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.     

Δ(3, 3) excitations and effective three-nucleon forces in finite nuclei

Contributions from three-body terms with intermediate Δ(3,3) isobar excitations to the ground state energies of nuclei are investigated. These terms can either be understood as three-body clusters in a many-body theory including isobar excitations explicitly or as contributions to an effective three-nucleon force. For the example ¹⁶O the resulting contribution is attractive and its value is typically about ?0.5 MeV per nucleon. This is smaller than the typical values of 1 MeV per nucleon repulsion obtained from the modifications of the effective two-body nucleon-nucleon interaction in nuclei due to intermediate Δ(3, 3) configurations. The gain in energy from the three-body terms including Δ(3,3) configurations, however, is of the same importance as the contribution from three-body terms including nucleons only.     

Subsidiary conditions and variational calculations of nuclear and neutron matters

The energy of nuclear and neutron matter is calculated within the framework of the variational approach including the contribution from three-body clusters. Two types of constrains for the two-body correlation function and realistic S-wave forces are used. It is shown that the energy strongly depends upon the type of constraint and that the variational calculation may lead to much more energy than the lowest order Brueckner theory calculations.     

Extending the VDPC+BCS formalism by including three-body forces

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.     

Sensitivity of the three-body calculations to different effects

The bound state of few-body systems in light nuclei is studied as a three-body problem. The three-body problem is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. Separable approximations are introduced to reduce the three-body problem to a set of coupled integral equations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system³H. The main interest of the present work is to investigate the sensitivity of the three-body binding energy to different effects in the problem. For this reason, we study the dependence of the three-body binding energy of different forms of local and separable two-body potentials, on the effective range of the two-body potentials, and on the percent of theD state in the deuteron wave function. Also, we test the sensitivity of the three-body binding energy to the considered number of terms from the separable expansion.     

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.     

Model Study of Three-Body Forces in the Three-Body Bound State

The Faddeev equation for the three-body bound state with two- and three-body forces is solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar two-meson exchange three-body forces. For two- and three- body forces of ranges and strengths typical of nuclear forces the single-particle momentum distribution and the two-body correlation function are similar to the ones found for realistic nuclear forces.     

A simplified approach to three-body correlations in nuclear matter through a non-zero particle spectrum

Self-consistent nuclear-matter calculations are presented which take into account Dahlblom's results for the contribution to the binding energy due to three-body correlations. We propose a justified parametrization of the single-particle potential for particle states, the energy contribution of which cancels approximately the energy from certain three-body correlations. Indications are given of how to fix this particle-state potential for a given two-body interaction. Two nucleon-nucleon potentials are used: the Reid soft-core potential and a fully momentum-dependent one-boson-exchange potential similar to the form proposed by Ingber and Potenza. The mechanism of the increase in the total wound due to three-body correlations is investigated and reasons are given why this does not prevent the saturation densities from moving to higher values. Due to three-body correlations and with self-consistency on the hole spectrum, the increase in nuclear-matter binding energy is 0.60 MeV/A for the Reid soft-core interaction and 0.68 Mev/A for the OBEP. The saturation momentum is shifted from 1.42 fm^?1 to 1.44 fm^?1 for the Reid potential and from 1.58 fm^?1 to 1.62 fm^?1 for the OBEP.     

Pion absorption in the resonance region

Pion absorption in the resonance region is studied microscopically in terms of the elementary coupling of mesons to nucleons and isobars. Particular emphasis is put on calculating the contribution from genuine two-body absorption and three-body absorption. At low energies the two-body absorption is the most important channel, but around resonance and beyond the three-body absorption becomes important and can account for about 50% of the total absorption cross section. Genuine multiparticle absorption by more than three particles is estimated to be a small fraction of the total. Comparison with the experimental data is made and good agreement with experiment is found for different nuclei and different energies.     

On the Uniqueness of the Solution to the Three-Body Problem with Zero-Range Interactions

We consider the uniqueness of the solution to a three-body problem with zero-range Skyrme interactions in configuration space. With the lowest, k⁰, two-body term alone the problem is known to have no unique solution as the system collapses – the variational estimate of the energy tends towards negative infinity, the size of the system towards zero. We argue that the next, k², two-body term removes the collapse and the three-body system acquires finite ground-state energy and size. The three-body interaction term is thus not necessary to provide a unique solution to the problem.     

Dynamical Study of Tensor Observables in the Energy Range of 80 keV to 95 MeV: Tests of Effective Two-Body Models

 Realistic interactions are used to study tensor observables in the energy range of 80 keV to 95 MeV deuteron laboratory energy, as well as the differential cross section for the two-body photodisintegration of . The Siegert form of the E1 multipole operator in the long-wavelength limit is taken as the sole component of the electromagnetic interaction. The three-body Faddeev equations for the bound-state and continuum wave functions are solved using the Paris, Argonne V14, Bonn-A, and Bonn-B potentials. The corresponding nucleon-nucleon t-matrices are represented in a separable form using the Ernst-Shakin-Thaler representation. The Coulomb force between protons is neglected and no three-nucleon force is included. The contribution of nucleon-nucleon P-wave components to the observables is carefully studied, not only in the angular distribution of the observables, but also as a function of the deuteron laboratory energy for fixed centre-of-mass angle. Comparison with data is shown wherever it exists. Results with simple Yamaguchi-type interactions with variable %D-state in the deuteron are compared with realistic interactions and one of these model potentials is used to study the results in terms of contributions from specific wave-function components or terms in the electromagnetic operator. Effective two-body models are examined by means of a derivation that is consistent with the underlying three-body calculation and that leads to an effective two-body t-matrix for neutron-deuteron elastic scattering carrying the same on-shell amplitudes as the original three-body equations. Received September 21, 1999; revised December 23, 1999; accepted February 9, 2000     

Theory of the Trojan-Horse method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross-section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross-sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two- and three-body cross-sections becomes very transparent. The appearing Trojan-Horse integrals are studied in detail.     

Scattering length scaling laws for ultracold three-body collisions

We present a simple and unifying picture that provides the energy and scattering length dependence for all inelastic three-body collision rates in the ultracold regime for three-body systems with short-range two-body interactions. Here, we present the scaling laws for vibrational relaxation, three-body recombination, and collision-induced dissociation for systems that support s-wave two-body collisions. These systems include three identical bosons, two identical bosons, and two identical fermions. Our approach reproduces all previous results, predicts several others, and gives the general form of the scaling laws in all cases.     

Cluster-variational calculations for extended nuclear systems

The energy as a function of density is calculated for neutron matter and for symmetrical nuclear matter, based on Jastrow trial wave functions. The energy expectation value is truncated in low cluster order. A detailed analysis of the two- and three-body cluster contributions and a special portion of the four-body contribution is given. Variation of a parameterized two-body correlation function is subjected to constraints designed to confine the trial wave function to the domain corresponding to rapid cluster convergence. Results are presented for a variety of model central potentials containing hard cores, for different sets of constraints, and for two- and three-parameter correlation functions. Calculations constrained by the “average Pauli condition” are found to yield results very close to those constrained by the “normalization” or “unitarity” condition, and the two-parameter correlation function appears to be quite adequate. The convergence of the cluster expansion, as reflected in the low orders, is good except at the highest densities considered. The three-body cluster contribution displays, in all cases, a remarkable internal cancellation between its “two-correlation-line” addends.     

Quasi-two-dimensional Bose–Einstein condensates with spatially modulated cubic–quintic nonlinearities

We investigate exact nonlinear matter wave functions with odd and even parities in the framework of quasi-two-dimensional Bose–Einstein condensates (BECs) with spatially modulated cubic–quintic nonlinearities and harmonic potential. The existence condition for these exact solutions requires that the minimum energy eigenvalue of the corresponding linear Schrödinger equation with harmonic potential is the cutoff value of the chemical potential λ. The competition between two-body and three-body interactions influences the energy of the localized state. For attractive two-body and three-body interactions, the larger the matter wave order number n, the larger the energy of the corresponding localized state. A linear stability analysis and direct simulations with initial white noise demonstrate that, for the same state (fixed n), increasing the number of atoms can add stability. A quasi-stable ground-state matter wave is also found for repulsive two-body and three-body interactions. We also discuss the experimental realization of these results in future experiments. These results are of particular significance to matter wave management in higher-dimensional BECs.     

Nucleation of crystalline phases of water in homogeneous and inhomogeneous environments

We employ two-body and three-body bond-orientational order-parameters, in conjunction with non-Boltzmann sampling to calculate the free energy barrier to nucleation of crystalline phases of water. We find that, as the coupling between the successive peaks of the direct correlation function increases, the free energy barrier to nucleation decreases. On this basis we explain the important parameters that govern the nucleation rate involving crystalline phases of water in different homogeneous and inhomogeneous environments, giving a "unified picture" of ice nucleation in water.     

Three-body entanglement induced by spontaneous emission in a three two-level atoms system

We study three-body entanglement induced by spontaneous emission in a three two-level atoms system by using the entanglement tensor approach. The results show that the amount of entanglement is strongly dependent on the initial state of the system and the species of atoms. The three-body entanglement is the result of the coherent superposition of the two-body entanglements. The larger the two-body entanglement is, the stronger the three-body entanglement is. On the other hand, if there exists a great difference in three two-body entanglement measures, the three-body entanglement is very weak. We also find that the maximum of the two-body entanglement obtained with nonidentical atoms is greater than that obtained with identical atoms via adjusting the difference in atomic frequency.     

Coherence of Disordered Bosonic Gas with Two-and Three-Body Interactions

We theoretically and numerically investigate the coherence of disordered bosonic gas with effective two-and three-body interactions within a two-site Bose-Hubbard model.By properly adjusting the two-and three-body interactions and the disorder,the coherence of the system exhibits new and interesting phenomena,including the resonance character of coherence against the disorder in the purely two-or three-body interactions system.More interestingly,the disorder and three-body interactions together can suppress the coherence of the purely three-body interactions system,which is different from the case in which the disorder and two-body interactions together can enhance the coherence in certain values of two-body interaction.Furthermore,when two-or threebody interactions are attractive or repulsive,the phase coherence exhibits completely different phenomena.In particular,if two-or three-body interactions are attractive,the coherence of the system can be significantly enhanced in certain regions.Correspondingly,the phase coherence of the system is strongly related to the effective interaction energy.The results provide a possible way for studying the coherence of bosonic gas with multi-atoms' interactions in the presence of the disorder.     

Information on three-body interactions from inversion of the energy equations

The inversion of the three energy equations, i.e. for the nuclear total energy, the sum of occupied single-particle state energies and the saturation condition, using the experimental data in ¹⁶O and ⁴⁰Ca, is carried out to determine whether three-body effective interactions are necessary in addition to density independent and dependent two-body interactions. In order to fit the data both in a non-relativistic and a relativistic framework, the three-body interaction energy is found to be large and repulsive. We also show that density-dependent two-body effective interactions, which are another requisite in the non-relativistic potential theory, are not necessarily needed in the relativistic mean field framework but allow to increase the effective nucleon mass.