Critical mass calculations using MCNP: An academic exercise

In introductory courses for nuclear engineering, the concept of critical dimension and critical mass are introduced. Students are usually taught that the geometrical shape which needs the smallest amount of fissionable material to reach criticality is a sphere. In this paper, this concept is explored further using MCNP code. Five different regular polyhedrons (i.e., the Platonic solids) and a sphere have been examined to demonstrate that sphere is indeed the optimal geometrical shape to minimize the critical mass. For illustration purpose, the fissile isotope used in this study is 239Pu, with a nominal density of 19.8 g/cm3.