The exponential transform is reviewed, with emphasis on its use as a guide to effective importance sampling in the solution of; the Boltzmann equation by Monte Carlo methods. Contributions of various workers are assembled, along with numerical results. Special consideration is given to approximate forms and to effective practical methods. Problems related to negative effective cross sections, tracking across discontinuities, directional biasing in inhomogeneous media, and high variance in back-scattered components are specifically treated.
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