  It is well known that in 1D the cross section of a point scatterer increases
along with the scatterer's strength (potential). In this paper we show that
this is an exceptional case, and in all the other cases, where a point defect
has a physical meaning, i.e., 0<d<1 and 1<d<=2 (d is the dimensions number),
the cross section does not increase monotonically with the scatterer's
strength. In fact, the cross section exhibits a resonance dependence on the
scatterer's strength, and in the singular 2D case it gets its maximum value for
an infinitely weak strength. We use this fact to show that two totally
different generalized functions can describe exactly the same physical entity
(the same scatterer).
