Transmission?reflection problem with a potential of the form of the derivative of the delta function

Regarding the quantum mechanical transmission?reflection problem in one dimension with a potential of the form of the derivative of the Dirac delta function ?'(x) = d?(x)/dx, Christiansen et al recently found that, depending on how ?'(x) is interpreted, there can be a resonance which leads to partial transmission. This is in contrast to the earlier consensus that such a potential allows no transmission. The ?'(x) can be regarded as the narrow-width limit of a certain function ?'(x) of a finite range. Christiansen et al assumed a rectangular function for ?'(x). We examine various other forms and how the resonance depends on the shape of ?'(x). We also present some general observations related to the 'threshold anomaly'.