Hierarchical fitting and scaling models for rotationally inelastic cross sections

A new method of scaling inelastic cross sections is presented which uses an intermediate-level parametrization of the collision dynamics. By expressing the scattering matrix as exp[-iB] and approximating B with a parametrized functional form, this procedure yields a unitary scaled S matrix and incorporates infinite-order rotational coupling into the scaled results. The inclusion of high order collision dynamics enables the scaled cross sections to exhibit physical behavior which is substantially more realistic and flexible than that allowed by traditional fitting methods. The intermediate level scaling procedure accurately produces complete matrices of rotationally inelastic cross sections for He-HD scattering generated from subsets of input cross sections.