Three-body Forces Research Articles

Tetraquarks and quark three-body forces

In this work, we construct the three-quark potentials inspired from nuclear physics and demonstrate that these are crucial to describe the meson and baryon spectrums using the same parameter set. We then apply this potential to the Tcc and χc1(3872) tetraquark states. We find that the quark three-body forces give additional repulsion on both states. This result supports the argument that these tetraquark states are molecular rather than compact states.

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.

LATTICE DYNAMICAL STUDY OF THORIUM SULPHIDE

Thorium sulfide (ThS) is a chemical compound composed of thorium and sulfur atoms, with the chemical formula ThS. It belongs to the class of sulfides. To understand the dimensional stability and thermal behaviour of thorium sulphide (ThS), a lattice dynamical research issued to investigate its vibrational characteristics. We study the density of states (DOS) and phonon dispersion in the 50–60 GHz frequency region using computational techniques. Important information about the stability of the ThS crystal structure are given by the phonon dispersion curves, namely the presence of imaginary phonon frequencies that point to dynamical stability. We identify the major modes of vibration and their contributions to the thermodynamic properties of ThS through studying the phonon density of states.Van der Waals' three-body force shell model is used in this study to theoretically investigate the lattice dynamical behaviour of (ThS...). Elastic constants, pressure derivatives, dispersion relation curve, combined density of states, equation of state, and specific ultrasonic properties of the ThS are among the parameters for which calculated values are gave.The stability of the structure and vibrational properties of thorium sulphide are now better known by lattice dynamical study, which provides the way to its effective application in a range of technological uses, from nuclear reactors to the production of creative materials. Keywords: lattice, dynamics, thermal, vibrational

Lellouch-Lüscher factor for the K → 3π decays

We derive an explicit expression for the Lellouch-Lüscher (LL) factor in the K → 3π decays at leading order (without derivative couplings). Several important technical details are addressed, like a proper decomposition into the isospin amplitudes, the choice of a minimal set of effective couplings and the renormalization, as well as the algorithm for the solution of the pertinent Faddeev equations in the infinite volume which is based on the contour deformation method. Most importantly, our numerical results demonstrate that the three-body force contributes very little to the LL factor. This result paves the way for the study of the K → 3π decays on the lattice.

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.

Broken seniority symmetry in the semimagic proton mid-shell nucleus Rh95

Lifetime measurements of low-lying excited states in the semimagic (N=50) nucleus Rh95 have been performed by means of the fast-timing technique. The experiment was carried out using γ-ray detector arrays consisting of LaBr3(Ce) scintillators and germanium detectors integrated into the DESPEC experimental setup commissioned for the Facility for Antiproton and Ion Research () Phase-0, Darmstadt, Germany. The excited states in Rh95 were populated primarily via the β decays of Pd95 nuclei, produced in the projectile fragmentation of a 850 MeV/nucleon Xe124 beam impinging on a 4g/cm2Be9 target. The deduced electromagnetic E2 transition strengths for the γ-ray cascade within the multiplet structure depopulating from the isomeric Iπ=21/2+ state are found to exhibit strong deviations from predictions of standard shell model calculations which feature approximately conserved seniority symmetry. In particular, the observation of a strongly suppressed E2 strength for the 13/2+→9/2+ ground state transition cannot be explained by calculations employing standard interactions. This remarkable result may require revision of the nucleon-nucleon interactions employed in state-of-the-art theoretical model calculations, and might also point to the need for including three-body forces in the Hamiltonian. Published by the American Physical Society 2024

Ab initio valence-space in-medium similarity renormalization group calculations for neutron-rich P, Cl, and K isotopes* *Supported by the National Key R&D Program of China (2023YFA1606403), the National Natural Science Foundation of China (12205340, 12175281, 12347106, 12121005), the Natural Science Foundation of Gansu Province, China (22JR5RA123, 23JRRA614), the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000), the Key Research

Neutron-rich P, Cl, and K isotopes, particularly those with neutron numbers of approximately , have attracted extensive experimental and theoretical interest. We utilize the ab initio valence-space in-medium similarity renormalization group approach, based on chiral nucleon-nucleon and three-nucleon forces, to investigate the exotic properties of these isotopes. Systematic calculations of the low-lying spectra are performed. A key finding is the level inversion between and states in odd-A isotopes, attributed to the inversion of and single-particle states. The ab initio calculations, which incorporate the three-nucleon forces, correlate closely with existing experimental data. Further calculations of effective proton single-particle energies provide deeper insights into the shell evolution for and sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for and sub-shells with neutron numbers ranging from 20 to 28. Additionally, systematic ab initio calculations are conducted for the low-lying spectra of odd-odd nuclei. The results correspond with experimental data and provide new insights for future research into these isotopes up to and beyond the drip line.

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.

Tests of the Envelope Theory for Three-Body Forces

Tests of the Envelope Theory for Three-Body Forces

Separation energies of light Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hypernuclei and their theoretical uncertainties

Separation energies of light Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hypernuclei (A≤5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A\\le 5$$\\end{document}) and their theoretical uncertainties are investigated. Few-body calculations are performed within the Faddeev-Yakubovsky scheme and the no-core shell model. Thereby, modern and up-to-date nucleon-nucleon, three-nucleon and hyperon-nucleon potentials derived within chiral effective field theory are employed. It is found that the numerical uncertainties of the few-body methods are well under control and an accuracy of around 1 keV for the hypertriton and of better than 20 keV for the separation energies of the Λ4He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\,4}_{\\varLambda }\ extrm{He}$$\\end{document} and Λ5He\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\,5}_{\\varLambda }\ extrm{He}$$\\end{document} hypernuclei can be achieved. Variations caused by differences in the nucleon-nucleon interaction are in the order of 10 keV for Λ3H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\,3}_{\\varLambda }\ extrm{H}$$\\end{document} and no more than 110 keV for A=4,5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A=4,\\,5$$\\end{document}Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document} hypernuclei, when recent high-precision potentials up to fifth order in the chiral expansion are employed. The variations are smaller than the expected contributions from chiral hyperon-nucleon-nucleon forces which arise at the chiral order of state-of-the-art hyperon-nucleon potentials. Estimates for those three-body forces are deduced from a study of the truncation uncertainties in the chiral expansion.

Single Folding Potential Calculations in 141Pr

In this study, Skyrme and Gogny forces have been used to describe interactions for Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) calculations, considering all nucleons to evaluate nucleon densities. The nucleon densities of the 141Pr were calculated by using the Skyrme-HF (SHF) method with Woods-Saxon Potential (SHF-WS) and with Harmonic Oscillator Potential (SHF-HO), HFB method with Skyrme (HFB-S) and with Gogny (HFB-G) interactions. In these calculations, the effects of the three-body force have been accounted for in both Skyrme and Gogny forces through a density-dependent term necessary to describe various properties of nuclei and nuclear matter. The root-mean-square (rms) radii of proton, neutron, and charge densities of the nucleus were calculated using the density-dependent Skyrme-type effective nucleon-nucleon (NN) interaction in the HF approach. The Folding potential, developed to describe nucleon-nucleus (n-Pr) elastic scattering data, was obtained by single folding potential to calculate reaction cross-section calculations for 141Pr target. The calculated cross-sections, obtained using density data from four different models, were compared with each other and with experimental data from the literature for analysis and interpretation of the results.

Elastic Properties of (CsCN)x(CsX)1-x, Mixed Crystal

The TOEC's elastic characteristics of mixed alkali cyanide-alkali halide crystal (CsCN)x(CsX)1-x (X= Cl) for x=0, 0.28, 0.59, and 0.96 at various temperatures have been examined using an Extended three-body force shell model (ETSM). The effect of coupling between the cyanide molecules' rotational and translational motion is included in this model. Finite elasticity, in which elastic stress is non-linear with elastic strain, is the responsibility of the TOECs. In some crystallographic planes, the elastic shear behaviour is asymmetric with regard to shear displacements. The knowledge of ion-core repulsive interactions; which vary with the interatomic separation; is related to the third order elastic constants.

Sound velocity, equation of state and strangeness in neutron star matter

This presentation in two parts starts with a brief review on the speed of sound in neutron star matter as inferred from observational data. It is pointed out that, in view of the strong constraints imposed by observed properties of the heaviest neutron stars, the equation of state must be very stiff. Stringent limits can be set on the possible appearance of phase transitions in neutron star cores. The second part discusses issues concerning the occurance of strangeness degrees of freedom, in particular of hyperons, in neutron stars. Here the focus is on the role of repulsive hyperon-nuclear three-body forces, potentially resolving the so-called hyperon puzzle.

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Dark matter effects on the properties of neutron stars: Optical radii

We study the effects of dark matter on the properties of neutron stars by employing a DM-admixed model. The Brueckner–Hartree–Fock theory with realistic three-body forces and a generic bosonic self-interacting dark matter model describe the equations of state for nuclear matter and DM, respectively. We study the complete set of stable ‘dark’ neutron stars and in particular the observable radii of these objects. A rich variety of stellar configurations is found and discussed in detail.

Chiral three-body forces and nuclear first-principles studies

Chiral three-body forces and nuclear first-principles studies

Towards the understanding of the genuine three-body interaction for p–p–p and p–p–Lambda

Three-body nuclear forces play an important role in the structure of nuclei and hypernuclei and are also incorporated in models to describe the dynamics of dense baryonic matter, such as in neutron stars. So far, only indirect measurements anchored to the binding energies of nuclei can be used to constrain the three-nucleon force, and if hyperons are considered, the scarce data on hypernuclei impose only weak constraints on the three-body forces. In this work, we present the first direct measurement of the p–p–p and p–p–Lambda systems in terms of three-particle correlation functions carried out for pp collisions at sqrt{s} = 13 TeV. Three-particle cumulants are extracted from the correlation functions by applying the Kubo formalism, where the three-particle interaction contribution to these correlations can be isolated after subtracting the known two-body interaction terms. A negative cumulant is found for the p–p–p system, hinting to the presence of a residual three-body effect while for p–p–Lambda the cumulant is consistent with zero. This measurement demonstrates the accessibility of three-baryon correlations at the LHC.

Zero-Range Hamiltonian for a Bose Gas with an Impurity

We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the standard approach, one obtains the Ter-Martirosyan Skornyakov Hamiltonian which is unbounded from below. In order to avoid such instability problem, we introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles, i.e., the impurity and a boson, when another boson approaches the common position of the first two particles. We show that the Hamiltonian defined with such regularized interaction is self-adjoint and bounded from below if the strength of the three-body force is sufficiently large. The method of the proof is based on a careful analysis of the corresponding quadratic form.

Three-body forces and Coulomb effects in the $$^3$$He($$\alpha ,\gamma )^7$$Be process

Three-body forces and Coulomb effects in the $$^3$$He($$\alpha ,\gamma )^7$$Be process

Dibaryon Resonances and Three-Body Forces in Large-Angle pd Elastic Scattering at Intermediate Energies

Dibaryon Resonances and Three-Body Forces in Large-Angle pd Elastic Scattering at Intermediate Energies