ON THE PRINCIPLE OF INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY; I: ONE-DIMENSIONAL CASE,
RAND CORP SANTA MONICA CALIF
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Consideration is given to a one-dimensional version of the reflection and transmission of neutrons, and the phenomenon of critical mass. Although the effects of fission, capture and forward and backward scattering are considered, collisions between neutrons are not taken into account. The basic model is stochastic, with standard transport theory derived on the basis of expected values. As the explicit form of the higher moments indicates, an expected value theory yields a quite inadequate view of the distribution of reflected and transmitted neutrons in the neighborhood of critical mass. Some numerical results describing these distributions obtained from the solution of forty simultaneous nonlinear differential equations are presented.