Towards high-order calculations of three-nucleon scattering in chiral effective field theory
E. Epelbaum, J. Golak, K. Hebeler, H. Kamada, H. Krebs, U. -G. Meißner, A. Nogga, P. Reinert, R. Skibiński, K. Topolnicki, Y. Volkotrub, H. Witała
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14 pages, 12 figures, 1 table; contribution to the EPJA topical issue on "The tower of effective (field) theories and the emergence of nuclear phenomena"
We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon-deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon-deuteron scattering data below pion production threshold will require the theory to be pushed to fifth chiral order. This conclusion is substantiated by an exploratory study of selected short-range contributions to the three-nucleon force at that order, which, as expected, are found to have significant effects on polarization observables at intermediate and high energies. We also outline the challenges that will need to be addressed in order to push the chiral expansion of three-nucleon scattering observables to higher orders.
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 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…
We use proton-nucleus reaction data at intermediate energies to test the emerging new generation of chiral nucleon-nucleon (NN) potentials. Predictions from a high quality one-boson-exchange (OBE) force are used for comparison and evaluation. Both the chiral and OBE models fit NN phase shifts accurately, and the differences between the two forces for proton-induced reactions are small. A comparison to a chiral model with a less accurate NN description sets the scale for the ability of such models to work for nuclear reactions.
I discuss the conditions under which the application of chiral perturbation theory to the NN potential gives reliable results for NN scattering phase shifts. ChiPT also yields a convergent expansion for the deuteron charge operator. For cutoffs < 1 GeV, this produces precise predictions for deuterium's quadrupole and charge form factors in the range Q^2 < 0.25 GeV^2.
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 NN data below 290 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 reliable NN potential derived from chiral effective Lagr…
We study the nonperturbative renormalization of the nucleon-nucleon (NN) interaction at next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) of chiral effective field theory. A systematic variation of the cutoff parameter is performed for values below the chiral symmetry breaking scale of about 1 GeV. The accuracy of the predictions is determined by calculating the $χ^2$ for the reproduction of the NN data for energy intervals below pion-production threshold. At NLO, the NN data are described well up to about 100 MeV laboratory energy and, at NNLO, up to about 200 MeV---with, e…
In the past decades, it has been shown that the three-body force is necessary for a fully microscopic understanding of nuclear many-body systems, and thus efficient schemes for storing and utilizing three-body matrix elements have been developed. However, three-body matrix elements still demand a lot of memory and/or storage and it readily exceeds the limitation of the state-of-the-art supercomputers. We explore the possibility of mimicking the effects of three-body forces in medium-mass region, especially lower $pf$ shell, by density-dependent effective nucleon-nucleon interactions combining …
We present the dominant two- and three-pion-exchange contributions to the nucleon-nucleon interaction at sixth order (next-to-next-to-next-to-next-to-next-to-leading order, N5LO) of chiral perturbation theory. Phase shifts with orbital angular momentum L>=4 are given parameter free at this order and allow for a systematic investigation of the convergence of the chiral expansion. The N5LO contribution is prevailingly repulsive and considerably smaller than the N4LO one, thus, establishing the desired trend towards convergence. Using low-energy constants that were extracted from an analysis of p…
I discuss our recent work on Green's function Monte Carlo (GFMC) calculations of light nuclei using local nucleon-nucleon interactions derived from chiral effective field theory (EFT) up to next-to-next-to-leading order (N$^2$LO). I present the natural extension of this work to include the consistent three-nucleon (3N) forces at the same order in the chiral expansion. I discuss our choice of observables to fit the two low-energy constants which enter in the 3N sector at N$^2$LO and present some results for light nuclei.
We analyze the results by chiral NN models for the two-nucleon system and calculate the predictions for the nucleon vector analyzing power of elastic nucleon-deuteron (Nd) scattering, Ay, by these models. Our conclusion is that a QUANTITATIVE chiral two-nucleon potential does not resolve the Nd Ay puzzle (when only two-body forces are included).
The standard way to demonstrate the relevance of chiral symmetry for the NN interaction is to consider higher partial waves of NN scattering which are controlled entirely by chiral pion-exchanges (since contacts vanish). However, in applications of NN-potentials to nuclear structure and reactions, the lower partial waves are the important ones, making the largest contributions. Lower partial waves are sensitive to the short-range potential, and so, when the short-range contacts were to dominate over the chiral pion-contributions in lower partial waves, then the predictions from "chiral potenti…
Recent chiral EFT calculations of nucleon polarizabilities reveal a problem in the current empirical determination of proton's electromagnetic polarizabilities. We also report on the progress in the empirical determination of the $Δ$(1232)-resonance magnetic moment in the process of $γp \to p π^0 γ'$ measured at MAMI.
We present a nucleon-nucleon potential at fifth order in chiral effective field theory. We find a substantial improvement in the description of nucleon-nucleon phase shifts as compared to the fourth-order results of Ref. [E. Epelbaum, H. Krebs, U.-G. Meißner, arXiv:1412.0142 [nucl-th]]. This provides clear evidence of the corresponding two-pion exchange contributions with all low-energy constants being determined from pion-nucleon scattering. The fifth-order corrections to nucleon-nucleon observables appear to be of a natural size which confirms the good convergence of the chiral expansion for…
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…
We discuss charge symmetry and charge independence breaking in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct a two-nucleon potential with bound and scattering states generated by means of a properly regularized Lippmann-Schwinger equation. We systematically introduce strong isospin-violating and electromagnetic operators in the theory. We use standard procedures to treat the Coulomb potential between two protons in momentum space. We present results for phase shifts in the proton-proton, the neutron-proton and the neu…
We review the recent baryon chiral perturbation theory results for the nucleon polarisabilities that describe the different regimes of nucleon Compton scattering --- real, virtual, and doubly virtual. We stress the importance of the empirical verification of the theory in the context of the calculation of the inelastic nucleon structure corrections, such as the two-photon exchange contributions. We also discuss the recently obtained constraints that relate the different regimes of nucleon Compton scattering and can provide additional information on the nucleon structure.
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.
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 match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting sche…
We calculate the form factors of the electromagnetic nucleon-to-$Δ$-resonance transition to third chiral order in manifestly Lorentz-invariant chiral effective field theory. For the purpose of generating a systematic power counting, the complex-mass scheme is applied in combination with the small-scale expansion. We fit the results to available empirical data.
We present the two- and three-pion exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N4LO, fifth order) of chiral effective field theory, and calculate nucleon-nucleon scattering in peripheral partial waves with L>=3 using low-energy constants that were extracted from pi-N analysis at fourth order. While the net three-pion exchange contribution is moderate, the two-pion exchanges turn out to be sizeable and prevailingly repulsive, thus, compensating the excessive attraction characteristic for NNLO and N3LO. As a result, the …
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.
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 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 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…
We report on the construction of an accurate relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading (NNLO) order. We compare the so-obtained neutron-proton phaseshifts with the next-to-next-to-next-to-leading order (N$^3$LO) nonrelativistic ones and we show that up to $T_\mathrm{lab.}=200$ MeV, the relativistic chiral nuclear force can describe the PWA93 phaseshifts and inelasticities as well as its N$^3$LO nonrelativistic counterparts. As a result, the relativistic chiral nuclear force can be readily used for relativistic ab initio nuclear structure, reaction, as we…
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 calculate the properties of isospin-asymmetric nuclear matter based on chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions. To this end, we develop an improved normal-ordering framework that allows to include general 3N interactions starting from a plane-wave partial-wave-decomposed form. We present results for the energy per particle for general isospin asymmetries based on a set of different Hamiltonians, study their saturation properties, the incompressibility, symmetry energy, and also provide an analytic parametrization for the energy per particle as a function of density a…
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…
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.
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…
I give a summary of recent results on nucleon polarizabilities, with emphasis on chiral perturbation theory. The predictive calculations of Compton scattering off the nucleon are compared to recent empirical determinations and lattice QCD calculations of the polarizabilities, thereby testing chiral perturbation theory in the single-baryon sector.
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…
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 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…
We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the $np$ phase shifts up to $T_\mathrm{lab}=200$ MeV and even higher can be achieved with a $\tildeχ^2/\mathrm{d.o.f.}$ less than 1. Both the next-to-leading order results and the next-to-next-to-leading order results describe the phase shifts equally well up to $T_\mathrm{lab}=200$ MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provi…
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 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 …
We present a new chiral expansion scheme for the nucleon-nucleon scattering amplitude which preserves unitarity exactly. Our effective field theory builds on the power counting rules for 2-nucleon reducible diagrams proposed in \cite{lutz}. We evaluate the leading order terms of the isospin one scattering amplitude and elaborate in detail on the $^1S_0$ phase shift. Our chiral description of the $^1S_0$-phase shift does compete in quality with modern phenomenological nucleon-nucleon potentials. We describe elastic and inelastic scattering quantitatively up to laboratory energies of $E_{\rm lab…
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…
