In this work the authors solved the steady state neutron diffusion equation for a multi-layer slab assuming the multi-group energy model. The method to solve the equation system is based on an expansion in Taylor Series resulting in an analytical expression. The results obtained can be used as initial condition for neutron space kinetics problems. The neutron scalar flux was expanded in a power series, and the coefficients were found by using the ordinary differential equation and the boundary and interface conditions. The effective multiplication factor k was evaluated using the power method. We divided the domain into several slabs to guarantee the convergence with a low truncation order. We present the formalism together with some numerical simulations.

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In this work the latest developments a Monte Carlo simulator with continuous energy is reported. This simulator makes use of a sum of three probability distributions to represent the neutron spectrum. Two distributions have known shape, but have varying population of neutrons in time, and these are the fission neutron spectrum and the Maxwell-Boltzmann distribution. The third distribution has an a priori unknown and possibly variable shape with time and is determined from parametrizations of Monte Carlo simulation. In this work the possible neutron-matter interactions are simulated with exception of the up-scattering of neutrons. In order to preserve the thermal spectrum, neutrons are selected stochastically as being part of the thermal population and have an energy attributed to them taken from a Maxwellian distribution, such an approximation is valid due to the fact that for fast neutrons up-scattering occurrence is irrelevant, being only appreciable at low energies. It is then shown how this procedure can emulate the up-scattering effect by the increase in the kinetic energy of the neutron population. Since the simulator uses tags to identify the reactions it is possible not only to plot the distributions by neutron energy, but also by the type of interaction with matter and with the identification of the target nuclei involved in the process.