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.
Zolotaryuk, A., Christiansen, P. L., & Iermakova, S. V. (2006). Scattering properties of point dipole interactions. Journal of Physics A: Mathematical and General, 39(29), 9329-9338. https://doi.org/10.1088/0305-4470/39/29/023