Determination of the critical condition by the multiple collision method, (2)

The previous work was an attempt to determine analytically the critical condition of a homogeneous slab by the multiple collision method or the Monte Carlo approach, where the elementary processes of the neutron were followed statistically in order of time. The present paper is concerned with a further development of the multiple collision method where some refined techniques are used. The critical condition for the monoenergetic neutron has been obtained by seeking the pole of a Laplace transform of the total number of neutrons which varies with time. The so-called c, the mean number of secondaries per collision, has been calculated within an error less than 10^-5 for every critical system with finite thickness. The asymptotic total number of neutrons in the system after a sufficiently long time has also been derived. Finally, comparing the derived critical condition with that in the diffusion theory, the extrapolation distance has been evaluated accurately for the system with thickness less than several times of the neutron mean free path. (author)