Efimov physics in heteronuclear four-body systems

We study three- and four-body Efimov physics in a heteronuclear atomic system with three identical heavy bosonic atoms and one light atom. We show that exchange of the light atom between the heavy atoms leads to both three- and four-body features in the low-energy inelastic rate constants that trace to the Efimov effect. Further, the effective interaction generated by this exchange can provide an additional mechanism for control in ultracold experiments. Finally, we find that there is no true four-body Efimov effect-that is, no infinite number of four-body states in the absence of two- and three-body bound states-resolving a decades-long controversy.     

The Efimov effect. Discrete spectrum asymptotics

We study a three-particle Schrödinger operatorH for which none of the two-particle subsystems has negative bound states and at least two of them have zero energy resonances. We prove that under this condition the numberN(z) of bound states ofH belowz<0 has the asymptotics asz-0, where the coefficient depends only on the ratio of masses of the particles.     

Efimov effect in Dirac semi-metals

The Efimov effect is defined as a quantum state with discrete scaling symmetry and a universal scaling factor. It has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity through a Coulombic interaction, the same kinetic scaling and the interaction energy results in the Efimov effect. However, even when the Fermi energy lies exactly at the Dirac point, the vacuum polarization of the electron-hole pair fluctuation can still screen the Coulombic interaction, which leads to deviations from the scaling symmetry and eventually breaks down of the Efimov effect. This energy distortion of the Efimov states due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by the recent experimental observations in two- and three-dimensional Dirac semi-metals, we herein investigate this many-body correction to the Efimov effect and the conditions that allow some of the Efimov-like quasi-bound states to be observed in these condensed matter experiments.     

Exact wave functions of a four-body system

In this Letter the exact wave functions of a model four-quark system in SU(2) color are calculated for spinless but isospinor quarks in Schrödinger equation as an analogue to the actual six-quark problem in SU(3) color which arises naturally in the study of dibaryon states. This model four-quark problem is shown to be exactly soluble for the admissible states of isospin I=2 provided that the pairwise interactions between the quarks are supplemented by some four-body counter terms (interpreted as four-body forces). This model correctly simulates the color with orbital structure expected of the corresponding fermionic 4N problem. Further the possible exact solutions such as these can prove to be useful as test cases for the study of the full q⁶ problem in SU(3) color with spin-dependent forces.     

Efimov effect in 2-neutron halo nuclei

This paper presents an overview of our theoretical investigations in search of Efimov states in light 2-neutron halo nuclei. The calculations have been carried out within a three-body formalism, assuming a compact core and two valence neutrons forming the halo. The calculations provide strong evidence for the occurrence of at least two Efimov states in ²⁰C nucleus. These excited states move into the continuum as the two-body (core-neutron) binding energy is increased and show up as asymmetric resonances in the elastic scattering cross-section of the n-¹⁹C system. The Fano mechanism is invoked to explain the asymmetry. The calculations have been extended to ³⁸Mg, ³²Ne and a hypothetical case of a very heavy core (A = 100) with two valence neutrons. In all these cases the Efimov states show up as resonances as the two-body energy is increased. However, in sharp contrast, the Efimov states, for a system of three equal masses, show up as virtual states beyond a certain value of the two-body interaction.     

Efimov effect in nuclear three-body resonance decays

We investigate the effects of the nearly fulfilled Efimov conditions on the properties of three-body resonances. Using the hyper-spheric adiabatic expansion method we compute energy distributions of fragments in a three-body decay of a nuclear resonance. As a realistic example we investigate the 1- state in the halo nucleus 11Li within a three-body model 9Li + n +n model. Characteristic features appear as sharp peaks in the energy distributions. Their origin, as in the Efimov effect, is in the large two-body s-wave scattering lengths between the pairs of fragments.     

Efimov effect in an analytically solvable model

The Efimov effect is demonstrated in a model consisting of two heavy particles and a light one when the light-heavy interaction leads to a zero-energy two-body bound state. The model is solved in the Born-Oppenheimer approximation with the light-heavy interaction taken to be a separable S-wave potential of Yamaguchi form. It is demonstrated that in the case of a- two-body zero-energy bound state the binding energy of the light particle in the two-center potential exactly yields an effective $\text{1}\text{r}{}^2$ potential for the relative motion of the heavies. If the light-heavy mass ratio is made small enough, infinitely many bound states (the Efimov effect) are obtained. The approach to this limit is studied and the nature of the potential for large scattering length is obtained. An upper bound for the number of bound states is calculated using a result of Bargmann and Calogero and Efimov's $\text{ln}\text{(}\text{a}\text{r}{}_0\text{)}$ result is found. We note that the long-range effect arises from the large extent of the bound state, the pair wave function being essentially $\text{exp}\text{(?}\text{r}\text{a}\text{)}$ when the scattering length a is large.     

Many-body systems and the Efimov effect

We employ a Birman-Schwinger type analysis to derive estimates on the number of bound-states of certainN-body systems with threshold-energy =inf _ess(H) supposed to be zero. For many-body systems without any substructure we show that eigenvalues of the Schrödinger operatorH absorbed at =0 are in the point-spectrum ofH. Furthermore we characterize a multiparticle equivalent of the Efimov effect.     

Four-body Efimov effect for three fermions and a lighter particle

We study three same-spin-state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384相似文献   

Pauli blocking effect on Efimov states near a Feshbach resonance

In this Letter we study the effect of Pauli blocking on Efimov states in a quantum Fermi gas and illustrate that the universal Efimov potential is altered at large distances. We obtain the universal spectrum flow of Efimov trimers when the Fermi density is varied and further consider the effect of scattering of trimers by the Fermi sea. We argue that the universal flow is robust against fluctuating particle-hole pairs that result in an infrared catastrophe in impurity problems.     

Correlated trapped bosons and the many-body Efimov effect

We study two-body correlations in systems of identical bosons. We use a Faddeev type of decomposition of the wave function where all pairs of particles are treated equally. At large scattering length appears a series of Efimov-like states, i.e., spatially extended, model-independent many-body bound states inside the trap. They may play a role in the decay of Bose-Einstein condensates.     

Continuum resonances with shielded Coulomb-like potential and Efimov effect

Motivated by the possibility of the second energy level (0 ₂ ⁺ ) of ¹²C (in a three-alpha model) to turn into an Efimov state, we study a simple non-realistic toy model formed by three bosons interacting by the phenomenological s-wave Ali-Bodmer potential plus a Coulomb interaction. An artificial three-body potential was used to create a resonance with energy close to the energy of the 0 ₂ ⁺ of ¹²C, 0.38 MeV. The strength of the Coulomb potential is decreased until the energies of the two alpha pairs are zero. The system was placed inside a harmonic trap and a stabilization method has been used to calculate the energies of the resonances. We found that the shielded-Coulomb potential, which keeps the long tail, is not able to produce the Efimov effect. The energy of the three alphas decreases only to 0.19 MeV when the two-body energy crosses the threshold to become bound.     

The Universality of the Efimov Three-body Parameter

In this paper we discuss the recent discovery of the universality of the three-body parameter (3BP) from Efimov physics. This new result was identified by recent experimental observations in ultracold quantum gases where the value of the s-wave scattering length, a = a _?, at which the first Efimov resonance is created was found to be nearly the same for a range of atomic species — if scaled as a _?/r _vdW, where r _vdW is the van der Waals length. Here, we discuss some of the physical principles related to these observations that emerge from solving the three-body problem with van der Waals interactions in the hyperspherical formalism. We also demonstrate the strong three-body multichannel nature of the problem and the importance of properly accounting for nonadiabatic effects.     

Efimov effect and the third cluster coefficient of binary mixtures

Because of the Efimov effect the three-body bound state contribution to the cluster coefficients diverges, if the pair interaction develops a zero energy two-body bound state. It is shown for a quantum Lorentz gas model and a Born-Oppenheimer model of a gas mixture that this divergence is cancelled by the continuum contribution. The behaviour of the third cluster coefficient of the Lorentz gas at extreme temperatures is discussed.     

Efimov physics in cold atoms

Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and the scattering length. In this review, we summarize the universal results that are currently known. We also summarize the experimental information that is currently available with an emphasis on 3-atom loss processes.