Multi-Group Neutron Diffusion Analysis for Beryllium Reflector Optimization in Medical Isotope Production Reactors

This study presents a comprehensive computational framework for optimizing beryllium reflector thickness in compact nuclear reactors designed for medical isotope production. Building upon classical multi-group diffusion theory, we developed a two-stage optimization algorithm incorporating temperature-dependent cross-sections, thermal up-scatter mechanisms, and multi-objective Pareto analysis. The model employs a refined 10-energy-group structure with enhanced thermal resolution and accounts for five critical medical isotopes including Molybdenum-99, Lutetium-177, Iodine-131, Yttrium-90, and Technetium-99m. Our analysis examines a compact reactor configuration consisting of a 5.0 cm radius, 10.0 cm height plutonium core surrounded by beryllium reflector with thickness varying from 0 to 30 cm. Results indicate that beryllium reflector thickness in the range of 12 to 15 cm provides optimal performance, yielding 35 to 40 percent production enhancement over bare systems while maintaining safe criticality with effective multiplication factors between 1.05 and 1.10. Among the evaluated nuclear data libraries, JENDL-3.2 showed the best agreement with experimental data, exhibiting deviations within plus or minus 5 percent compared to other contemporary libraries. This work addresses the critical need for optimized compact reactor designs in medical isotope production, which remains particularly relevant given current global supply constraints and increasing clinical demand.