Invariant imbedding and radiation dosimetry V: finite order intensity of radiation in a target slab

Abstract

In a series of our papers invariant imbedding was used to derive the integro-differential and integral recurrence relations for the finite order scattering and transmission functions, the finite order X and Y functions, by which the diffusely reflected and transmitted intensities of finite order scattered radiation can be numerically computed. In the present paper, extending the Bellman-Krein-like recurrence relation for the Fredholm resolvent to the derivation of a modified decomposition formula, we show how to express the internal intensities of finite order radiation in terms of the finite order X, Y, f, and g functions. Then, once the finite order X and Y functions have been determined by the use of the preceding methods, making use of the integral recurrence relations for the finite order f and g functions, we can obtain the numerical solution of the finite order internal radiation field. Hence the absorbed dose distribution of finite order gamma radiation and neutron beams can be directly computed.