Long jumps in the strong-collision model

The jump-length probability distribution for a classical particle diffusing in a periodic potential is calculated in the framework of a strong-collisi on model, where each collision of the particle with the thermal bath reequi librates the velocity. Exact numerical results are obtained by the matrix-c ontinued-fraction method, and two different analytical approximations are d eveloped. In the first approximations it is assumed that an activated parti cle is always retrapped in the cell where it suffers the first collision; i n the second approximation it is assumed that only the collisions giving a final total energy which is lower than the activation barrier are effective for retrapping. This second analytical approximation is in excellent agree ment with the numerical data.