Kinetic Equation for a Dilute Gas with Short-Range Forces

The kinetic equation for a dilute gas with short-range forces is derived by a method which we believe to be physically more transparent than other methods. We first derive a density expansion for the correlation functions, the coefficients of which are functionals of $F_1$, the first distribution function. These functionals relax to time-independent functionals over a time interval $\tau$ (which we argue to be of the order of the duration of a collision) after a time ${\tau }_0$ (which is characterized by the phases) from the initial time. The functionals contain $F_1$ over the interval $\tau$ and therefore the resulting kinetic equation is non-Markoffian. The non-Markoffian behavior is removed by further expanding the correlation functions in a parameter that is the ratio of the duration of a collision to the mean free time. The results for the correlation functions are carried to first order and agree with those of other methods for configurations where the particles are interacting, and therefore lead to the same kinetic equation, but are otherwise different.