In attempting to develop a fluidlike model of plasma dynamics in a current sheet, kinetic effects due to chaotic non-adiabatic particle motion must be included in any realtistic description. Using drift variables described by the Kruskal averaging procedure, to construct distribution functions may provide an approach in which to develop the fluid description. However, the drift motion is influenced by abrupt changes in the value of the generalized first adiabatic invariant J. In this letter, we indicate how the changes in J derived from separatrix crossing theory can be incorporated into the drift variable approach to generating distribution functions. In particular, we propose a method to determine distribution functions for an ensemble of particles following interaction with the tail current sheet by treating the interaction as a scattering problem characterized by changes in the invariant.