Abstract
In this paper, Buckingham's theorem on physically similar systems is applied for the first time to the derivation of interpolation curves of numerical data. A simplified dependence of the curves on a limited number of effective dimensionless parameters is found by a novel approach. In particular, the method is applied to Monte Carlo modelling and the calculation is considered of the backscattering coefficient η from a general substrate in the elastic regime. A single dimensionless backscattering parameter is introduced and a simple scaling law is determined, indicating how the configuration of the many variables involved can eventually change without affecting the result. The validity of the law is demonstrated in the 5 to 100 keV energy range, with substrate thicknesses ranging from 10 to 21000A˚and for all the substrates of the periodic table.
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