INDEX overlap densities

For field-based measures and overlap of electron density functions then the Carbo index can be used (49), which is equivalent to the Cosine coefficient. 

Thin film interference arises when multiple reflections, from index of refi action variations, overlap in space and time and waves superpose. The connection with studies of shocked materials is that a shock wave moving through a transparent material represents an interface between an ambient density and a higher-density, and thus different refractive index, material. Ideally, there are two films produced, the shocked and the unshocked, with different refractive indices and the thickness of each change with time during passage of the shock. 

If the functions f and g are correlated, then C = 1. By omitting the factors -1 in numerator and denominator of Eq. [38], we obtain the index proposed by Carbo et al.226 The basic features of this parameter are contained in the numerator, which is essentially an overlap integral between f(t) and g(r). This integral with first-order density functions can be seen as the simplest example of a more general family of quantum similarity measures.23.236... 

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