Scattering properties of point dipole interactions

Abstract

The scattering properties of a three-parameter family of point dipole-like interactions constructed from a sequence of barrier-well rectangles are studied in the zero-range limit. Besides the real (unrenormalized) delta'-interaction, the derivative of Dirac's delta function, a whole family of point dipole interactions with a renormalized coupling constant are analysed. Depending on the parameter values, all these interactions being self-adjoint extensions of the one-dimensional Schrodinger operator are shown to be divided into four types: (i) interactions will full transparency, (ii) non-transparent interactions, (iii) partially transparent interactions acting effectively as a delta-interaction and (iv) interactions with partial transparency at discrete resonant values of the coupling constant.