  In a previous work of 2014 on a quantum system governed by the repulsive
Hamiltonian, the author proved uniqueness for short-range interactions
described by a scattering operator consisting of regular and singular parts. In
this paper, the singular part is assumed to have much stronger singularities
and the same uniqueness theorem is proved. By applying the time-dependent
method invented by Enss and Weder in 1995, the high-velocity limit for a wider
class of the scattering operator with stronger singularities also uniquely
determines the interactions of a multi-dimensional system.
