Space-dependent Calculations Of The Bohnel Multiplicity Moments For Cylinders

In a recent paper, presented at previous INMM conferences, a general transport theory calculation of the factorial moments of the number of neutrons emitted spontaneously from a sample were derived. In contrast to the original derivations, made in the so-called point model, in thetransport model the spatial and angular dependence of the internal fission chain is taken into account with a one-speed transport theory treatment. Quantitative results were given for a spherical item, and the bias of the point model what regards the estimation of the fission rate, as compared to the more exact space-dependent model, was estimated as a function of the size of the sphere and the alpha factor. In the present work the formalism, as well as the quantitative work, is extended to the treatment of items with cylindrical shapes, which are more relevant in many practical applications. Results are presented for both "square", as well as for flat and tall cylinders. This way the differences between the cylinder and the sphere on one hand, and that between the various cylinder shapes can be estimated. The results show that the bias depends on the geometry of the cylinder quite moderately, but similarly to the case of the sphere, the bias of the point model is quite significant for larger item sizes and alpha values, as well as it is non-conservative (underestimates the fissile mass).