Three-body States Research Articles

Reshaped three-body interactions and the observation of an Efimov state in the continuum

Efimov trimers are exotic three-body quantum states that emerge from the different types of three-body continua in the vicinity of two-atom Feshbach resonances. In particular, as the strength of the interaction is decreased to a critical point, an Efimov state merges into the atom-dimer threshold and eventually dissociates into an unbound atom-dimer pair. Here we explore the Efimov state in the vicinity of this critical point using coherent few-body spectroscopy in 7Li atoms using a narrow two-body Feshbach resonance. Contrary to the expectation, we find that the 7Li Efimov trimer does not immediately dissociate when passing the threshold, and survives as a metastable state embedded in the atom-dimer continuum. We identify this behavior with a universal phenomenon related to the emergence of a repulsive interaction in the atom-dimer channel which reshapes the three-body interactions in any system characterized by a narrow Feshbach resonance. Specifically, our results shed light on the nature of 7Li Efimov states and provide a path to understand various puzzling phenomena associated with them.

Ultra-Low Energy Nuclear Fusion by Cs(2H,γ)La

We found that certain three-body excited states of 55133Cs13H2 in the Pd12 cuboctahedron molecule could interfere with the three-nucleon resonance states of Cs+t+t or 57139 La∗ which transfer from the 7/2+ state of CsH2 to 7/2+ state of La∗ by the E2 transition, and down to the La ground state, although the molecular ground state and the first excited state of 55133Cs13H2 are very stable. The three-body calculation is performed by using six potentials. We also found that the critical fusion value of t × ρ × T (t:duration time, ρ: plasma density, T : temperature or energy) for the ultra low energy molecular synthesis is almost the same as that for the thermal nuclear fusion, or higher. It is claimed that the radioactive nuclear waste products of the nuclear fission, could form via nuclear fusion a stable nucleus due to our ultra-low energy molecule-nucleus transition.

Universal geometry of two-neutron halos and Borromean Efimov states close to dissociation

The geometry of Borromean three-body halos, such as two-neutron halo nuclei or triatomic molecules close to dissociation, is investigated using a three-body model. This model enables to analytically derive the universal geometric properties found recently within an effective-field theory for halos made of a core and two resonantly-interacting particles [Phys. Rev. Lett., 128, 212501 (2022)]. It is shown that these properties not only apply to the ground three-body state, but also to all the excited (Efimov) states where the core-particle interaction is resonant. Furthermore, a universal geometry persists away from the resonant regime between the two particles, for any state close to the three-body threshold. This “halo universality”, which applies equally to all states, is different from the Efimov universality, which is only approximate for the ground state. It is explained by the separability of the hyper-radius and hyper-angles close to the three-body dissociation threshold.

Quantum state transfer on 1-dimensional and 2-dimensional topological Heisenberg spin models

The geometrical significance of winding number is used to study the topological characteristics of a single-excitation Heisenberg XY spin model represented by the Su–Schrieffer–Heeger (SSH) model. Due to the presence of topological edge states, the quantum state may be conveyed from the first site to the last site with a high degree of fidelity. Also examined is a Heisenberg XY model on the kagome lattice. In the topological phase of the kagome lattice, the three corner states are not affected by the Dzyaloshinskii–Moriya (DM) interactions. For the kagome lattice with and without the DM interactions, the state of a spin on one corner site can be transferred to the other two corner sites in various ways during the topological phase. The quantum state transfer (QST) for the XY model on the kagome lattice without the DM interactions is symmetrical and can only produce a three-body entangled state. In contrast, the QST for the XY model on the kagome lattice with the DM interactions is in an asymmetrical form, similar to one-way propagation, and it can produce both product states and three-body entangled states.

Studies of three-and four-body hypernuclei with heavy-ion beams, nuclear emulsions and machine learning

Interests on few-body hypernuclei have been increased by recent results of experiments employing relativistic heavy ion beams. Some of the experiments have revealed that the lifetime of the lightest hypernucleus, hypertriton, is significantly shorter than 263 ps which is expected by considering the hypertriton to be a weakly-bound system. The STAR collaboration has also measured the hypertriton binding energy, and the deduced value is contradicting to its formerly known small binding energy. These measurements have indicated that the fundamental physics quantities of the hypertriton such as its lifetime and binding energy have not been understood, therefore, they have to be measured very precisely. Furthermore, an unprecedented Λnn bound state observed by the HypHI collaboration has to be studied in order to draw a conclusion whether or not such a bound state exists. These three-body hypernuclear states are studied by the heavy-ion beam data in the WASA-FRS experiment and by analysing J-PARC E07 nuclear emulsion data with machine learning.

Multichannel hyperspherical model for Efimov physics with van der Waals interactions controlled by a Feshbach resonance

Here we present a four-channel model that incorporates a magnetically tunable Feshbach resonance in a system of three atoms that interact via pairwise van der Waals interactions. Our method is designed to model recent experiments where the tunability of the scattering length has been used to study three-body Efimov states, which appear in the limit of a diverging two-body scattering length. Using this model, we calculate three-body adiabatic and effective potential curves and study how the strength (or width) of the Feshbach resonance affects the three-body potential that is connected to the Efimov effect. We find that the position of the repulsive barrier, which has been used to explain the so-called van der Waals universality in broad resonances, is slightly shifted as the narrow resonance limit is approached and that this shift is correlated to the appearance of two avoided crossings in the adiabatic energy landscape. More importantly, the attractive well is markedly shifted upward in energy and is extremely shallow for the narrowest resonance. We argue that this behavior is connected to the breakdown of van der Waals universality for weak (narrow) resonances.

Cross sections for single-electron capture from heliumlike targets by fast heavy nuclei

Single charge-exchange in collisions of heavy bare nuclei with the ground state of two-electron atomic targets is described perturbatively as a four-body problem. The employed four-body boundary-corrected continuum intermediate state (BCIS-4B) method considers the correlated and uncorrelated target wave functions ${\ensuremath{\varphi}}_{i}.$ A thorough examination is performed for the formation of any final hydrogen-like $nlm$ state of the captured electron. For arbitrary projectile and target nuclear charges, the nine-dimensional integral in the transition amplitude is reduced to a two-dimensional numerical quadrature. The general analysis is applied to one-electron capture by protons from helium targets beginning with the lower edge (10 keV) of intermediate energies and extending to the higher (12.5 MeV) domain. These include the main peaks (Massey, Thomas) due to single and double scattering, respectively. The results encompass over 70 state-selective and state-summed cross sections $(n\ensuremath{\le}6,\phantom{\rule{0.16em}{0ex}}0\ensuremath{\le}l\ensuremath{\le}n\ensuremath{-}1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}l\ensuremath{\le}m\ensuremath{\le}l).$ In comparison to measurements, the electronic correlations in ${\ensuremath{\varphi}}_{i}$ greatly improve the overall performance of the BCIS-4B method around the Massey peak, below about 100 keV. Moreover, while largely outperforming the three-body boundary-corrected continuum intermediate state method, the cross sections in the BCIS-4B with the correlated ${\ensuremath{\varphi}}_{i}$ compare excellently overall with the available experimental data at 10 to 12 500 keV. Hence, the BCIS-4B method, with its built-in two main capture mechanisms (one-step Massey and two-step Thomas) is capable of spanning impact energies covering three or more orders of magnitude at which the state-summed cross sections vary over 11 orders of magnitude.

Effect of Third-Particle Material and Contact Mode on Tribology Contact Characteristics at Interface

A moving pair with two-body contact is the ideal situation assumed in previous analyses. However, all moving pairs are in a three-body contact state at the start of operation or immediately after the start of operation, such as bearings, ball-screws, gears and engines. This work studies the influence of wear particles (SUJ2), environmental particles (SiO2 and Al2O3) and nano-additives (CuO) on the tribological contact characteristics under different particle concentrations, particle sizes, surface roughnesses and contact modes. The three-body microcontact analysis revealed that the differences in the real contact area, particle contact area and separation of the four-particle materials in the three-body s–s and p–s contact modes are rather small. Under the three-body hybrid contact mode, the difference is relatively large and the sequence of the real contact area value obtained due to the elastic modulus for the four-particle material at this interface is Al2O3 > SUJ2 > CuO > SiO2. The order of the other two contact characteristics is reversed. The difference increases as the particle size or particle concentration increases. The order of the critical load required to transform three kinds of contact modes is SiO2 > CuO > SUJ2 > Al2O3. On the nearly initial three-body hybrid contact mode, the plastic contact area ratio at the interface first increases to a critical value and then decreases as the load increases because the original plastic contact spot area and contact spot number increases with the increase in load. At the same time, the elasto-plastic contact area ratio decreases to a low value and then increases. The elastic contact area ratio at the interface decreases as the load increases. Among the four third-particle materials, the experimental results and theoretical predictions show that the environmental particles, Al2O3, cause the maximum friction and wear observed at the interface.

Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

The Faddeev equations in coordinate space are solved to study the ΩNN and ΩΩN three-body systems using the latest ΩNS25 and ΩΩ S01 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the ΩNN system by examining three NN potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Ωd(T=0) in maximum spin 5/2+ confirm ground state binding energy of 20.953, 19.368, and 20.439 MeV and a matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Ωd(0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Ωd(0)5/2+ ground states.

D1(2420) and its interactions with a kaon: Open charm states with strangeness

In this work we present an attempt to describe the $X_1(2900)$ found by the LHCb collaboration, in the experimental data on the invariant mass spectrum of $ D^-K^+$, as a three-meson molecular state of the $K\rho\bar D$ system. We discuss that the interactions in all the subsystems are attractive in nature, with the $\rho \bar D$ interaction generating $\bar D_1(2420)$ and the $K \rho$ resonating as $K_1(1270)$. We find that the system can form a three-body state but with a mass higher than that of $X_1(2900)$. We investigate the $K \rho D$ system too, finding that the three-body dynamics generates an isoscalar state, which can be related to $D_{s1}^*(2860)$, and an exotic isovector state. This latter state has a mass similar to that of the $X_0(2900)$ and $X_1(2900)$ states found by LHCb, but a very small width ($\sim 7.4 \pm 0.9$ MeV) and necessarily requires more than two quarks to describe its properties. We hope that our findings will encourage experimental investigations of the isovector $K \rho D$ state. Finally, in the pursuit of finding a description for $X_1(2900)$, we study the $\pi\bar K^* D^*$ system where $ \bar K^*D^*$ forms $0^+$, $1^+$ and $2^+$ states. We do not find a state which can be associated with $X_1(2900)$.

Competition between pairing and tripling in one-dimensional fermions with coexistent s - and p -wave interactions

We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity s-wave and odd-parity p-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as Cooper triple by solving the corresponding in-medium variational equations. We further feature the phase diagram consisting of the s- and p-wave Cooper pairing phase, and Cooper tripling phase, in the plane of s- and p-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both s- and p-wave interactions are moderately strong.

Study of light hypernuclei in Europe: The hypertriton and nnΛ puzzles

The current understanding of light hypernuclei, which are sub-atomic nuclei with strangeness, is being challenged and studied in detail by several European research groups and collaborations. In recent years, studies of hypernuclei using high-energy heavy ion beams have reported unexpected results on the three-body hypernuclear state 3ΛH, named the hypertriton. For some time, reports of a shorter lifetime and larger binding energy than what was previously accepted have created a puzzling situation for its theoretical description; this is known as the "hypertriton puzzle". With the inclusion of the most recent experimental measurements, the current status of the hypertriton puzzle is evolving. Additionally, the possible neutral bound state of a Λ hyperon with two neutrons, nnΛ, has raised questions about our understanding of the formation of light hypernuclei either in bound or resonance states. These results have initiated several ongoing experimental programs all over the world to study these three-body hypernuclear states precisely. We are studying these light hypernuclear states by employing heavy ion beams at 2AGeV on a fixed carbon target with the WASA detector system and the Fragment Separator (FRS) at GSI. The WASA-FRS experimental campaign was performed during the first quarter of 2022, and this paper presents a short overview of the campaign and how it seeks to tackle the hypertriton and nnΛ puzzles. Data analysis is ongoing, and several preliminary results will be reported.

Stability against three-body clustering in one-dimensional spinless p -wave fermions

We theoretically investigate in-medium two- and three-body correlations in one-dimensional spinless fermions with attractive two-body p-wave interaction. By investigating the variational problem of two- and three-body states above the Fermi sea, we elucidate the fate of the in-medium two- and three-body cluster states. The one-dimensional system with the strong p-wave interaction is found to be stable against the formation of three-body clusters even in the presence of the Fermi sea, in contrast to higher-dimensional systems that suffer the strong three-body loss associated with the trimer formation.

Toffoli gate based on a three-body fine-structure-state-changing Förster resonance in Rydberg atoms

We have developed an improved scheme of a three-qubit Toffoli gate based on fine structure state changing three-body Stark-tuned Rydberg interaction. This scheme is a substantial improvement of our previous proposal [I.I.Beterov et al., Physical Review A 98, 042704 (2018)]. Due to the use of a different type of three-body F\"orster resonance we substantially simplified the scheme of laser excitation and phase dynamics of collective three-body states. This type of F\"orster resonance exists only in systems with more than two atoms, while the two-body resonance is absent. We reduced the sensitivity of the gate fidelity to fluctuations of external electric field and eliminated the necessity to use external magnetic field for fine tuning of the resonant electric field value, compared to the previous scheme of Toffoli gate based on Rydberg atoms. A gate fidelity of >99% was demonstrated in the calculations.

Single-electron transfer from helium atoms to energetic multiply-charged nuclei

The three-body boundary-corrected continuum intermediate state (BCIS-3B) method is employed to compute single-electron capture cross sections. These data are for collisions in which a target helium atom in its ground state He(1s2) is impacted by multiply charged nuclei (specifically H+,He2+,Li3+,Be4+,B5+,C6+,N7+,O8+,F9+). Intermediate and high projectile energies are considered (20 keV/amu-3 MeV/amu). The obtained results are tabulated for total cross sections (state-selective Qnlm as well as state-summed Qnl,Qn and QΣ). Cross section Qnlm corresponds to a fixed triple of the hydrogenlike quantum numbers {n,l,m}. In Qnl,Qn and QΣ, the sums over m∈[−l,l],l∈[0,n−1] and n∈[1,nmax] are carried out, respectively. For n>nmax in QΣ, the Oppenheimer n−3 scaling rule is adopted. The values of nmax are set to 4 (for H+,He2+,Li3+), 5 (for Be4+), 6 (for B5+) and 7 (for C6+,N7+,O8+,F9+). Exhaustive comparisons of the theoretical findings for QΣ with the corresponding experimental data are performed. It is determined that the BCIS-3B method is in excellent agreement with the available measurements. The present database for the examined capture processes is deemed to be of notable practical usefulness in versatile applications of particular relevance to plasma physics, astrophysics, fusion research and ion therapy in medicine.

Three-body continuum states and Efimov physics in noninteger geometry

Continuum structures of three short-range interacting particles in a deformed external one-body field are investigated. We use the equivalent $d$ method employing noninteger dimension, $d$, in a spherical calculation with a dimension-dependent angular momentum barrier. We focus on dimensions close to the critical dimension, $d={d}_{E}$, between 2 and 3, defined by zero two-body energies, where the Efimov effect can occur. We design for this dimension region a schematic, long-distance realistic, square-well based, three-body spherical model, which is used to derive analytic expressions for the wave functions, scattering lengths, phase shifts, and elastic-scattering cross sections. The procedure and the results are universal, valid for all short-range potentials, and for large scattering lengths. We discuss the properties and validity of the derived expressions by means of the simplest system of three identical bosons. The derived expressions are particularly useful for very small energies, where full numerical calculations are often not feasible. For energies where the numerical calculations can be performed, a good agreement with the analytic results is found. These model results may be tested by scattering experiments for three particles in an equivalent external deformed oscillator potential. The cross sections all vanish in the zero-energy limit for $d<3$ with definite $d$-dependent power of energy.

Three-body resonances in pionless effective field theory

We investigate the appearance of resonances in three-body systems using pionless effective field theory at leading order. The Faddeev equation is analytically continued to the unphysical sheet adjacent to the positive real energy axis using a contour rotation. We consider both, the three-boson system and the three-neutron system. For the former, we calculate the trajectory of Borromean three-body Efimov states turning into resonances as they cross the three-body threshold. For the latter, we find no sign of three-body resonances or virtual states at leading order. This result is validated by exploring the level structure of three-body states in a finite volume approach.

Effect of fermion indistinguishability on optical absorption of doped two-dimensional semiconductors

We study the optical absorption spectrum of a doped two-dimensional semiconductor in the spin-valley polarized limit. In this configuration, the carriers in the Fermi sea are indistinguishable from one of the two carriers forming the exciton. Most notably, this indistinguishability requires the three-body trion state to have p-wave symmetry. To explore the consequences of this, we evaluate the system's optical properties within a polaron description, which can interpolate from the low density limit -- where the relevant excitations are few-body bound states -- to higher density many-body states. In the parameter regime where the trion is bound, we demonstrate that the spectrum is characterized by an attractive quasiparticle branch, a repulsive branch, and a many-body continuum, and we evaluate the doping dependence of the corresponding energies and spectral weights. In particular, at low doping we find that the oscillator strength of the attractive branch scales with the square of the Fermi energy as a result of the trion's p-wave symmetry. Upon increasing density, we find that both the repulsive and attractive branches blueshift, and that the orbital character of the states associated with these branches interchanges. We compare our results with previous investigations of the scenario where the Fermi sea involves carriers distinguishable from those in the exciton, for which the trion ground state is s-wave.

Cooper triples in attractive three-component fermions: Implication for hadron-quark crossover

We investigate many-body properties of equally populated three-component fermions with attractive three-body contact interaction in one dimension. A diagrammatic approach suggests the possible occurrence of Cooper triples at low temperature, which are three-body counterparts of Cooper pairs with a two-body attraction. We develop a minimal framework that bridges the crossover from tightly-bound trimers to Cooper triples with increasing chemical potential and show how the formation of Cooper triples occurs in the grand-canonical phase diagram. Moreover, we argue that this non-trivial crossover is similar to the hadron-quark crossover proposed in dense matter. A coexistence of medium-induced triples and the underlying Fermi sea at positive chemical potential is analogous to quarkyonic matter consisting of baryonic excitations and the underlying quark Fermi sea. The comparison with the existing quantum Monte Carlo results implies that the emergence of these kinds of three-body states can be a microscopic origin of the peak of the sound velocity along the crossover.

Tritonlike Molecules of Three Identical Baryons

In nuclear physics, triton and helium-3 nucleus can be understood as three-body hadronic molecules. Analogous to the loosely bound structures for the triton and helium-3 nucleus, whether there is a bound state formed by three hadrons leaves us an open issue. Based on the one-boson exchange model as well as the adoption of the variational approach, we make a comprehensive investigation on the tritonlike systems of three identical baryons N N N , Λ Λ Λ , Ξ Ξ Ξ , and Σ Σ Σ . We predict that the three-body molecular states for the systems of three identical hadrons of baryon octet are probably existent as long as their two-body subsystems have bound states. The numerical results of this work may be helpful for the theoretical and experimental researches on the trihadron molecules in future.