On the sampling of step length in Monte Carlo simulation of trajectories with very small mean free path

In an event-by-event simulation of the trajectory of a particle moving in matter it is usually assumed that the probability for the particle to travel a distance s without interaction is exp(-s/lambda), where lambda = (n . sigma)(-1) is the total mean free path, n the number of scatterers per unit volume and sigma the total cross section per scatterer. The step length s between scattering events is then generated by means of a sampling formula s = -lambda ln(1-R), where R a random number in the interval 0 > D, conventional and M sampling produce the same result. Present results further indicate that conventional sampling using the corrected total mean free path lambda(c) is a good approximation to M sampling.

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