Hard spheres
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Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong repulsion that atoms and spherical molecules experience at very close distances.
[edit] Formal definition
Hard spheres of diameter σ are particles with the following pairwise interaction potential:
where 
and 
are the positions of the two particles.
[edit] Virial coefficients
The first three virial coefficients for hard spheres can be determined analytically
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= 
= 
= 
Higher-order ones can be determined numerically using Monte Carlo integration. We list
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= 
= 
[edit] Literature
- J. P. Hansen and I. R. McDonald Theory of Simple Liquids Academic Press, London (1986)
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