Unified Neutron Transport Theory

Abstract

I remember very well my first encounter with neutron transport theory. It was in 1948 or 1949 at Oak Ridge, where I was involved in critical mass calculations for a plant that performed chemical processing of uranium solutions. We had been using semi-empirical formulas provided for us by our consultant Richard Feynman, whose later accomplishments you know, and by Eugene Greuling author of a classic paper on the theory of the water boiler reactor. I was fortunate to be able to attend a series of lectures given by Dr.A.M.Weinberg at a reactor course attended by the staff of Admiral Hyman Rickover. President Carter may have been one of my classmates. Prior to these presentations by Dr.Weinberg, our calculational models were based on simple diffusion theory, coupled with some elementary neutron slowing concepts. I was amazed to see the complexity of the development of the spherical harmonics solution from the general transport equation involving spatial, energy, and angle coordinates. As many of you know, Dr.Weinberg and his co-author Dr.Eugene Wigner extended the material in these lectures to form their famous text book. However, the difficulties I and other students had in appreciating the theory led me to believe that for pedagogical purposes it was preferable to establish a strong foundation in reactor physics based on the neutron balances in diffusion theory and later to introduce transport theory as a generalization. In my own text ‘Nuclear Reactor Physics’ which came out in 1957, I used this approach. Dr. Allan Henry, who now has his own fine text in reactor analysis agrees. You see, what we are comparing are the two choices usually available in science and engineering either (a) to go from the general to the specific limited approximation or special case or (b) to supply a succession of corrective improvements or extensions to a simple first order theory. I suppose that all education and research is actually a combination of these techniques.