Increasing efficiency in Monte Carlo simulations by a killing-and-splitting strategy

We have derived a procedure which increases the efficiency of Monte Carlo simulations. It aims at special cases in ion-solid simulations where the probability of success becomes particularly small. Efficiency results from killing and splitting trajectories according to a certain importance figure assigned to a number of sites along the ion trajectory. A much simple case, however, is studied which, on the one hand, retains the essentials of ion-solid simulations, without, on the other hand, going into unnecessary complications.