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 < R < 1. It is here argued that this conventional sampling method, which basically assumes that the scattering medium may be regarded as a homogeneous continuum, may be erroneous unless lambda is much larger than the average distance d(nn) between nearest neighbour scatterers, estimated by d(nn) = n(-1/3). An alternative sampling method (M sampling) is proposed with a fixed step length D = d(nn) and a finite probability I = 1-exp(-D/lambda) of a single elastic or inelastic scattering event at the end of each step. According to this method, conventional sampling may exaggerate the number of events per unit path length; the corrected mean free path between events is found to be lambda(c) = D/(1-exp(-D/lambda)). The correction is substantial when lambda is comparable to or smaller than D, in practice for very low energy particles in liquids and solids. Consequently, quantities like stopping power may then be overestimated, while transport mean free path may be underestimated. In the opposite limit lambda >> 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.

Ämnesord

NATURVETENSKAP  -- Kemi -- Fysikalisk kemi (hsv//swe)

NATURAL SCIENCES  -- Chemical Sciences -- Physical Chemistry (hsv//eng)

Nyckelord

Track simulation

Mean free path

Step length

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