History and evolution of buildup factors

The gamma-ray buildup factor is a term whose origin is lost in the mists of the early history of the Manhattan Project.' Its introduction stems from the observation that the calculations for the uncollided photons, i.e., those that have arrived at R without suffering any collisions, are usually a relatively simple matter, involving only an exponential kernel. The buildup factor is then a multiplicative factor, which corrects the answer that is proportional to the uncollided flux density to include the effects of the scattered photons. This paper further summarizes and traces efforts since 1954 at calculating and mathematically defining buildup factors.