Study of neutron migration ion a multiplying medium according to the intensity and distribution of absorptions

The calculation of the neutron migration area assumes a simple form in two limiting cases: the case of pure slowing down and the case of purely thermal diffusion. In a thermal reactor, through these two schemes can be more or less applied at the start and finish of the life of the neutron, we must also consider a transition zone, in which the phenomena are obviously far more complex. How is the link to be made, and in what way does it depend on the distribution law of the captures? Two different methods have been developed to solve this problem. In the first one, the neutron is tracked through successive collisions, and attention is particularly concentrated on the variation of the absorption probability; in the second one, the spectrum is considered as a whole, the balance of neutrons arriving and disappearing at each velocity being written down. It is proved, moreover, that the two methods are based on the same formulation. The first one gives rise to interesting interpretations which permit a deep understanding of the physical phenomena; the second produces easier calculation, through the new thermalization operators developed at Saclay, The parameters of the problem are being studied successively (thermalization model, absorption law, variation law of the diffusion coefficient, geometrical parameters of the cell, relative importance of the leakages) For each of then, numerical applications are presented. (author)