Time asymptotic behavior of the burnett correlation function in the Lorentz model

For a Lorentz gas of hard spheres an exact formula is obtained that relates the coefficient $w$ in the asymptotic behavior of the Burnett correlation function $W(t)\approx wt^{-d/2}$ to the integral of the equilibrium two-body correlation function. The results of calculation of the asymptotic behaviors of the velocity correlation functions in the framework of the microscopic approach are compared with the conclusions of the phenomenological mode coupling theory.