Statistical fluctuations of the number of neutrons in a pile

The theory of the statistical fluctuations in a pile is extended to the space dependent case, and gives the fluctuations of the number of neutrons in a cell of the core or reflector of the pile. This number changes through elementary processes occurring at random, which are, capture, source, fission and scattering. Of all these processes, fission is the only one which changes more than one neutron at a time and so is responsible of the deviation of the fluctuations from a Poisson law. The importance of this deviation depends on the dimensions of the cell compared to the slowing down length. When the dimensions are small, the fluctuations close to a Poisson law. (author)