Hansen-Goos hard sphere equation of state

The Hansen-Goos hard sphere equation of state is given by (Eq. 5):

$\rho k_{B}T{\kappa }_T=\frac{(1-\eta {)}^4}{(1+2\eta -\gamma {\eta }^3+\delta {\eta }^4{)}^2}$

where (Eq. 7)

$\gamma =2(19-\frac{B_4}{V^3})\approx 1.270463$

and (Eq. 8)

$\delta =-\frac{3}{7}+\frac{5\gamma }{8}+\frac{4}{7}\sqrt{1-\frac{21\gamma }{32}+\frac{105{\gamma }^2}{1024}}\approx 0.694605$

and where ${\kappa }_T$ is the isothermal compressibility, $\rho$ is the number density and $\eta$ is the packing fraction.