On the use of the average chord length

The average chord length has been traditionally used in reactor physics for the estimation of escape probabilities for bodies of small optical size and in elementary formulas in shelfshilding analysis. In this work, the role of the average chord length in the estimation of transmission probabilities of homogeneous bodies is analyzed and the correct chord length distribution is derived from the incoming angular flux distribution. The concept of average projection area is used to derive a generalization of Dirac's original formula to the case of an angular flux uniformly entering a non-convex body