Universal lowenergy properties of three twodimensional bosons
Abstract
Universal lowenergy properties are studied for three identical bosons confined in two dimensions. The shortrange pairwise interaction in the lowenergy limit is described by means of the boundary condition model. The wave function is expanded in a set of eigenfunctions on the hypersphere, and the system of hyperradial equations is used to obtain analytical and numerical results. Within the framework of this method, exact analytical expressions are derived for the eigenpotentials and the coupling terms of hyperradial equations. The derivation of the coupling terms is generally applicable to a variety of threebody problems provided the interaction is described by the boundary condition model. The asymptotic form of the total wave function at a small and a large hyperradius ρ is studied, and the universal logarithmic dependence ∼ln^{3}ρ in the vicinity of the triplecollision point is derived. Precise threebody binding energies and the (2+1) scattering length are calculated.
 Publication:

Physical Review A
 Pub Date:
 October 2006
 DOI:
 10.1103/PhysRevA.74.042506
 arXiv:
 arXiv:physics/0606013
 Bibcode:
 2006PhRvA..74d2506K
 Keywords:

 36.10.k;
 03.65.Ge;
 21.45.+v;
 34.50.s;
 Exotic atoms and molecules;
 Solutions of wave equations: bound states;
 Fewbody systems;
 Scattering of atoms and molecules;
 Physics  Atomic Physics
 EPrint:
 30 pages with 13 figures