  Different from the usual harmonic oscillator, the time-decaying harmonic
oscillator accelerates particles and generates scattering states. We study one
of the multidimensional inverse scatterings in this two-body quantum system
perturbed by short-range potential functions that have a bounded part and a
locally singular part. Applying the Enss--Weder time-dependent method, we prove
that the scattering operator determines the potential functions uniquely.
