The diffusion theory of neutron thermalization experiements

The theory of the pulsed neutron experiment and the 2 zone exponential experiment is developed in this thesis. The energy dependent diffusion approximation to the Boltzniann neutron transport equation is used throughout. A concise operator and vector foi^malism is introduced ii^ich permits a unified treatment of the variety of representations (multigroup, polynomial expansion, etc. ) of the diffusion equation. Familiarity with this formalism is developed by first considering the well understood eigenvalue theory of the asymptotic pulsed neutron experiment. New material is presented in Chapter 3 in that the theory of the pre-asymptotic pulsed neutron experiment given assumes a finite and not an instantaneous pulse. Part of the contents of this chapter have been presented at the IAEA Symposium on Neutron Thermalization and Reactor Spectra, Ann Arhor (1967). In Chapter 4 the operator formalism allows the energy dependent theory of the exponential experiment to be treated in a manner which is new and amenable to numerical calculation. In both this chapter and the preceeding chapters the results of computations are compared with either experiment or other calculations. Finally, in order to complement an earlier discussion of the discrete eigenvalue spectra of the thermalization operator, a review of the properties of the continuous spectrum is given