Loosely bound states of three particles

F. Coester

Zheng Zhen, J. H. Macek

The adiabatic hyperspherical technique is applied to a three-body system interacting via a short-range potential. Analytical expressions for the effective hyper-radial potential have been obtained without explicit use of the two-body potential. Possible loosely bound states of the system have been analyzed quantitatively and the result confirms the prediction by V. Efimov (Yad. Fiz. 10, 107 (1969) [Sov. J. Nucl. Phys. 10, 62 (1970)]). At the same time, some new characteristics of the three-body system are obtained.

H.‐W. Hammer, Jin-Yi Pang, Akaki Rusetsky

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.

V.N. Efimov

Nicolas Douguet, Viatcheslav Kokoouline

Z. Chyliński

The hypothesis of an internal symmetry of quantum systems, presented in previous papers and recapitulated here, implies a modified geometrical interpretation of the nonrelativistic internal wave functions of loosely bound systems. This reinterpretation modifies the vertices of loosely bound composite particles and can be tested in elastic, inelastic, and dissociation processes. Three effects which follow from this hypothesis are analyzed.