Further Properties of the Radial Distribution Function

From the definition of g R it follows that the average number of particles in a spherical shell of radius R (from a center of a given particle) and width dR is 

The quantity Ncjh(Rm) may be referred to as the coordination number of particles, computed for the particular sphere of radius R. A choice of o Rm 2a will give a coordination number that conforms to the common usage of this concept. There exist other methods of defining the concept of coordination number, which are summarized and discussed by Pings (1968). 

A function related to the pair correlation function is the potential of average force (and torque), defined by  

We henceforth specialize to spherical particles. A similar treatment can be carried out for the more general case of rigid particles, but this will be of no use to us. 

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