  Intermediate energy scale physics plays a very important role in
non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this
article we obtain the universal scaling relations for the generalized
reflection coefficient, i.e., the fraction of atoms scattered out of the
initial state, at intermediate energies scales. These intermediate energies are
larger than the trap frequency, but necessarily smaller than the effective
range of the inter-atomic potential. For harmonically confined one and two
dimensional geometries, whenever the energy of the system is commensurate with
a transverse energy level, it is shown that the system becomes non-interacting.
For energies close to a transverse energy level, the reflection coefficient and
scattering dynamics take on universal scaling forms, only depending on the
difference between the energy of the particles and the transverse energy level.
In this article, the universal power law behaviors of these scattering
observables are obtained.
