Effective-range description of a Bose gas under strong one- or   two-dimensional confinement
  We point out that theories describing s-wave collisions of bosonic atoms confined in one- or two-dimensional geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries. 
Pascal Naidon, Eite Tiesinga, William F. Mitchell, and Paul S.   Julienne