Abstract: In this paper, we present a quantum statistical
mechanical formulation from our recently analytical expressions for
partial-wave transition matrix of a three-particle system. We report
the quantum reactive cross sections for three-body scattering
processes 1+(2,3)→1+(2,3) as well as recombination
1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The
analytical expressions of three-particle transition matrices and their
corresponding cross-sections were obtained from the threedimensional
Faddeev equations subjected to the rank-two non-local
separable potentials of the generalized Yamaguchi form. The
equilibrium quantum statistical mechanical properties such partition
function and equation of state as well as non-equilibrium quantum
statistical properties such as transport cross-sections and their
corresponding transport collision integrals were formulated
analytically. This leads to obtain the transport properties, such as
viscosity and diffusion coefficient of a moderate dense gas.