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)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \gamma =2(19-{\frac {B_{4}}{V^{3}}})\approx 1.270463}

and (Eq. 8)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \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.