Three-body Forces Research Articles

Realistic shell-model calculations for p -shell nuclei including contributions of a chiral three-body force

In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or two valence nucleons and those belonging to the core. For nuclei with more than two valence particles, both induced - turned on by the two-body potential - and genuine three-body forces come into play. Since it is difficult to perform shell-model calculations with three-body forces, these contributions are estimated for the ground-state energy only. In order to establish the reliability of our approximations, we focus attention on nuclei belonging to the p shell, aiming to benchmark our calculations against those performed with the ab initio no-core shell-model. The obtained results are satisfactory, and pave the way to the application of our approach to nuclear systems with heavier masses.

In-medium enhancement of the modified Urca neutrino reaction rates

We calculate modified Urca neutrino emission rates in the dense nuclear matter in neutron star cores. We find that these rates are strongly enhanced in the beta-stable matter in regions of the core close to the direct Urca process threshold. This enhancement can be tracked to the use of the in-medium nucleon spectrum in the virtual nucleon propagator. We describe the in-medium nucleon scattering in the non-relativistic Bruckner–Hartree–Fock framework taking into account two-body as well as the effective three-body forces, although the proposed enhancement does not rely on a particular way of the nucleon interaction treatment. Finally we suggest a simple approximate expression for the emissivity of the neutron branch of the modified Urca process that can be used in the neutron stars cooling simulations with any nucleon equation of state of dense matter.

Many-body correlations in shell model effective interactions derived by ab initio methods and the Vlow-k approach**Supported by National Natural Science Foundation of China (11505056, U1732138, 11605054, 11790325, 11305108, 11575290, 11675148, 11747312, 11775316) and the Outstanding Young Talent Research Fund of Zhengzhou University (1521317002)

We investigate many-body correlations caused by two- and three-body (2-, 3bd) forces. Shell-model effective interactions derived from ab initio methods (coupled-cluster method, no-core shell model) are adopted. Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence. We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.

Temperature dependence of thermodynamic properties of MoS2 monolayer and single-wall nanotubes: Application of the developed three-body force field

MoS2 nanostructures, especially mono-, multilayer nanothin films as well as single- and multiwall nanotubes are rather interesting popular objects in nanomaterials chemistry. The thermodynamic properties of inorganic nanotubes, and the temperature dependence of their properties can be efficiently investigated by first-principles and molecular mechanics methods in the framework of harmonic approximation. At the same time, only thin single-wall nanotubes are available for the first-principles calculations. The classical mechanics is suitable to simulate very large atomic systems and their phonon frequencies, but developing sufficiently accurate force field is rather tedious work. Herein, we report the force field fitted to the experimental and first-principles data on the structure of 2H- and 3RMoS2 polytypes of bulk crystal, structure of monolayer and several bilayers, vibrational frequencies of 2HMoS2 bulk and monolayer, relative energetic stability of polytypes experimental and first-principles data, elastic constants, strain energy of a (12, 12) MoS2 nanotube. The thermodynamic functions and their temperature dependence for the armchair and zigzag nanotubes are calculated within the formalism of molecular mechanics using elaborated interatomic potential. The results of molecular mechanics and first-principles method application to the thinnest nanotubes are compared.

Role of nuclear correlations and kinematic effects on neutrino emission from the modified Urca processes

The neutrino emissivity from the proton branch of the modified Urca process is calculated. Angular integrations in momentum space are performed numerically without recourse to widely used, but unjustified in this specific case, approximations. To deal with nuclear correlation effects, the independent-pair approximation for nucleon quasiparticles is assumed. The realistic nuclear correlation effects are extracted from a modified extended version of the lowest-order constrained variational method in asymmetric nuclear matter in $\ensuremath{\beta}$ equilibrium with electrons and muons that allows for three-body nucleon interactions and fits all semiempirical saturation parameters of nuclear matter quite well. Two-body nucleon interaction is modeled by a realistic Argonne AV18 potential and the three-body potential used is a phenomenological Urbana UIX, generalizing parametrization of its component strengths in a manner suitable for application in asymmetric nuclear matter. Limiting to the two-body forces only, we find that, at fixed temperature, neutrino emissivity is a (weakly) decreasing function of density. This is also the case for the neutron branch of the modified Urca process analyzed by us in a recent paper. Inclusion of the modified three-body force effects changes this behavior. Quantitatively the value of the emissivity at each density increases and qualitatively the overall effect of the modified three-body force addition is such that dependence on density becomes weak in a density range from ${n}_{0}$ to $3.5{n}_{0}$. An updated version of neutron branch results obtained using our modified three-body force model is also presented. This is done using exact treatment of the angular integrations of nuclear transition rate in momentum space.

The role of the elemental nature of A = 3 nuclei in neutron-rich nuclei

The idea of treating the trinucleon systems as elementary entities in the elementary particle model (EPM) as an Effective Field Theory has been a success in explaining the weak charge-changing processes in nuclei. The EPM results are found to be as good as those obtained from nuclear microscopic models using two-and three-body forces. We extend this concept to investigate the validity of the elemental nature of [Formula: see text] nuclei through studies of nuclear structure of neutron-rich nuclei. By treating neutron-rich nuclei as primarily made up of tritons as its building blocks, we extract one- and two-triton separation energies of these nuclei. Calculations have been performed here within relativistic mean field (RMF) models with latest interactions. Clear evidence arises of a new shell structure with well-defined predictions of new magic nuclei. These unique predictions have been consolidated by standard one- and two-neutron separation energy calculations. The binding energy per nucleon plots of these nuclei also confirm these predictions. We make unambiguous prediction of six magic nuclei: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

Quantum Anomaly and Thermodynamics of One-Dimensional Fermions with Three-Body Interactions.

We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.

Tensor Fermi liquid parameters in nuclear matter from chiral effective field theory

We compute from chiral two- and three-body forces the complete quasiparticle interaction in symmetric nuclear matter up to twice nuclear matter saturation density. Second-order perturbative contributions that account for Pauli-blocking and medium polarization are included, allowing for an exploration of the full set of central and noncentral operator structures permitted by symmetries and the long-wavelength limit. At the Hartree-Fock level, the next-to-next-to-leading order three-nucleon force contributes to all noncentral interactions, and their strengths grow approximately linearly with the nucleon density up that of saturated nuclear matter. Three-body forces are shown to enhance the already strong proton-neutron effective tensor interaction, while the corresponding like-particle tensor force remains small. We also find a large isovector cross-vector interaction but small center-of-mass tensor interactions in the isoscalar and isovector channels. The convergence of the expansion of the noncentral quasiparticle interaction in Landau parameters and Legendre polynomials is studied in detail.

Chiral NNLOsat descriptions of nuclear multipole resonances within the random-phase approximation

We study nuclear multipole resonances in the framework of the random phase approximation using the chiral potential NNLO$_{\text{sat}}$. This potential includes two- and three-body terms that has been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main foci have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, $^4$He, $^{16,22,24}$O, and $^{40,48}$Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential $V_{\text{low-}k}$, based on the N$^3$LO two-body potential by Entem and Machleidt [Phys. Rev. \textbf{C68}, 041001 (2011)]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLO$_{\text{sat}}$ can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the $V_{\text{low-}k}$ potential that simultaneously describe the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich $^{22,24}$O show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that $^{22}$O and $^{24}$O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. The first component of this functional is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. A second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. We obtain a set of microscopically-constrained functionals for local chiral potentials from leading-order up to next-to-next-to-leading order with and without three-body forces and contributions from $\Delta$ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei and the fission barrier of $^{240}$Pu. Quantitatively, they perform noticeable better than the more phenomenological Skyrme functionals. The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies. This result is especially promising since all the fits have been performed at the single reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction have not been taken into account yet.

Auxiliary field diffusion Monte Carlo calculations of light and medium-mass nuclei with local chiral interactions

Quantum Monte Carlo methods have recently been employed to study properties of nuclei and infinite matter using local chiral effective field theory interactions. In this work, we present a detailed description of the auxiliary field diffusion Monte Carlo algorithm for nuclei in combination with local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We show results for the binding energy, charge radius, charge form factor, and Coulomb sum rule in nuclei with $3\le A\le16$. Particular attention is devoted to the effect of different operator structures in the three-body force for different cutoffs. The outcomes suggest that local chiral interactions fit to few-body observables give a very good description of the ground-state properties of nuclei up to $^{16}$O, with the exception of one fit for the softer cutoff which predicts overbinding in larger nuclei.

Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length

We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in $^{39}$K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $-8$ and $-10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.

Simulating The Residual Three-body Force in a Small System

The effect of residual three-body force on the small system was investigated in this paper. A one-level and two-level system were chosen as the model to study the feature of three-body force due to their simplicity and lower symmetry. In both systems, we found a consistent result, that the inclusion of three-body force will enhance and accelerate the pairing condensation, which is shown by a higher pairing gap and lower energy as compared to the system with only two-body pairing force. Some interesting results on the behavior of the residual three-body force were also presented here.

Proton-4He elastic scattering at 350–1728MeV energies: Three-body force effect

An approach for the three-body force effect is used to study p-[Formula: see text] elastic scattering at energies 350–1728[Formula: see text]MeV. The multiple scattering theory of Glauber and the optical limit approximation are used in calculations of elastic scattering differential cross-section at 350, 600, 800, 1000 and 1728[Formula: see text]MeV. The inclusion of 2[Formula: see text]-exchange three-nucleon force improves the agreement with the experimental data for both approximations. The results of optical limit approximation without three-nucleon force effect are clearly smaller than the results of multiple scattering theory for [Formula: see text] due to the absence of multiple scattering terms in the first. However, with inclusion of three-nucleon force, the results of both approximations are approximately similar.

Potential energy surfaces of the low-lying electronic states of the Li + LiCs system

Ab initio quantum chemistry calculations are performed for the mixed alkali triatomic system. Global minima of the ground and first excited doublet states of the trimer are found and Born-Oppenheimer potential energy surfaces of the Li atom interacting with the LiCs molecule were calculated for these states. The lithium atom is placed at various distances and bond angles from the lithium-caesium dimer. Three-body nonadditive forces of the Li2Cs molecule in the global minimum are investigated. Dimer-atom interactions are found to be strongly attractive and may be important in the experiments, particularly involving cold alkali polar dimers.

Three-body correlations and conditional forces in suspensions of active hard disks.

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to the direction of propulsion and the positions of the surrounding particles. We further relate our theory to the effective swimming speed of the active disks, which is relevant for the physics of MIPS. To test and validate our theory, we additionally run particle-resolved computer simulations, for which we explicitly calculate the three-body forces. In this context, we discuss the modeling of active Brownian swimmers with nearly hard interaction potentials. We find very good agreement between our simulations and numerical solutions of our theory, especially for the nonequilibrium pair-distribution function. For our analytical results, we carefully discuss their range of validity in the context of the different levels of approximation we applied. This discussion allows us to study the individual contribution of particles to three-body forces and to the emerging structure. Thus, our work sheds light on the collective behavior, provides the basis for further studies of correlations in active suspensions, and makes a step towards an emerging liquid state theory.

Correction: Solvation of Li+ by argon: how important are three-body forces?

Correction for 'Solvation of Li+ by argon: how important are three-body forces?' by Frederico V. Prudente et al., Phys. Chem. Chem. Phys., 2017, 19, 25707-25716.

Neutron star properties from optimised chiral nuclear interactions

AbstractWe adopt two- and three-body nuclear forces derived at the next-to-next-to-leading-order in the framework of effective chiral perturbation theory to calculate the equation of state of β-stable neutron star matter using the Brueckner–Hartree–Fock many-body approach. We use the recent optimized chiral two-body nuclear interaction at next-to-next-to-leading-order derived by Ekström et al. and two different parametrizations of the three-body next-to-next-to-leading-order interaction: the first one is fixed to reproduce the saturation point of symmetric nuclear matter while the second one is fixed to reproduce the binding energies of light atomic nuclei. We show that in the second case the properties of nuclear matter are not well determined whereas in the first case various empirical nuclear matter properties around the saturation density are well reproduced. We finally calculate various neutron star properties and in particular the mass-radius and mass-central density relations. We find that the adopted interactions based on a fully microscopic framework, are able to provide an equation of state which is consistent with the present data of measured neutron star masses.

Extracting observables from lattice data in the three-particle sector

The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.

Hubbard-Stratonovich-like Transformations for Few-Body Interactions

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the an-alytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three-and more-body inter-actions, is presented.