Degree Name

Doctor of Philosophy


School of Mathematics


The Doppler broadening of resonance profiles for crystalline fuels is discussed. The development of broadened profiles is obtained using the distribution of nuclear velocities within a crystal because of thermal vibration. Several models of nuclear movement are set up, from which expressions for the velocity distribution are obtained. The velocity distrr'butions are used to derive broadened profiles. Successive models are of increasing complexity. Each broadened profile is compared with the accepted profile for t crystalline material, namely, that profile obtained by Lr:.iib using totally different considerations. The accepted profile is the profile obtained for the velocity distribution of a free gas, but at an 'effective* temperature rather than the actual temnerature. The comparison of a profile is used as a guide as to whether the model of nuclear movement is adequate, and if not, the model it modified. The method of presentation illustrates that no simple oscillatoiy model of crystal movement adequately predicts a suitable broadened profile. Further the presentation indicates how two dynamically different systems - a solid and a gas - can lead to essentially the sam-^ broadened profile. The broadened profiles are found to be expressible in terms of functions which are generalisations of those functions normally encountered in expressions for broadened profiles. These functions are discu.-^sed at some length; their properties are derived, and methods of their evaluation are suggested. The discussion of the generalised functions occupies a substantial proportion of the week.