. The extension of this approach to many-body systems is briefly sketched.
Within the self-consistent Green's functions formalism, we study the effects of three-body forces on the in-medium spectral function, self-energy and effective mass of the nuclear matter constituents, analyzing the density and momentum dependence.
Surface properties of neutron-neutron (T=1) pairing in semi-infinite nuclear matter in a hard wall potential are investigated in BCS approximation using the Gogny force. Surface enhancement of the gap function, pairing tensor and correlation energy density is put into evidence.
The effect of a microscopic three-body force on the saturation properties of nuclear matter is studied within the Brueckner-Hartree-Fock approach. The calculations show a decisive improvement of the saturation density along with an overall agreement with the empirical saturation point. With the three-body force the symmetry energy turns more rapidly increasing with density, which allows for the direct URCA process to occur in $β$-stable neutron star matter. The influence of the three-body force on the nuclear mean field does not diminish the role of the ground state correlations.
We formulate the quark meson coupling model as a many-body effective Hamiltonian. This leads naturally to the appearance of many-body forces. We investigate the zero range limit of the model and compare its Hartree-Fock Hamiltonian to that corresponding to the Skyrme effective force. By fixing the three parameters of the model to reproduce the binding and symmetry energy of nuclear matter, we find that it allows a very satisfactory interpretation of the Skyrme force.
The application of the effective field theory (EFT) method to nuclear systems is reviewed. The roles of degrees of freedom, QCD symmetries, power counting, renormalization, and potentials are discussed. EFTs are constructed for various energy regimes of relevance in nuclear physics, and are used in systematic expansions to derive nuclear forces in terms of a number of parameters that embody information about QCD dynamics. Two-, three-, and many-nucleon systems, including external probes, are considered.
A shortlist of Skyrme force parameterizations, recently found to have passed a series of constraints relating to nuclear matter properties is analyzed for their ability to reproduce data in finite nuclei. We analyse binding energies, isotope shifts and fission barriers. We find that the subset of forces have no common ability to reproduce (or otherwise) properties of finite nuclei, despite passing the extensive range of nuclear matter constraints.
The first practical method to evolve many-body nuclear forces to softened form using the Similarity Renormalization Group (SRG) in a harmonic oscillator basis is demonstrated. When applied to He4 calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force.
We give a short review of the quark-meson coupling (QMC) model, the quark-based model of finite nuclei and hadron interactions in a nuclear medium, highlighting on the relationship with the Skyrme effective nuclear forces. The model is based on a mean field description of nonoverlapping nucleon MIT bags bound by the self-consistent exchange of Lorentz-scalar-isoscalar, Lorentz-vector-isoscalar, and Lorentz-vector-isovector meson fields directly coupled to the light quarks up and down. In conventional nuclear physics the Skyrme effective forces are very popular, but, there is no satisfactory in…
The attempts to find the right (underlying) theory for the nuclear force have a long and stimulating history. Already in 1953, Hans Bethe stated that "more man-hours have been given to this problem than to any other scientific question in the history of mankind". In search for the nature of the nuclear force, the idea of sub-nuclear particles was created which, eventually, generated the field of particle physics. I will review this productive history of hope, error, and desperation. Finally, I will discuss recent ideas which apply the concept of an effective field theory to low-energy QCD. The…
We review recent progress in implementing high-precision chiral two- and three-body forces in nuclear many-body systems beyond light nuclei. We begin with applications to finite nuclei, which we study through the nuclear shell model and self-consistent mean field theory. We then turn our attention to infinite nuclear matter treated within the framework of Landau's theory of normal Fermi liquids.
We substantiate our statement that the deuteron remains bound in the chiral limit. We critically discuss recent claims that effective field theory cannot give a definite answer to this question.
We present calculations for symmetric nuclear matter using chiral nuclear interactions within the Self-Consistent Green's Functions approach in the ladder approximation. Three-body forces are included via effective one-body and two-body interactions, computed from an uncorrelated average over a third particle. We discuss the effect of the three-body forces on the total energy, computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on single-particle properties. Saturation properties are substantially improved when three-body forces are included, but there is still some underlyi…
The properties of pairing correlation in nuclear matter are investigated by using various versions of Skyrme forces. Truncation of states involving pairing correlation, necessary due to zero range nature of the Skyrme force, is discussed in detail. A plateau appears in pairing gap versus cutoff for each force. We propose to choose the cutoff parameter in the middle of the plateau so that the parameterization is independent of nuclides.
I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.
I outline why the renormalisation group is needed to analyse the scale dependence and hence determine the power counting for effective theories of strongly interacting systems. I summarise the results of several such analyses for two- and three-body forces in nuclear physics. These show that a number of terms should be significantly promoted relative to naive dimensional analysis.
We investigate single-particle properties in infinite nuclear matter using a variety of interactions. One of the focal points is to study the impact of chiral three-nucleon forces on the nucleon self-energy and related quantities, such as spectral function and momentum distribution. We also present results for pairing correlations in nuclear matter. We find characteristic and systematic differences between the predictions obtained with the (softer) chiral interactions and those based on one-boson-exchange or phenomenology.
Yoichiro Nambu put a great foot print in nuclear physics in the era of its fundamental developments including his pioneering insight into essential ingredients of repulsive core of nuclear force and its relation to the saturation of nuclear matter. The present review article focuses onto recent developments of the interaction models between colliding nuclei in terms of Brueckner's G-matrix theory staring from realistic nuclear forces and the saturation property of symmetric nuclear matter as well as neutron-star matter. A recently proposed unique scenario of extracting the saturation property …
A new method is developed for treating the effect of the neutron-proton mass difference in isospin-violating nuclear forces. Previous treatments utilized an awkward subtraction scheme to generate these forces. A field redefinition is used to remove that mass difference from the Lagrangian (and hence from asymptotic nucleon states) and replace its effect by effective interactions. Previous calculations of static Class II charge-independence-breaking and Class III charge-symmetry-breaking potentials are verified using the new scheme, which is also used to calculate Class IV nuclear forces. Two-b…
The eigenvalue problem of a short-range potential is revisited in view of the increased interest in simple models imitating the nuclear forces. This is in order to conduct calculations of vibronic energies in fermion-boson coupled systems.
Three body effects are studied for both asymmetric nuclear matter and pure neutron matter to calculate the nuclear Equation of State . The Brueckner Hartree Fock approximation is used using CD Bonn B and Argonne V18 potentials. A two body density dependent Skyrme potential is added to reproduce the empirical saturation point. Good agreement is obtained in comparison with exact calculation including three body forces.
A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin-orbit splittings in neutron drops. This result is obtained from relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.
