Soft-core mean spherical approximation

Junzo Chihara (along with Madden and Rice) extended the Percus Yevick equation for Lennard-Jones systems to provide a soft-core mean spherical approximation, the SMSA,

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(r) = \beta \Phi_2 (r) - \gamma (r) + \ln \left( 1 + \gamma (r) - \beta \Phi_2 (r) \right)}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_2 (r)} is the pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma (r)} is the indirect correlation function, and $\beta =1(/k_{B}T)$, where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} is the Boltzmann constant.

References

1. Junzo Chihara "Integral Euqations for Fluids with Long-Range and Short-Range Potentials - Application to a Charged Particle System", Progress of Theoretical Physics, 50 pp. 409-423 (1973)
2. Junzo Chihara "Integral Equations for Neutral and Charged Quantum Fluids Including Extension of the Percus-Yevick Equation" Progress of Theoretical Physics, 50 pp. 1156-1181 (1973)
3. William G. Madden and Stuart A. Rice "The mean spherical approximation and effective pair potentials in liquids", Journal of Chemical Physics 72 pp. 4208-4215 (1980)