Michael C. Birse
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.
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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.
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.
Nuclear forces and nuclear excited states
本研究基于核壳模型分析两核子相互作用的中心力、自旋力、张量力对sd壳层原子核低激发态的贡献，发现中心力主导激发能，自旋轨道力与张量力在部分核中作用关键，且哈密顿量投影法更适合评估各力贡献。
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.
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.
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.
After a brief historical review, we present recent progress in our understanding of nuclear forces in terms of chiral effective field theory.
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.
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.
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.
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.
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…
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.
As follows from the energies of single-particle states in ^{40}Ca, ^{90}Zr and ^{208}Pb nuclei the contribution of many-particle NN forces to the nuclear single-particle potential is at least the sum of repulsive and attractive parts resulting from three-particle and four-particle forces respectively. In addition the specified nucleon density distributions in the above nuclei are determined from both the 1 GeV proton-nucleus elastic scattering and the single-particle energies.
We have studied the structure of K- pp comprehensively by solving this three-body system in a variational method, starting from the Ansatz that the Lambda(1405) resonance (~ Lambda*) is a K-p bound state. The structure of K-pp reveals a molecular feature, namely, the K- in Lambda* as an "atomic center" plays a key role in producing strong covalent bonding with the other proton. We point out that strongly bound Kbar nuclear systems are formed by ``super strong" nuclear force due to migrating real bosonic particles Kbar a la Heitler-London-Heisenberg, whereas the normal nuclear force is caused b…
In order to simulate the relativistic effects of the Dirac Brueckner Hartree Fock approach for finite nuclei the part of the Urbana 3 nucleon (3N) force is considered, which represents the enhancement of the small components of the Dirac spinors for the nucleons in the nuclear medium. This 3N force is included in a Brueckner Hartree Fock calculation with rearrangement terms using a realistic model for the NN interaction. The strength of the 3N force is adjusted to reproduce the empirical saturation point of nuclear matter and then used in corresponding studies of the closed shell nuclei $^{16}…
Nucleus-nucleus optical potentials are constructed from an energy density functional approach first outlined by Brueckner et al. The interaction term of the energy density functional comes from the complex nucleon self-energy computed in nuclear matter with two- and three-body chiral nuclear forces. Nuclear density distributions are calculated from Skyrme functionals constrained to the equations of state calculated from the same chiral forces used for the self-energy. Predictions for elastic scattering cross sections and fusion cross sections are compared to experimental data. Very good agreem…
The nd doublet and quartet scattering lengths have been calculated based on the modern NN and 3N interactions. We also studied the effect of the electromagnetic interactions in the form introduced in AV18. Switching them off for the various nuclear force models leads to shifts of up to +0.04 fm for doublet scattering length, which is significant for present day standards. The electromagnetic effects have also a noticeable effect on quartet scattering length, which otherwise is extremely stable under the exchange of the nuclear forces. For the current nuclear force models there is a strong scat…
We propose a method for microscopic calculations of nuclear ground-state properties in the framework of density functional theory. We discuss how the density functional is equivalent to the effective action for the density, thereby establishing a constructive framework for density functional calculations from nuclear forces. The presented approach starts from non-interacting nucleons in a background potential (a simple approximation for the mean field). The nuclear forces are then gradually turned on, while the background potential is removed. The evolution equation yields the ground-state ene…
The renormalization of singular chiral potentials as applied to NN scattering and the structure of the deuteron is discussed. It is shown how zero range theories may be implemented non-perturbatively as constrained from known long range NN forces.
Realistic nuclear potentials, derived within chiral perturbation theory, are a major breakthrough in modern nuclear structure theory, since they provide a direct link between nuclear physics and its underlying theory, namely the QCD. As a matter of fact, chiral potentials are tailored on the low-energy regime of nuclear structure physics, and chiral perturbation theory provides on the same footing two-nucleon forces as well as many-body ones. This feature fits well with modern advances in ab-initio methods and realistic shell-model. Here, we will review recent nuclear structure calculations, b…
Using a relativistic Dirac-Brueckner analysis the pion contribution to the ground state energy of nuclear matter is studied. Evidence is presented that the role of the tensor force in the saturation mechanism is substantially reduced compared to its dominant role in a usual non-relativistic treatment. The reduction of the pion contribution in nuclear matter is due to many-body effects present in a relativistic treatment. In particular, we show that the damping of OPEP is actually due to the decrease of $M^*/M$ with increasing density.
During the past two decades, it has been demonstrated that chiral effective field theory represents a powerful tool to deal with nuclear forces in a systematic and model-independent way. Two-, three-, and four-nucleon forces have been derived up to next-to-next-to-next-to-leading order (N3LO) and (partially) applied in nuclear few- and many-body systems---with, in general, a good deal of success. This may suggest that we are finally done with the nuclear force problem; but that would be too optimistic. There are still some pretty basic open issues that have been swept under rug and, finally, n…
We present mini-proceedings of the international workshop on "Chiral Forces in Low Energy Nuclear Physics - the LENPIC Meeting" held at the Jagiellonian University, Krakow, Poland from February 10 to 11, 2017. The workshop focused on the new generation of chiral forces with the semi-local regularization and their applications to few- and many-nucleon systems. Included short contributions summarize talks given by E.Epelbaum, K.Hebeler, R.Roth, H.Witala, A.Calci, P.Reinert, J.P.Vary, H.Kamada, I.Ciepal, H.Krebs, H.Le, K.Topolnicki, K.Vobig and Yu.Volkotrub.
Implementation of chiral two-nucleon forces to nuclear many-body methods with Gaussian-wave packets
针对手征有效场理论未应用于高斯波包核多体方法的问题，本文提出计算手征两核力两体矩阵元的形式体系，可视化矩阵元并分析力的贡献，为团簇现象的从头算研究奠定基础。
We explore the effects of a microscopic nuclear three-body force on the threshold baryon density for kaon condensation in chemical equilibrium neutron star matter and on the composition of the kaon condensed phase in the framework of the Brueckner-Hartree-Fock approach. Our results show that the nuclear three-body force affects strongly the high-density behavior of nuclear symmetry energy and consequently reduces considerably the critical density for kaon condensation provided that the proton strangeness content is not very large. The dependence of the threshold density on the symmetry energy …
In recent years, nuclear physics has benefited greatly from the development of powerful ab initio many-body methods and their combination with interactions from chiral effective field theory. With increasing computational power and continuous development of these methods, we are entering an era of precision nuclear physics. Indeed, uncertainties from nuclear Hamiltonians now dominate over uncertainties from many-body methods. This review summarizes the current status of, and future directions in, deriving and constraining nuclear Hamiltonians.
In recent years, the Similarity Renormalization Group has provided a powerful and versatile means to soften interactions for ab initio nuclear calculations. The substantial contribution of both induced and initial three-body forces to the nuclear interaction has required the consistent evolution of free-space Hamiltonians in the three-particle space. We present the most recent progress on this work, extending the calculational capability to the p-shell nuclei and showing that the hierarchy of induced many-body forces is consistent with previous estimates. Calculations over a range of the flow …
Chiral effective field theory is being developed into a precision tool for low-energy nuclear physics. I review the state of the art in the two-nucleon sector, discuss applications to few-nucleon systems and address challenges that will have to be faced over the coming years.
We calculate thermodynamic quantities in symmetric nuclear matter within the self-consistent Green's functions method including three-body forces. The thermodynamic potential is computed directly from a diagrammatic expansion, implemented with the CD-Bonn and Nijmegen nucleon-nucleon potentials and the Urbana three-body forces. We present results for entropy and pressure up to temperatures of 20 MeV and densities of 0.32 fm^-3. While the pressure is sensitive to the inclusion of three-body forces, the entropy is not. The unstable spinodal region is identified and the critical temperature assoc…
Similarity renormalization group for nuclear forces
本文介绍了用于生成低分辨率核力的相似性重整化群方法，分析了其对哈密顿量对角化的影响及多体相互作用的作用，推动了核的第一性原理计算发展。
Landau's Fermi Liquid parameters are calculated for non-superfluid pure neutron matter in the presence of a strong magnetic field at zero temperature. The particle-hole interactions in the system, where a net magnetization may be present, are characterized by these parameters in the framework of a multipolar formalism. We use either zero- or finite-range effective nuclear forces to describe the nuclear interaction. Using the obtained Fermi Liquid parameters, the effect of a strong magnetic field on some bulk magnitudes such as isothermal compressibility and spin susceptibility is also investig…
The energy per particle, symmetry energy, pressure, Free energy are calculated for asymmetric nuclear matter using BHF approach and modern nucleon-nucleon CD-Bonn, Nijm1, Argonnev18 and Reid93 potentials. To obtain saturation in nuclear matter we add three-body interaction terms which are equivalent a la Skyrme to a density-dependent two-nucleon interaction. Good agreement is obtained in comparison with previous theoretical estimates and experimental data.
We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne $V18$ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, th…
We present a simplified method to generate the Hartree-Fock Gamow basis from realistic nuclear forces. The Hartree-Fock iteration in the harmonic-oscillator basis is first performed, and then the obtained HF potential is analytically continued to the complex-k plane, finally by solving the Schrödinger equation in the complex-k plane the Gamow basis is obtained. As examples, the method is applied to 4He and 22O with the renormalized chiral N3LO potential. The basis obtained which includes bound, resonant and scattering states can be further used in many-body calculations to study weakly bound n…
Spatial correlation characteristics of the anomalous density matrix $κ$ in a slab of nuclear matter with the Paris and Argonne v18 forces are calculated. A detailed comparison with predictions of the effective Gogny force is made. It is found that the two realistic forces lead to very close results which are qualitatively similar to those for the Gogny force. At the same time, the magnitude of $κ$ for realistic forces is essentially smaller than the one for the Gogny force. The correlation characteristics are practically independent of the magnitude of $κ$ and turn out to be quite close for th…
I examine the evolution of nuclear forces under the similarity renormalization group (SRG) using traces of the many-body configuration-space Hamiltonian. While SRG is often said to "soften" the nuclear interaction, I provide numerical examples which paint a complementary point of view: the primary effect of SRG, using the kinetic energy as the generator of the evolution, is to shift downward the diagonal matrix elements in the model space, while the off-diagonal elements undergo significantly smaller changes. By employing traces, I argue that this is a very natural outcome as one diagonalizes …
Brueckner calculations including a microscopic three-body force have been extended to isospin asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs isospin asymmetry $β=(N-Z)/A$ is fulfilled in the whole asymmetry range $0\leβ\le 1$ up to high densities. The three-body force provides a strong enhance…
We derive the effective interaction between two quasiparticles in symmetric nuclear matter resulting from the leading-order chiral three-nucleon force. We restrict our study to the L=0,1 Landau parameters of the central quasiparticle interaction computed to first order. We find that the three-nucleon force provides substantial repulsion in the isotropic spin- and isospin-independent component F_0 of the interaction. This repulsion acts to stabilize nuclear matter against isoscalar density oscillations, a feature which is absent in calculations employing low-momentum two-nucleon interactions on…
Nuclear symmetry energy and the role of three-body forces
本研究在LOCV框架下引入基于同位旋依赖参数化的修订三体力，结合AV18两体力，成功再现冷核物质饱和参数，并预测中子星最大质量超过2倍太阳质量。
Within the framework of an isospin-dependent quantum molecular dynamics model, the zero-range 2-body part of the Skyrme interaction is replaced by a finite-range Gaussian 2-body interaction. From the transverse momentum analysis in the reaction of system $^{93}$Nb + $^{93}$Nb at energy of 400 MeV/nucleon and impact parameter $b$=3 fm, it is shown that the finite-range nuclear force enhances the transverse momentum of the reaction system and it can partly replace the momentum dependent part of the nucleon-nucleon interaction.
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