Exact solution of the Percus Yevick integral equation for hard spheres

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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 (Ref. 1Eq. 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

  1. [PRL_1963_10_000321]
  2. [JMP_1964_05_00643]
  3. [PR_1964_133_00A895]