Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

48 Monte Carlo Particle Transport Methods: Neutron and Photon CalculationsIn general, from the computational point of view, one can choose from two basicallydifferent approaches. In the first case the energy is allowed to change continuously. Then,the uncertainties in the shape of the near-resonance part of the cross-section curve may causesignificant errors, especially since interpolation between different energies is a hard task.Similarly, problematic is the interpolation between different elements, and even variousisotopes of the same element may have significantly different cross-sections at the sameneutron energy.The other method is the use of the so-called multigroup treatment. Here, the energyrange of interest is artificially divided into several groups and the cross-sections are averagedover them. Needless to say, the more groups are used the more accurate results may beexpected. The fundamental problem with the multigroup treatment is that the cross-sectionsmust be averaged by the flux-energy curve, which is not known in advance. Anyhow, thepreparation of the multigroup cross-section libraries is a very difficult task and has its ownlarge literature. In the following we shall discuss only the pointwise cross-sections.Even in the pointwise (continuous energy) treatment, neutrons that have slowed downby a sequence of scattering events to equilibrium with the thermal motion of atoms arehandled in a separate group. These thermal neutrons either lose or gain energy during thescatterings, therefore, one can say that the "end" of slowing down is thermalization.Generally, neutrons whose energies are less than about 0.5 eV are called thermal neutrons.Classification and description of the neutron interactions are given in several textbooks,see e.g., References 20, 1, and 8.For the actual cross-sections, the reader is again advised to review the large compilations,such as the ENDF 3 0 and the Livermore 32 libraries.1. CaptureUsing a somewhat loose terminology one could say that capture of neutrons is thecounterpart of the absorption of photons. Really, in this process the history of the neutronis terminated — like that of the photon at a photoelectric interaction. Significant differencein the treatment arises only in coupled neutron-photon transport codes, since an importantkind of capture events is radiative capture, where the emission of a photon follows theabsorption of neutron.The cross-section for capture typically does not exceed a few percent of the scatteringcross-section. Radiative capture is, however, a more important reaction for thermal neutrons.For nuclides which have a capture resonance near the thermal region capture represents themain contribution to the total cross-section. The thermal capture cross-section of cadmiumfor example, is higher by a factor of more than 300, than the scattering cross-section.2. Elastic ScatteringIn an elastic scattering between two particles (the incident neutron and the target nucleus)the momentum and the energy are conserved. The basic assumptions involved in the abovestatement are that the target atoms are initially free and at rest.The change in neutron energy, from E 0to E, and the scattering angle (in the laboratorysystem) are linked by the following relation:(3.13)where A = m,/m n, the ratio of the mass of the target to that of the neutron or. with verygood approximation, the mass number of the target nucleus. The new energy is determined