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 $a_s\to \pm \mathrm{\infty }$. 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.