Two-body Forces Research Articles

Λ6He (1−, 2−) spin doublet in a Λ + n + α cluster model

The spin singlet and spin triplet states of the helium-6-lambda hypernucleus are studied in configuration space as a three-body problem, using the hyperspherical method. This hypernucleus is treated as a Λ + n + α cluster model. Since the α particle core has a spin of 0, this is an ideal hypernucleus from which to understand spin dependence in hyperon-nucleon potentials. In this paper, the hyperon-nucleon potential considered is the GLM-YN0 Λ-n potential, which is a simulation of the NSC97f potential obtained through inverse scattering theory. Due to violations of the cluster structure, two-body potentials underbind the helium-6-lambda hypernucleus. This issue is addressed by including a three-body force to complement these two-body forces. A three-body force, whose strength is spin dependent, is used to guide predictions of the spin triplet state of helium-6-lambda which is not yet known experimentally.

Discovering dynamic laws from observations: The case of self-propelled, interacting colloids.

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equationof motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Saturation of nuclear matter in the relativistic Brueckner-Hatree-Fock approach with a leading order covariant chiral nuclear force

Nuclear saturation is a crucial feature in nuclear physics that plays a fundamental role in understanding various nuclear phenomena, ranging from properties of finite nuclei to those of neutron stars. However, a proper description of nuclear saturation is highly nontrivial in modern nonrelativistic ab initio studies because of the elusive three-body forces. In this letter, we calculate the equation of state for nuclear matter in the relativistic Brueckner-Hartree-Fock (RBHF) framework with the leading order covariant chiral nuclear force. We show that a simultaneous description of the nucleon-nucleon scattering data and the saturation of the symmetric nuclear matter can be achieved. In this regard, the relativistic effects nicely explain the saturation of nuclear matter. As a result, the present study based on the covariant chiral nuclear force shows that in the RBHF framework, one can achieve saturation with a leading order covariant chiral nuclear force with only two-body forces, in contrast to the vast majorities of studies in the non-relativistic framework, where the next-to-next-to-leading order two-body and three-body chiral forces are needed. This study sets the foundation for studying nuclear saturation with the covariant chiral force in the RBHF framework, which allows for a systematic understanding of one of the key features of nuclear physics more microscopically.

Correlation of the hyperon potential stiffness with hyperon constituents in neutron stars and heavy-ion collisions

The breaking of SU(6) symmetry to a more general flavor SU(3) symmetry could serve as a potential explanation for the “hyperon puzzle” of neutron stars by adjusting the hyperon potentials. Specifically, when the soft relativistic mean-field (RMF) Λ hyperon potentials fall within the domains of chiral SU(3) interactions NLO13 with two-body forces, the maximum mass of neutron stars is expected to be lower than 2.0 M⊙, whereas it can exceed 2.0M⊙ if the RMF Λ hyperon potentials are sufficiently stiff to be consistent with those from chiral SU(3) interactions NLO13 with three-body forces. In our investigation involving these two types of Λ hyperon potentials, we explore how the hyperon yields and flows are affected in heavy-ion collisions. We find that the inclusion of hyperon potentials results in better agreement of the Λ directed flows with data but without clear differentiation in the stiffness of the hyperon potentials. Similarly negligent is the disparity in the rapidity distributions of the Λ collective flows predicted by the stiff and soft hyperon potentials. In contrast, the Λ collective flows beyond the central rapidity region turn out to be sensitive to the stiffness of the RMF equation of state (EOS) with the preference of a soft RMF EOS to a stiff one. Notably, the transverse momentum distributions of Λ hyperon production are sensitive to both the stiffness of the RMF EOS and Λ hyperon potential at high transverse momenta.

Glass transition temperatures of binary oxides from ab initio simulations

The glass transition temperatures of common binary oxides, including those with low glass-forming ability, are estimated using pair distribution functions (PDFs) from ab initio molecular dynamics simulations. The computed glass transition temperatures for good glass-formers such as silica (SiO2), germania (GeO2), and boron oxide (B2O3) are in agreement with measured values. These calculations are then used to compute the glass transition temperatures of alumina (Al2O3), tantala (Ta2O5), and telluria (TeO2), which are known to exhibit low glass-forming ability. For Al2O3 and Ta2O5, we also compute the simulated caloric curve from molecular dynamics simulations using two-body empirical force fields. Finally, we discuss the possibility of extracting the glass transition temperature by measuring the thermal broadening of the PDFs from scattering measurements.

Coexistence of quartets and pairs in even-even N > Z nuclei

We analyse the structure of the ground states of even-even N>Z nuclei with nucleons moving in the same major shell and interacting via realistic two-body forces of shell model type. We describe the ground states of these nuclei as a product of two terms, one representing the proton-neutron subsystem with an equal number of protons and neutrons and the other one associated with the excess neutrons. The first term is expressed by means of quartets made of two neutrons and two protons coupled to total isospin T=0. The second term is represented as a neutron pair condensate. Quartets and pairs are constructed variationally. The accuracy of this approximation is discussed for nuclei with valence nucleons in the sd and pf major shells.

Amorphous Zirconia-doped Tantala modeling and simulations using explicit multi-element spectral neighbor analysis machine learning potentials (EME-SNAP)

We model amorphous Zirconia-doped Tantala with machine learning interactomc potentials based on explicit multielement spectral neighbor analysis (EME-SNAP). These atomic structure models can reproduce partial radial distribution functions obtained from first-principles calculations and elastic moduli found from experimental measurements. The two-body pair forces calculated from EME-SNAP further affirm that the potentials capture the atomic interactions well. Molecular dynamics simulations of simulated annealing with EME-SNAP show that the final density of the amorphous models depends on the thermal history even when the annealing rate is kept constant, which captures experimental observations of history-dependent densities. Mechanical spectroscopy is also simulated using both Morse-Beest-Kramer-Santen pair potentials and EME-SNAP. The success in applying the EME-SNAP to amorphous Zirconia-doped Tantala pushes the boundaries of simulation accuracy and system size and enables better and more realistic atomistic modeling for amorphous systems. There are still some limitations in applying the potentials generated in this paper. They are only optimized for trained amorphous phases; high-temperature stability and transferability need to be further investigated.

Local position-space two-nucleon potentials from leading to fourth order of chiral effective field theory

We present local, position-space chiral NN potentials through four orders of chiral effective field theory ranging from leading order (LO) to next-to-next-to-next-to-leading order (N3LO, fourth order) of the Delta-less version of the theory. The long-range parts of these potentials are fixed by the very accurate pi-N LECs as determined in the Roy-Steiner equations analysis. At the highest order (N3LO), the NN data below 190 MeV laboratory energy are reproduced with the respectable chi^2/datum of 1.45. A comparison of the N3LO potential with the phenomenological Argonne v_18 (AV18) potential reveals substantial agreement between the two potentials in the intermediate range ruled by chiral symmetry, thus, providing a chiral underpinning for the phenomenological AV18 potential. Our chiral NN potentials may serve as a solid basis for systematic ab initio calculations of nuclear structure and reactions that allow for a comprehensive error analysis. In particular, the order by order development of the potentials will make possible a reliable determination of the truncation error at each order. Our new family of local position-space potentials differs from existing potentials of this kind by a weaker tensor force as reflected in relatively low D-state probabilities of the deuteron (P_D less or equal 4.0% for our N3LO potentials) and predictions for the triton binding energy above 8.00 MeV (from two-body forces alone). As a consequence, our potentials may lead to different predictions when applied to light and intermediate-mass nuclei in ab initio calculations and, potentially, help solve some of the outstanding problems in microscopic nuclear structure.

Extending the VDPC+BCS formalism by including three-body forces* *Supported by the National Natural Science Foundation of China (11405109)

Recently, Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian. The present study extends this formalism by including three-body forces. The result is the same as the so-called variation after particle-number projection in the BCS case, but now, the particle number is always conserved, and the time-consuming projection is avoided. Specifically, analytical formulas of the average energy are derived along with its gradient for a three-body Hamiltonian in terms of the coherent-pair structure. Gradient vanishment is required to obtain analytical expressions for the pair structure at the energy minimum. The new algorithm iterates on these pair-structure expressions to minimize energy for a three-body Hamiltonian. The new code is numerically demonstrated when applied to realistic two-body forces and random three-body forces in large model spaces. The average energy can be minimized to practically any arbitrary precision.

Monopole effects and spin-trap structures in neutron-rich Te isotopes

A new Hamiltonian is established for the particle nuclei near $^{132}\mathrm{Sn}$ by including both core excitations and neutron intruder orbit ${i}_{13/2}$. In this Hamiltonian, the two-body force strengths and monopole terms are determined by the data in $^{133}\mathrm{Sn}$, $^{134}\mathrm{Sn}$, $^{133}\mathrm{Sb},^{134}\mathrm{Sb}$, $^{134}\mathrm{Te}$, $^{135}\mathrm{Te}$, and $^{135}\mathrm{I}$. According to this interaction, the level spectra and electromagnetic transitions are described well in the model space including six proton orbits ($0{g}_{9/2},0{g}_{7/2},1{d}_{5/2},1{d}_{3/2},2{s}_{1/2},0{h}_{11/2}$), and eight neutron orbits ($1{d}_{3/2},0{h}_{11/2},1{f}_{7/2},2{p}_{3/2},2{p}_{1/2},0{h}_{9/2},1{f}_{5/2},0{i}_{13/2}$). This work shows that the neutron intruder orbit ${i}_{13/2}$ is necessary to describe particle nuclei near $^{132}\mathrm{Sn}$. The configuration including orbit ${i}_{13/2}$ forms a spin-trap structure and wins the competition of the lowest states at level $13/{2}^{+}$ in $^{137,139}\mathrm{Te}$. Spin-trap structures are also existed in levels ${2}^{\ensuremath{-}}$ and ${9}^{\ensuremath{-}}$ in $^{136,138}\mathrm{Te}$. Due to the decay block by spin-trap structures, these states are predicted as good isomers.

To Shell Model, or Not to Shell Model, That Is the Question

The present review takes steps from the domain of the shell model into open shell nuclei. The question posed in the title is to dramatize how far shell model approaches, i.e., many nucleons occupying independent-particle configurations and interacting through two-body forces (a configuration interaction problem) can provide a description of nuclei as one explores the structure observed where neither proton nor neutron numbers match closed shells. Features of doubly closed and singly closed shell nuclei and adjacent nuclei are sketched, together with the roles played by seniority, shape coexistence, triaxial shapes and particle–core coupling in organizing data. An illuminating step is taken here to provide a detailed study the reduced transition rates, B(E2;21+→01+), in the singly closed shell nuclei with doubly closed shell plus or minus a pair of identical nucleons, and the confrontation between such data and state-of-the-art shell model calculations: this amounts to a review of the effective charge problem. The results raise many questions and point to the need for much further work. Some guidance on criteria for sharpening the division between the domain of the shell model and that of deformation-based descriptions of nuclei are provided. The paper is closed with a sketch of a promising direction in terms of the algebraic structure embodied in the symplectic shell model.

Multimode photon blockade

Interactions are essential for the creation of correlated quantum many-body states. Although two-body interactions underlie most natural phenomena, three- and four-body interactions are important for the physics of nuclei1, exotic few-body states in ultracold quantum gases2, the fractional quantum Hall effect3, quantum error correction4 and holography5,6. Recently, a number of artificial quantum systems have emerged as simulators for many-body physics, featuring the ability to engineer strong interactions. However, the interactions in these systems have largely been limited to the two-body paradigm and require building up multibody interactions by combining two-body forces. Here we implement a scheme to create a higher-order interaction between photons stored in multiple electromagnetic modes of a microwave cavity. The system is dressed such that there is collectively no interaction until a target total photon number is reached across multiple distinct modes, at which point the photons interact strongly. In our demonstration, we create interactions involving up to three bodies and across up to five modes. We harness the interaction to prepare single-mode Fock states and multimode W states, which we verify by introducing a multimode Wigner tomography method. A method to engineer higher-order interactions between photons provides a route to create non-classical and entangled states across multiple modes.

Higher-order synchronization on the sphere

We construct a system of N interacting particles on the unit sphere in d-dimensional space, which has d-body interactions only. The equations have a gradient formulation derived from a rotationally-invariant potential of a determinantal form summed over all nodes, with antisymmetric coefficients. For d = 3, for example, all trajectories lie on the two-sphere and the potential is constructed from the triple scalar product summed over all oriented two-simplices. We investigate the cases d = 3, 4, 5 in detail, and find that the system synchronizes from generic initial values for both positive and negative coupling coefficients, to a static final configuration in which the particles lie equally spaced on . Completely synchronized configurations also exist, but are unstable under the d-body interactions. We compare the relative effect of two-body and d-body forces by adding the well-studied two-body interactions to the potential, and find that higher-order interactions enhance the synchronization of the system, specifically, synchronization to a final configuration consisting of equally spaced particles occurs for all d-body and two-body coupling constants of any sign, unless the attractive two-body forces are sufficiently strong relative to the d-body forces. In this case the system completely synchronizes as the two-body coupling constant increases through a positive critical value, with either a continuous transition for d = 3, or discontinuously for d = 5. Synchronization also occurs if the nodes have distributed natural frequencies of oscillation, provided that the frequencies are not too large in amplitude, even in the presence of repulsive two-body interactions which by themselves would result in asynchronous behaviour.

Instability of the body-centered cubic lattice within the sticky hard sphere and Lennard-Jones model obtained from exact lattice summations.

A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to lattice vectors of a cuboidal unit cell. As a result, we obtain analytical expressions in terms of lattice sums for the cohesive energy where the interaction is described by a Lennard-Jones (LJ) interaction potential or a sticky hard-sphere (SHS) model with a r^{-n} long-range attractive term. These lattice sums are evaluated to computer precision by expansions in terms of a fast converging Bessel function series. Applying the whole range of lattice parameters for the SHS and LJ potentials we prove that the bcc phase is unstable (or, at best, metastable) toward distortion into the fcc phase in the low temperature and pressure limit. Even if more accurate potentials are used, such as the extended LJ potential for argon or chromium, the bcc phase remains unstable. This strongly indicates that the appearance of a low temperature bcc phase for several elements in the periodic table is due to higher than two-body forces in atomic interactions.

Effect of Nucleon Dressing on Triton Binding Energy

The effect of nucleon dressing by pions, on the binding energy of three nucleons interacting via two-body forces, is calculated for the first time within a conventional nuclear physics approach. It is found that the dressing increases the binding energy of the triton by an amount approximately in the range from 0.3 MeV to 0.9 MeV, depending on the model used for dressing. This suggests that nucleon dressing may help explain the underestimation of the triton binding energy in previous calculations using only two-nucleon forces.

Multilevel summation for periodic electrostatics using B-splines.

Fast methods for calculating two-body interactions have many applications, and for molecular science and cosmology, it is common to employ periodic boundary conditions. However, for the 1/r potential, the energy and forces are ill-defined. Adopted here is the model given by the classic Ewald sum. For the fast calculation of two-body forces, the most celebrated method is the fast multipole method and its tree-code predecessor. However, molecular simulations typically employ mesh-based approximations and the fast Fourier transform. Both types of methods have significant drawbacks, which, in most respects, are overcome by the less well-known multilevel summation method (MSM). Presented here is a realization of the MSM, which can be regarded as a multilevel extension of the (smoothed) particle mesh Ewald (PME) method, but with the Ewald softening replaced by one having a finite range. The two-level (single-grid) version of MSM requires fewer tuning parameters than PME and is marginally faster. Additionally, higher-level versions of MSM scale well to large numbers of processors, whereas PME and other two-level methods do not. Although higher-level versions of MSM are less efficient on a single processor than the two-level version, evidence suggests that they are more efficient than other methods that scale well, such as the fast multipole method and tree codes.

On the many-body nature of intramolecular forces in FFLUX and its implications.

FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3Natoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to Natoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

Calculation of the Li6 ground state within the hyperspherical harmonic basis

We have studied the solution of the six-nucleon bound state problem using the hyperspherical harmonic (HH) approach. For this study we have considered only two-body nuclear forces. In particular we have used a chiral nuclear potential evolved with the similarity renormalization group unitary transformation. A restricted basis has been selected by performing a careful analysis of the convergence of different HH classes. Finally, the binding energy and other properties of $^{6}\mathrm{Li}$ ground state are calculated and compared with the results obtained by other techniques. Then, we present a calculation of matrix elements relevant for direct dark matter search involving $^{6}\mathrm{Li}$. The results obtained demonstrate the feasibility of using the HH method to perform calculations beyond $A=4$.

Deuteron EDM induced by CP -violating couplings of pseudoscalar mesons

We analyze contributions to the electric dipole (EDM) and Schiff (SFM) moments of deuteron induced by the CP-violating three-pseudoscalar meson couplings using phenomenological Lagrangian approach involving nucleons and pseudoscalar mesons $P=\pi, K, \eta, \eta'$. Deuteron is considered as a proton-neutron bound state and its properties are defined by one- and two-body forces. One-body forces correspond to a picture there proton and neutron are quasi free constituents of deuteron and their contribution to the deuteron EDM (dEDM) is simply the sum of proton and neutron EDMs. Two-body forces in deuteron are induced by one-meson exchange between nucleons. They produce a contribution to the dEDM, which is estimated using corresponding potential approach. From numerical analysis of nucleon and deuteron EDMs we derive stringent limits on CP-violating hadronic couplings and $\bar\theta$ parameter. We showed that proposed measurements of proton and deuteron EDMs at level of $\sim 10^{-29}$ by the Store Ring EDM and JEDI Collaborations will provide more stringent upper limits on the CP violating parameters.

Virial coefficients of trapped and untrapped three-component fermions with three-body forces in arbitrary spatial dimensions

Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmonic trapping potential of frequency $\omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $\Delta b_4$ and $\Delta b_5$ as functions of $\Delta b_3$. Additionally, we argue that in the $\omega \to 0$ limit the relationship $b_n^\text{T} = n^{-d/2} b_n$ holds between the trapped (T) and homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $\Delta b_3^\text{T}$ in 1D with three-body forces and $\Delta b_2^\text{T}$ in 2D with two-body forces.