Song and Mason equation of state for hard convex bodies

The Song and Mason equation of state (EOS) for hard convex bodies is given by (Eq. 25 of Ref. 1):

$\frac{p}{\rho kT}\approx 1+\frac{\eta }{(1-\eta {)}^3}((1+3\alpha )-(2+3\alpha -3{\alpha }^2)\eta +(1+[{(\frac{B_4}{v_0^3})}_{HS}-12]\alpha -7{\alpha }^2){\eta }^2)$

where $\eta$ is the packing fraction, given by $\eta =\rho v_0$ where $v_0$ is the volume of one particle, and

$\alpha =\frac{RS}{3v_0}$

where $S$, the surface area, and $R$ the mean radius of curvature. ${(\frac{B_4}{v_0^3})}_{HS}$ is the fourth virial coefficient for the hard sphere model.

References

1. Yuhua Song and E. A. Mason "Equation of state for a fluid of hard convex bodies in any number of dimensions", Physical Review A 41 pp. 3121 - 3124 (1990)