The collision energy and the semiaxes of the hard ellipsoid are relate
d by an analytical expression to obtain the parameters K, and either t
he range of the potential, alpha, or the anisotropy of the potential,
delta, for the potential model V(r, theta) = Ke(-alpha r)(1 + delta(2)
cos(2) theta). The hard shape theory has been used to optimize the se
miaxes of the ellipsoid by fitting cross sections to quantum results.
This inversion procedure showed an average error of 7% in the alpha or
delta parameter and about 15% in the K parameter.