Investigation of the effects of anharmonicity on the resonance line shape of U-238

In an attempt to solve the problem, the effect of anharmonicity on the resonance line shape is investigated, starting with Lamb's original formula for the transition probability. Because anharmonicity manifests itself through the non-commutativity of the displacement operators, the theory of cumulants was used to account for that effect. Then the phonon damping and shift resulting from the cubic anharmonicity, i.e. the anharmonicity arising from the cubic term in the potential energy expansion are introduced. The shift and frequency, temperature and polarization dependent phonon damping functions are evaluated using Krivoglaz's expressions. The equations are general and could be applied to capture and fission as well. The theory is then applied to the 6.67 eV and 80.74 eV resonances of U in UO2, and compared to the harmonic model at room temperature and 12000K. For both resonances, the cross section is lower in the wings and taller at the peak at room temperature, the difference being as much as 23% and 10.43% respectively. At 12000K, the reverse trend was observed; the anharmonic model being higher at the wings by as much as 4.3% and 38% respectively. The relative decrease in the width is 4.25% and 10% respectively. The results obtained show that there should be more self-shielding at room temperature and this leads to lower reaction rates and better agreement with experiments. At higher temperatures, there ought to be more Doppler effect and better agreement with experiments