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The direct evaluation of the configurational partition function of a liquid is very difficult because of the complicated dependence of the potential energy in the liquid.For this reason a formalism of distribution function or correlation function is conveniently adopted in the liquids.

Where the correlation function is written as $ h(R)=g(R)^s-1\ $. and again correlation function written as a dimensionless function as $ g^{(s)}$ = $\large \frac{n^{(s)}}{n^s}$.

In the right hand side of this equation, why do we use brackets in the power of the nominator but do not use brackets in the power of denominator?

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It would help if you provide some reference for that notation. I don't get what the exponent in the first formula means. Further, you mention "direct correlation function" in the title, but it's not in the question body. –  leonbloy Jan 4 '13 at 17:03
BTW, your $g(R)$ is this: en.wikipedia.org/wiki/Radial_distribution_function –  leonbloy Jan 4 '13 at 17:08

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