Asymptotic phase shifts and Levinson theorem for 2D potentials with   inverse square singularities
  The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the singularity strength of the potential. For the m-wave phase shift the asymptotic behaviour is calculated for short wavelengths. 
Denis D. Sheka, Boris A. Ivanov, and Franz G. Mertens