A model study on atom-atom interactions with large scattering length in quasi-two dimensional traps

We carry out a model study on two-atom interactions and bound states in quasi-two dimensional traps. The interactions are modeled by two-parameter potentials with parameters being the range r(0) and the s-wave scattering length a(s). We show that one can make use of two forms of finite-range model potentials: one for a(s) > 0 and the other for a(s) < 0. Both potentials reduce to same form in the limits a(s) -> +/-infinity. We investigate into the dependence of the binding energies and the wave functions of two-atom trap-bound states on a(s) and r(0). In particular, we study the effects of a(s) ranging from large negative to large positive values on the bound state properties. Our results show that long-range interactions with infinite scattering length significantly alter the ground-state energy of the two atoms in a quasi-two or two dimensional trap. In contrast, short-range interactions can not significantly change the ground-state energy of two atoms in a 2D harmonic trap.