M1 properties, comprising magnetic moments and radiative capture of thermal neutron observables, are studied in two- and three-nucleon systems. We utilize meson exchange current derived up to N$^3$LO using heavy baryon chiral perturbation theory a la Weinberg. Calculations have been performed for several qualitatively different realistic nuclear Hamiltonians, which permits us to analyze model dependence of our results. Our results are found to be strongly correlated with the effective range parameters such as binding energies and the scattering lengths. Taking into account such correlation, the results are in good agreement with the experimental data with small model-dependence.
The NN results are presented from the extended-soft-core (ESC) interactions. They cosist of local- and non-local-potentials due to (i) one-boson-exchange (OBE), pseudo-scalar-, vector-, scalar-, and axial-vector-nonets, (ii) diffractive exchanges, (iii) two-pseudoscalar-exchange, and (iv) meson-pair-exchange (MPE). Fits to the pp- and np-data for 0 < T(lab) < 350 MeV have typical χ^2/Ndata= 1.15. Used are less than 20 parameters, which are coupling constants and cut-off masses. The couplings follow rather closely the pattern predicted by the quark-pair-creation model. As a result the 11 OBE-co…
We calculate the complete $T$ matrices of the elastic nucleon-nucleon scattering up to third order in SU(3) heavy baryon chiral perturbation theory. The phase shifts with orbital angular momentum $L\geq 2$ and the mixing angles with $J\geq 2$ are evaluated by using low-energy constants that were extracted from the meson-baryon analysis. It turns out that our prediction is consistent with the empirical phase shifts and mixing angles data, and also the results from SU(2) heavy baryon chiral perturbation theory. The errors from the low-energy constants are analyzed in detail. Our calculation prov…
By solving the Schrödinger equation for the three-quark system in the hyperspherical harmonic approach, we have studied the low energy part of the nucleon and $Δ$ spectra using a quark-quark interaction which reproduces the nucleon-nucleon phenomenology. The quark-quark hamiltonian considered includes, besides the usual one-gluon exchange, pion and sigma exchanges generated by the chiral symmetry breaking. The baryonic spectrum obtained is reasonable and the resulting wave function gives consistency to the ansatz used in the two baryon system.
We apply the quark delocalization and color screening model to nucleon-baryon scattering. A semi-quantitative fit to N-N, N-Lambda and N-Sigma phase shifts and scattering cross sections is obtained without invoking meson exchange. Quarks delocalize reasonably in all of the different flavor channels to induce effective nucleon-baryon interactions with both a repulsive core and with an intermediate range attraction in the cases expected.
We consider a symmetry-preserving approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Within this framework the leading-order amplitude is calculated by solving renormalizable equations and corrections are taken into account perturbatively.
The recent Investigations in the chiral quark model show that kaon productions of nucleon play an important role in understanding the structure of baryons. The evidences of a third $S_{11}$ resonance in the second resonance region and two narrow states around 2 GeV suggest a set of the molecular type baryons with hidden strangeness. Confirming these states requires further theoretical and experimental studies of the strangeness production.
To obtain an understanding of the structure and reactions of nuclear systems from first principles has been a long-standing goal of nuclear physics. In this respect, few- and many-body systems provide a unique laboratory for studying nuclear interactions. During the past decades, the development of accurate representations of the nuclear force has undergone substantial progress. Particular emphasis has been devoted to chiral effective field theory (EFT), a low-energy effective representation of quantum chromodynamics (QCD). Within chiral EFT, many studies have been carried out dealing with the…
We summarize the current status of our understanding of nuclear forces based upon chiral symmetry--an idea that was advocated by Gerry Brown already several decades ago.
We derive the leading contribution to the four-nucleon force within the framework of chiral effective field theory. It is governed by the exchange of pions and the lowest-order nucleon-nucleon contact interaction and includes effects due to the nonlinear pion-nucleon couplings and the pion self interactions constrained by the chiral symmetry of QCD. The resulting four-nucleon force does not contain any unknown parameters and can be tested in few- and many-nucleon studies.
We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of …
We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next- to-leading order. The resulting new chiral force NNLOopt yields χ^2 \approx 1 per degree of freedom for laboratory energies below approximately 125 MeV. In the A = 3, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use NNLOopt to study properties of key nuclei and neutron matter, and demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitl…
The three-nucleon bound and scattering equations are solved in momentum space for a coupled-channel Hamiltonian. The Hamiltonian couples the purely nucleonic sector of Hilbert space with a sector in which one nucleon is excited to a $Δ$ isobar. The interaction consists of irreducible two-baryon and irreducible three-baryon potentials. The calculation keeps only the purely nucleonic one among the irreducible three-baryon potentials. The coupled-channel two-baryon potential yields additional reducible contributions to the three-nucleon force. The Coulomb interaction between the two protons is in…
Results from an ongoing study of baryon-baryon systems with strangeness S=-1 and -2 within chiral effective field theory are reported. The investigations are based on the scheme proposed by Weinberg which has been applied rather successfully to the nucleon-nucleon interaction in the past. Results for the hyperon-nucleon and hyperon-hyperon interactions obtained to leading order are reviewed. Specifically, the issue of extrapolating the binding energy of the H-dibaryon, extracted from recent lattice QCD simulations, to the physical point is addressed. Furthermore, first results for the hyperon-…
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.
It is shown that most of the models for analyzing meson-baryon reactions in the nucleon resonance region can be derived from a Hamiltonian formulation of the problem. An extension of the coupled-channel approach to include $ππN$ channel is briefly described and some preliminary results for the $N^*(1535)$ excitation are presented.
We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon scattering T-matrix. Analytic expressions are presented for each of these in both isospin-symmetric nuclear matter as well as nuclear matter with a small isospin asymmetry. The results are combined with the low-momentum nucleon-nucleon potential V(low-k) to obtain an effective density-dependent interaction suitable for nuclear structure calculations. The in-med…
We perform calculations for the binding energies and low-lying levels of ${}^{10,11,12,13,14,15,16,17,18,19,20,21,22}C$ nuclei starting from the chiral $N3LO$ nucleon-nucleon potential within the framework of the Hybrid Multideterminant scheme. The calculations are restricted to 4 major harmonic oscillator shells, via the Lee-Suzuki renormalization scheme. The results are compared with the experimental data.
In this proceeding we summarize results for baryonic contact terms derived within SU(3) chiral effective field theory. The four-baryon contact terms, necessary for the description of the hyperon-nucleon interaction, include SU(3) symmetric and explicit chiral symmetry breaking terms. They also include four-baryon contact terms involving pseudoscalar mesons, which become important for three-body forces. Furthermore we derive the leading order six-baryon contact terms in the non-relativistic limit and study their contribution to the $ΛNN$ three-body contact interaction. These results could play …
We solve the ab initio no-core shell model (NCSM) in the complete Nmax = 8 basis for A = 7 and A = 8 nuclei with two-nucleon and three-nucleon interactions derived within chiral effective field theory (EFT). We find that including the chiral EFT three-nucleon interaction in the Hamiltonian improves overall good agreement with experimental binding energies, excitation spectra, transitions and electromagnetic moments. We predict states that exhibit sensitivity to including the chiral EFT three-nucleon interaction but are not yet known experimentally.
We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected,…
We outline the structure of the nuclear force in the framework of chiral effective field theory of QCD and review recent applications to processes involving few nucleons.
We investigate the roles of chiral three-nucleon force (3NF) in nucleon-nucleus elastic scattering, using the standard framework based on the Brueckner-Hartree-Fock method for nuclear matter and the $g$-matrix folding model for the nucleon-nucleus scattering. In nuclear matter, chiral 3NF at NNLO level (mainly the 2$π$-exchange diagram) makes the single particle potential less attractive for the singlet-even channel and more absorptive for the triplet channels. The single-particle potential calculated from chiral two-nucleon force (2NF) at N$^{3}$LO level is found to be close to that from Bonn…
The properties of nuclear matter are studied using state-of-the-art nucleon-nucleon forces up to fifth order in chiral effective field theory. The equations of state of symmetric nuclear matter and pure neutron matter are calculated in the framework of the Brueckner-Hartree-Fock theory. We discuss in detail the convergence pattern of the chiral expansion and the regulator dependence of the calculated equations of state and provide an estimation of the truncation uncertainty. For all employed values of the regulator, the fifth-order chiral two-nucleon potential is found to generate nuclear satu…
A density-dependent effective potential for the baryon-baryon interaction in the presence of the (hyper)nuclear medium is constructed, based on the leading (irreducible) three-baryon forces derived within SU(3) chiral effective field theory. We evaluate the contributions from three classes: contact terms, one-pion exchange and two-pion exchange. In the strangeness-zero sector we recover the known result for the in-medium nucleon-nucleon interaction. Explicit expressions for the Lambda-nucleon in-medium potential in (asymmetric) nuclear matter are presented. Our results are suitable for impleme…
We construct the leading order hyperon-nucleon potential in chiral effective field theory. We show that a good description of the available data is possible and discuss briefly further improvements of this scheme.
Present day chiral nucleon-nucleon potentials up to N3LO and three nucleon forces at N2LO are used to analyze nucleon-deuteron radiative capture at deuteron lab energies below E_d= 100 MeV. The differential cross section and the deuteron analyzing powers A_y(d) and A_{yy} are presented and compared to data. The theoretical predictions are obtained in the momentum-space Faddeev approach using the nuclear electromagnetic current operator with exchange currents introduced via the Siegert theorem. The chiral forces provide the same quality of data description as a combination of the two-nucleon AV…
We study the perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering for p- and d-waves within the effective field theory approach. The one pion exchange potential is fully iterated at the leading order in the expansion, a choice generating a consistent and well-defined power counting that we explore in detail. The results show that perturbative chiral two pion exchange reproduces the data up to a center-of-mass momentum of k_cm ~300 MeV at NNLO and that the effective field theory expansion convergences up to k_cm ~ 350 MeV.
In these lecture notes I discuss an algebraic model of baryons and pentaquarks, in particular a stringlike collective model is considered in which the radial excitations of baryons and pentaquarks are interpreted as rotations and vibrations of the strings. The algebraic structure of the model makes it possible to derive closed expressions for physical observables, such as masses and electromagnetic and strong couplings. The model is applied to the mass spectrum and magnetic moments of baryon resonances of the nucleon and delta families and to exotic baryons of the theta family. The ground pent…
We derive the long-range contributions to the tree-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion. We give both momentum and coordinate space representations.
We present the first study of pairing in nuclei including three-nucleon forces. We perform systematic calculations of the odd-even mass staggering generated using a microscopic pairing interaction at first order in chiral low-momentum interactions. Significant repulsive contributions from the leading chiral three-nucleon forces are found. Two- and three-nucleon interactions combined account for approximately 70% of the experimental pairing gaps, which leaves room for self-energy and induced interaction effects that are expected to be overall attractive in nuclei.
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…
The chiral soliton model including pi, rho, omega mesons is extended for the case when the scalar - isoscalar sigma meson has an anomalous dimension - d. The form factor of the sigma - nucleon interaction calculated and to be found not highly sensitive to the value of d.
We apply the relativistic chiral SU(3) Lagrangian density to kaon-nucleon scattering imposing constraints from the pion-nucleon s- and p-wave threshold parameters at chiral order $Q^2$. The s and u channel decouplet baryon exchange is included explicitly and is found to play a crucial role in understanding the empirical s- and p-wave nuclear kaon dynamics quantitatively.
We analyse the interplay between nucleon-nucleon potentials deduced from chiral perturbation theory and a coarse grained representation of the short distance interactions by delta-shells potentials below a certain cut-off distance. While we find that the number of parameters is greatly reduced when Chiral Two Pion Exchange contributions are included we also observe that discerning the necessity of improvements on the interaction requires a detailed analysis of all error sources. Our points are best illustrated by computing deuteron static properties as well as electromagnetic form factors afte…
We calculate hyperon-nucleon and hyperon-hyperon interactions at next-to-leading order in SU(3) baryon chiral perturbation theory extending earlier work by the Bonn-Juelich group. The constructed potentials in momentum space include all one- and two-meson exchange terms generated by the SU(3) chiral Lagrangian. Effects from intermediate decuplet baryons are considered as well. These chiral baryon-baryon potentials, together with appropriate contact terms, provide a new basis for systematic studies of hyperon-nucleon scattering and light hypernuclei.
We demonstrate a computational scheme which drastically decreases the required time to get theoretical predictions based on chiral two- and three-nucleon forces for observables in three-nucleon continuum. For a three-nucleon force containing N short-range terms all workload is reduced to solving N+1 Faddeev-type integral equations. That done, computation of observables for any combination of strengths of the contact terms is done in a flash. We demonstrate on example of the elastic nucleon-deuteron scattering observables the high precision of the proposed emulator and its capability to reprodu…
We study the nucleon-nucleon interaction in a chiral constituent quark model by using the resonating group method, convenient for treating the interaction between composite particles. The calculated phase shifts for the 3S1 and 1S0 channels show the presence of a strong repulsive core due to the combined effect of the quark interchange and the spin-flavour structure of the effective quark-quark interaction. Such a symmetry structure stems from the pseudoscalar meson exchange between the quarks and is a consequence of the spontaneous breaking of the chiral symmetry. We perform single and couple…
We have studied neutron-rich carbon isotopes in terms of the shell model employing a realistic effective hamiltonian derived from the chiral N3LOW nucleon-nucleon potential. The single-particle energies and effective two-body interaction have been both determined within the framework of the time-dependent degenerate linked-diagram perturbation theory. The calculated results are in very good agreement with the available experimental data, providing a sound description of this isotopic chain toward the neutron dripline. The correct location of the dripline is reproduced.
We study perturbativeness of chiral nuclear forces in the $^3P_0$ channel. In previous works, the focus has been on one-pion exchange, and the applicable window of perturbative pion exchanges has been shown to span from threshold to the center-of-mass momentum $k \simeq$ 180 MeV. We will examine, instead, whether cancellation of short and long-range parts can sufficiently soften the $^3P_0$ chiral force to make it more amenable to perturbation theory. The result is encouraging, as the combined $^3P_0$ force is shown to be perturbative up to $k \simeq$ 280 MeV, covering many nuclear-structure c…
The central two-pion exchange NN potential at large distances is studied in the framework of relativistic chiral symmetry and related directly to the nucleon scalar form factor, which describes the mass density of its pion cloud. This relationship is well supported by phenomenology and allows the dependence of the asymptotic potential on the nucleon mass to be assessed. Results in the heavy baryon limit are about 25% larger than those corresponding to the empirical nucleon mass in the region of physical interest. This indicates that it is very important to keep this mass finite in precise desc…
We compute various nucleon polarizabilities in chiral perturbation theory implementing the $Δ$-full ($Δ$-less) approach up to order $ε^3 + q^4$ ($q^4$) in the small-scale (chiral) expansion. The calculation is carried out using the covariant formulation of $χ$PT by utilizing the extended on-mass shell renormalization scheme. Except for the spin-independent dipole polarizabilities used to fix the values of certain low-energy constants, our results for the nucleon polarizabilities are pure predictions. We compare our calculations with available experimental data and other theoretical results. Th…
We present an exploratory study consisting in the formulation of a relativistic quantum mechanics to describe the few-nucleon system at low energy, starting from the quantum field theoretical chiral Lagrangian involving pions and nucleons. To this aim we construct a Bakamjian-Thomas mass operator and perform a truncation of the Fock space which respects at each stage the relativistic covariance. Such truncation is justified, at sufficiently low energy, in the framework of a systematic chiral expansion. As an illustration we discuss the bound state observables and low-energy phaseshifts of the …
Kaon production cross sections in nucleon-nucleon, nucleon-delta and delta-delta interactions are studied in a boson exchange model. For the latter two interactions, the exchanged pion can be on-mass shell, only contributions due to a virtual pion are included via the Peierls method by taking into account the finite delta width. With these cross sections and also those for pion-baryon interactions, subthreshold kaon production from heavy ion collisions is studied in the relativistic transport model.
In a one-pion plus one-kaon exchange model, we calculate the kaon production cross sections in nucleon-nucleon, nucleon-delta and delta-delta interactions. We find that this model describes reasonably well the experimental data on kaon production in the proton-proton interaction. Near the kaon production threshold, the cross section obtained from this model is smaller than that from the linear parameterization of Randrup and Ko. For kaon production cross sections from the nucleon-delta and delta-delta interactions, the cross sections are singular in free space, so we calculate them in a nuclea…
I report on recent progress in the description of baryon-baryon systems within chiral effective field theory. In particular, I discuss results for the strangeness S=-3 to -4 baryon-baryon systems, obtained to leading order.
The main progress in the field of nucleon-nucleon (NN) potentials, which we have seen in recent years, is the construction of some very quantitative (high-quality/high-precision) NN potentials. These potentials will serve as excellent input for microscopic nuclear structure calculations and will allow for a systematic investigation of off-shell effects. After this enormous quantitative work, it is now time to re-think the NN problem in fundamental terms. We need a derivation of the nuclear force which observes Lorentz invariance and the symmetries of QCD.
Long-range contributions to the three-nucleon force that have been recently worked out in chiral effective field theory at next-to-next-to-next-to-leading order are for the first time included in the triton and the doublet nucleon-deuteron scattering length calculations. The strengths of the two short-range terms available at this order in the chiral expansion are determined from the triton binding energy and the neutron-deuteron doublet scattering length. The structure of the resulting three-nucleon force is explored and effects for the two-nucleon correlation function in the triton are inves…
We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the "bare" chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding …
We apply improved nucleon-nucleon potentials up to fifth order in chiral effective field theory, along with a new analysis of the theoretical truncation errors, to study nucleon-deuteron (Nd) scattering and selected low-energy observables in 3H, 4He, and 6Li. Calculations beyond second order differ from experiment well outside the range of quantified uncertainties, providing truly unambiguous evidence for missing three-nucleon forces within the employed framework. The sizes of the required three-nucleon force contributions agree well with expectations based on Weinberg's power counting. We ide…
We estimate four-nucleon force effects between different 4He wave functions by calculating the expectation values of four-nucleon potentials which were recently derived within the framework of chiral effective field theory. We find that the four-nucleon force is attractive for the wave functions with a totally symmetric momentum part. The additional binding energy provided by the long-ranged part of the four-nucleon force is of the order of a few hundred keV.
We discuss the application of the chiral N3LO forces to three-nucleon reactions and point to the challenges which will have to be addressed. Present approaches to solve three-nucleon Faddeev equations are based on a partial-wave decomposition. A rapid increase of the number of terms contributing to the chiral three-nucleon force when increasing the order of the chiral expansion from N2LO to N3LO forced us to develop a fast and effective method of automatized partial wave decomposition. At low energies of the incoming nucleon below about 20MeV, where only a limited number of partial waves is re…
We present a model of baryonic matter which contains free constituent quarks in addition to bound constituent quarks in nucleons. In addition to the common linear sigma-model we include the exchange of vector-mesons. The percentage of free quarks increases with baryon density but the nucleons resist a restoration of chiral symmetry.
We present an accurate nucleon-nucleon (NN) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three and contact terms (which represent the short range force) up to order four. Within this framework, the NN phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral NN potential may serve as a reliable starting point for testing the chiral effective field theory approach in exact few-nucleon and microscopic nuclear many-body calculations.
We discuss the masses of the ground state baryon octet and the nucleon sigma terms in the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. In order to obtain a consistent power counting for renormalized diagrams the extended on-mass-shell renormalization scheme is applied.
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
Owing to the Kubo relation, the shear viscosities of pionic and nucleonic components have been evaluated from their corresponding retarded correlators of viscous stress tensor in the static limit, which become non-divergent only for the non-zero thermal widths of the constituent particles. In the real-time thermal field theory, the pion and nucleon thermal widths have respectively been obtained from the pion self-energy for different meson, baryon loops and the nucleon self-energy for different pion-baryon loops. We have found a non-monotonic momentum distributions of pion and nucleon thermal …
The effects of the spin-orbit and the tensor parts of the instanton-induced interaction on the excited nonstrange baryons up to $N$=2 and on the two-nucleon systems are investigated. The spin-orbit force from the instanton-induced interaction cancels most of that from the one-gluon exchange in the excited baryons while the spin-orbit force in the nucleon systems remains strong after the inclusion of the instanton-induced interaction. The model including the spin-orbit and the tensor terms of the instanton-induced interaction as well as the one-gluon exchange is found to reproduce successfully …
We present an accurate nucleon-nucleon ($NN$) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three. We show that a quantitative fit of the $NN$ $D$-wave phase shifts requires contact terms (which represent the short range force) of order four. Within this framework, the $NN$ phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral $NN$ potential represents a reliable starting point for testing the chiral effective field theory approach in exact few…
