Mathematical Verification of a Certain Monte Carlo Sampling Technique and Applications of the Technique to Radiation Transport Problems

The first section of this paper is a mathematical construction of a certain Monte Carlo procedure for sampling from the distribution The construction begins by defining a particular random variable λ. The distribution function of λ is developed and found to be identical to F(X). The definition of λ describes the sampling procedure. Depending on the behavior of Σ(x), it may be more efficient to sample from F(X) by obtaining realizations of λ than by the more conventional procedure described in the paper. Section II is a discussion of applications of the technique to problems in radiation transport where F(X) is frequently encountered as the distribution function for nuclear collisions. The first application is in charged particle transport where Σ(x) is essentially a continuous function of x. An application in complex geometries where Σ(x) is a step function, and changes values numerous times over a mean path, is also cited. Finally, it is pointed out that the technique has been used to improve the efficiency of estimating certain quantities, such as the number of absorptions in a material.