The exact solution for the Percus Yevick integral equation for hard spheres
was derived by M. S. Wertheim in 1963 Ref. 1 (See also Ref. 2)
(and for mixtures by in Lebowitz 1964 Ref. 3).
The direct correlation function is given by (Ref. 1 Eq. 6)
where
and R is the hard sphere diameter.
The equation of state is (\cite{PRL_1963_10_000321} Eq. 7)
Everett Thiele (1963 \cite{JCP_1963_39_00474}) also studied this system,
resulting in (Eq. 23)
where (Eq. 24)
and
and
and where .
The pressure via the pressure route (Eq.s 32 and 33) is
and the compressibility route is
References
- [PRL_1963_10_000321]
- [JMP_1964_05_00643]
- [PR_1964_133_00A895]