A Generalization of the Dirac Chord Method to Include Charged-Particle Phenomena

The Dirac chord method is applied to the calculation of the escape probability of heavy charged particles from a uniform isotropic source of arbitrary convex geometry. This leads to the distribution of path lengths traveled by particles before escaping from the source. The path-length distribution, which is a function only of the Dirac chord distribution, may be used to average nuclear characteristics over the source geometry. As an illustration, the standard formula for the neutron-escape probability is reproduced. Expressions are then derived for the spectrum and energy self absorption of heavy-charged-particle sources. Specific results for spherical, slab, and cylindrical sources are obtained with the assumption that the range is proportional to an arbitrary power of the particle energy.