Expansion of the classical differential cross section in a Fourier series

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Abstract
The procedure for expanding the classical differential cross sections I(ϑ) determined from a classical trajectory study in a Fourier sine series is developed. Simple expressions for the uncertainty in the differential cross section are presented. A smoothing technique, which utilizes a Gaussian filter, guarantees that I(ϑ) is everywhere nonnegative. This is recommended as the best way to display a differential cross section computed from a finite number of reactive trajectories. The results are applied to a model system and compared with the histogram technique.