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National Advisory Committee for Aeronautics, Technical Notes - Analytical Method for Determining Transmission and Absorption of Time Dependent Radiation Through Thick Absorbers - III - Absorbers with Radioactive Daughter Products

Matrix methods have been applied to the problem of calculating
transmission, reflection, and conversion to heat of time-dependent
nuclear radiations (references 1 and 2). The analyses that were
made, however, assumed single-step decay of induced radioactive
atoms to stable ones. Many isotopes decay in several steps to
stable materials, emitting a variety of types of radiation during
the process. The transuranic radioactive isotopes are examples of
multistep decay elements, as are certain isotopes of elements
commonly used as structural materials such as iron and copper.

The matrix methods of references 1 and 2 developed at the
NACA Lewis laboratory were therefore extended to include the multi-
step decay processes. The addition of these processes to the prob-
lems considered in references 1 and 2 makes the defining equations
quite lengthy even thong: matrix notation is used. In order to
facilitate presentation, tensornotation and the summation conven-
tion, when feasiblejare used.

The assumption is made in references 1 and 2 that the source
intensity is unaffected by back-reflected radiation from the
absorber; that is, the time-dependency of the source is assumed
to be known explicitly for all times of interest. In practice,
however, the radiation back-reflected to the source includes radi-
ation from the radioactivities vithin the absorber. Thus, although
it is unlikely that the source will be noticeably affected by radi-
ation reflected in the literal sense, enough of the aforementioned
radiation originating within the absorber may quite possibly reach
the source to induce a new radioactivity therein. If the contri-
bution of the new activity to the total source intensity is not
negligible, the time-dependecy of the radiation from the source
will be significantly altered.

The change in source intensity as a function of time des-
cribed in the preceding paragraph can be quantitatively calculated
by methods shown herein.