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If <math>\phi(r)</math> was zero for all r - i.e., if the molecules did not exert any influence on each other, then g(r) = 1 for all r. Then from (1) the mean local density would be equal to the mean density <math>\rho</math>: the presence of a molecule at O would not influence the presence or absence of any other molecule and the gas would be ideal. As long as there is a <math>\phi(r)</math> the mean local density will always be different from the mean density <math>\rho</math> due to the interactions between molecules.
[[File:Lennard-Jones Radial Distribution Function.svg|thumb|500px|[[Lennard–Jones potential|Lennard-Jones fluid]] at <math>T^* = 0.71, \; n^* = 0.844</math>.]]
When the density of the gas gets higher, the so called low-density limit (2) is not applicable anymore because the molecules attracted to and repelled by the molecule at O also repel and attract each other. The correction terms needed to correctly describe g(r) resemble the [[virial equation]], which is an expansion in the density:
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