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,

$B(r)=\beta {\mathrm{\Phi }}_{12}(r)-\gamma (r)+\ln (1+\gamma (r)-\beta {\mathrm{\Phi }}_2(r))$

where ${\mathrm{\Phi }}_{12}(r)$ is the pair potential, $\gamma (r)$ is the indirect correlation function, and $\beta =1(/k_{B}T)$, where $k_B$ 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)