  In the kinetic theory of dense fluids the many-particle collision bracket
integral is given in terms of a classical collision operator defined in the
phase space. To find an algorithm to compute the collision bracket integrals,
we revisit the eigenvalue problem of the Liouville operator and re-examine the
method previously reported[Chem. Phys. 20, 93(1977)]. Then we apply the notion
and concept of the eigenfunctions of the Liouville operator and knowledge
acquired in the study of the eigenfunctions to obtain alternative forms for
collision integrals. One of the alternative forms is given in the form of time
correlation function. This form, on an additional approximation, assumes a form
reminiscent of the Chapman-Enskog collision bracket integral for dilute gases.
It indeed gives rise to the latter in the case of two particles. The
alternative forms obtained are more readily amenable to numerical simulation
methods than the collision bracket integras expressed in terms of a classical
collision operator, which requires solution of classical Lippmann-Schwinger
integral equations. This way, the aforementioned kinetic theory of dense fluids
is made more accessible by numerical computation/simulation methods than
before.
