Physics of Atomic Nuclei

Low-energy properties of three resonantly interacting particles

V.N. Efimov

Published Apr 1, 1979• 43 citations

Abstract

The scattering and bound states of a system of three resonantly interacting particles are analyzed. The characteristics of the scattering and the bound states are shown to be independent of the particular nature of the two-particle forces; instead, these characteristics are governed simply by the fact that resonances occur. The resonances lead to an effective long-range interaction among the three particles. The physical characteristics of the system obey a scaling law. Explicit equations are derived for the particle pair scattering length, for the particle pair scattering cross section at and above the threshold for disintegration of the three-particle system, and for the ternary-collision amplitude at zero energy. The properties of the system are compared with those of a system of two resonantly interacting particles.

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Physics of Atomic Nuclei

Low-energy properties of three resonantly interacting particles

V.N. Efimov

Published Apr 1, 1979• 43 citations

OpenAlex

Abstract

Related papers

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arXiv:2101.12654Physical Review CSep 8, 20207 citations

The effect of the force range

{\mathit{r}}_{0}

on an effective long-range interaction in a system of three resonantly interacting particles is considered. By employing a boundary-condition approach, it is explicitly shown that the account of the force range gives rise to a correction

{\mathit{r}}_{0}

{\mathit{R}}^{3}

in the effective long-range interaction. The correction is universal (i.e., independent of detail structure of the force), and is attractive for symmetric

{0}^{+}

three-particle states. The effect of the correction on the well-known correlation between the three-particle binding energy and the particle-pair scattering length is calculated.

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass

m

and a particle of the mass

m_1

with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio

m/m_1

for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at

m/m_1 \\ge \\lambda_1 \\approx 8.17260

and

m/m_1 \\ge \\lambda_2 \\approx 12.91743

, respectively. For

m/m_1 \\alt \\lambda_1

and

m/m_1 \\alt \\lambda_2

, the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.