Three-particle Bound State Research Articles

Three-particle quantization condition in a finite volume: 1. The role of the three-particle force

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory formalism allows us to explicitly investigate the role of the three-particle force. Moreover, we discuss relaxing the unitary limit of infinite scattering length and demonstrate a smooth transition from the weakly bound three-particle state to a two-particle bound state of a particle and a deeply bound dimer.

Applying the relativistic quantization condition to a three-particle bound state in a periodic box

Using our recently developed relativistic three-particle quantization condition, we study the finite-volume energy shift of a spin-zero three-particle bound state. We reproduce the result obtained using non-relativistic quantum mechanics by Meissner, Rios and Rusetsky, and generalize the result to a moving frame.

Progress in three-particle scattering from LQCD

We present the status of our formalism for extracting three-particle scattering observables from lattice QCD (LQCD). The method relies on relating the discrete finite-volume spectrum of a quantum field theory with its scattering amplitudes. As the finite-volume spectrum can be directly determined in LQCD, this provides a method for determining scattering observables, and associated resonance properties, from the underlying theory. In a pair of papers published over the last two years, two of us have extended this approach to apply to relativistic three-particle scattering states. In this talk we summarize recent progress in checking and further extending this result. We describe an extension of the formalism to include systems in which two-to-three transitions can occur. We then present a check of the previously published formalism, in which we reproduce the known finite-volume energy shift of a three-particle bound state.

Observation of Negative and Positive Trions in the Electrochemically Carrier-Doped Single-Walled Carbon Nanotubes

Understanding of electronic and optical features of single-walled carbon nanotubes (SWNTs) has been a central issue in science and nanotechnology of carbon nanotubes. We describe the detection of both the positive trion (positively charged exciton) and negative trion (negatively charged exciton) as a three-particle bound state in the SWNTs at room temperature by an in situ photoluminescence spectroelectrochemistry method for an isolated SWNT film cast on an ITO electrode. The electrochemical hole and electron dopings enable us to detect such trions on the SWNTs. The large energy difference between the singlet bright exciton and the negative and positive trions showing a tube diameter dependence is determined by both the exchange splitting energy and the trion binding energy. In contrast to conventional compound semiconductors, on the SWNTs, the negative trion has almost the same binding energy to the positive trion, which is attributed to nearly identical effective masses of the holes and electrons.

Quantum cluster expansion study of BEC in three-component Fermi gas

We study the system of a mixture of interconvertible monomers, dimers and trimers in a three-component ultracold Fermi gas, where dimers and trimers are formed in a two- and three-particle bound state, respectively. We use the Lee–Yang quantum cluster expansion method to calculate the grand partition function and estimate the transition temperature of Bose–Einstein condensation (BEC) of the dimers. We point out that provided the number density of particles is above the critical value, the dimers show a BEC transition at a finite temperature.

Positronium-Ion Decay

We present a precise theoretical prediction for the decay width of the bound state of two electrons and a positron (a negative positronium ion), Gamma(Ps-)=2.087 963(12)/ns. We include O(alpha2) effects of hard virtual photons as well as soft corrections to the wave function and the decay amplitude. An outcome of a large-scale variational calculation, this is the first result for second-order corrections to a decay of a three-particle bound state. It will be tested experimentally in the new positronium-ion facility in Garching in Germany.

Coordinate asymptotic behavior of the radial three-particle wave function for a bound state involving two charged particles

The asymptotic expression for the radial component of the wave function for a three-particle bound state involving two charged particles is derived in an explicit form. This expression contains a three-particle asymptotic normalization factor C(φ), where φ is a hyperangle in the six-dimensional space of intrinsic coordinates of the three-particle system. The resulting expressions are used to analyze the asymptotic behavior of the wave functions for the 9Be nucleus that were calculated within the α + α + n three-particle model for various forms of the an potential. A comparison of the asymptotic expression derived here and the asymptotic expressions for model wave functions makes it possible to extract C(φ) values, which turned out to be sensitive to the form of αn interaction. This permits deducing information about two-particle interaction from a comparison of the theoretical values of C(α) with their phenomenological counterparts found from an analysis of experimental differential cross sections for relevant nuclear reactions.

Exact solutions of generalized three-particle Bargmann-Wigner equations in the strong-coupling limit

Starting from a non-linear isospinor-spinor field equation, generalized three-particle Bargmann-Wigner equations are derived. In the strong-coupling limit, exact solutions of these equations are obtained. This will be demonstrated for a special class ofJ=1/2 bound-state solutions which are calculated in the rest frame of the three-particle bound state.

Variational two- and three-particle solutions of the relativistic Yukawa model.

The variational method, within the Hamiltonian formalism of quantum field theory, is used to derive momentum space wave equations for any number of fermions interacting via a massive scalar field. These coupled equations are shown to be exactly solvable in the limit of fixed fermions. Approximate solutions are given in the two- and three-particle bound state case for various mass combinations and various strengths of the coupling of the fermion and scalar fields.

Three-particle Coulomb on-shell vertex functions. Behavior of the amplitude for simultaneous transfer of two charged particles in the vicinity of the nearest singularity in cos ?

The connection between the on-shell vertex function (OSVF) and the asymptotic normalized coefficient of the three-particle wave function of the bound system in the configuration space is found. The explicit form of the leading singular term of the OSVF and its Faddeev component for decay of the three-particle bound state into three charged particles is established. An expression is found for the leading singular term of the exact (in the model of four charged particles) amplitude of sub-Coulomb binary reactions in the vicinity of the nearest singularity.

Binding of two fermions with a third different particle by a point interaction

It is shown that two Fermi particles having masses m 1 and a third different particle with mass m 2 interacting via point forces create a three-particle bound state at a sufficiently small ratio m 2 m 1 .

The Z = 0 condition for a three-particle bound state

In an earlier work it was pointed out in the framework of a model field theory that the vanishing of wave function- and vertex-renormalization constants was not a sufficient condition to make an elementary particle equivalent to a three-particle bound state. In the present paper, this result is attributed to the lack of certain direct couplings amongst the multiple channels of the model. It is demonstrated that with the introduction of suitable extra couplings, the Z = 0 condition is sufficient for the compositeness of a particle in the model.

Separable expansion of potential in multidimensional space. Three-body problem

The problem of the three-particle bound state is solved by the method of separable expansion of the total potential V = V/sub 12/ + V/sub 23/ + V/sub 31/ in the six-dimensional space. In a concrete calculation for a sum of two-body potentials of the Gaussian type, a rapid convergence of the proposed procedure is established. The wavefunction of the system considered is presented as a series in matrix elements of the potential V, which are explicitly calculated in the given case. 1 table. (RWR)

Three-particle ground state: Sensitivity to equivalent interactions

The sensitivity of a three-particle bound state to the choice among a variety of typical potentials each giving the same low energy scattering parameters and bound state energies is studied. As a simple test of this model dependence of the binding energy of the LAMBDA -d bound system is obtained using the separable Yamaguchi potential for a range of values for the scattering length and effective range.

New Reduction of the Faddeev Equations and Its Application to the Pion as a Three-Particle Bound State

A new separation of the angular momentum in the Faddeev equations is given. This separation makes use of the relative angular momentum of two particles, which is combined with the angular momentum of the third particle in the over-all center-of-mass system. With the assumption that the two-body amplitudes factorize in the initial and final momenta, the Faddeev equations are reduced to a coupled set of integral equations in one variable. This set is furthermore simplified in the case of identical particles to only one integral equation. Thereby the statistics is correctly taken into account. The resulting equation is used to investigate possible bound states of three pions with total angular momentum zero, isospin one, and odd parity. The two-body amplitude which determines the kernel is approximated by the isospin-zero, $s$-wave effective-range formula of Chew and Mandelstam. Use is also made of relativistic kinematics. The pion is found as a bound state of three pions in this model. The outcome is, however, strongly dependent on a physical cutoff parameter in the two-body form factor. As a result a detailed investigation of the form factor is desirable.