STUDIES ON NEW PROPERTIES AND EVALUATION OF NUCLEAR DOPPLER BROADENING FUNCTIONS AND THEIR TEMPERATURE DERIVATIVES USING STEFFENSEN INTEGRAL INEQUALITY

Abstract

The study of Doppler Broadening Functions (also referred to as Voigt Line Shape Functions), has inherent mathematical and physical interest. Evaluation of these functions to high accuracies continues to be of great importance not only in reactor physics but also in the study of stellar absorption and meteorological radiative absorption phenomena. The methods used to evaluate these improper integrals range from Padè approximations, Fourier analysis, contour integration and a number of ingenious numerical algorithms. In this study we use the method of integral inequalities to obtain analytic forms for the upper and lower bounds, which themselves provide very good approximation. newlineLikewise explicit knowledge of the temperature and energy derivatives of the Doppler Broadening Functions not only provides analytical insight of how the cross section slope varies with energy and temperature but also specifies extreme points, exact locations of which are important for cross section interpolation. This is required for the studies where fuel temperatures are not uniform. In reactors, nuclides exist in conditions where the temperatures are different or changing due to feedbacks. Calculation of Doppler broadened cross sections at all the required temperatures for all the nuclides are time consuming. Accurate and efficient interpolation schemes are thus still a topic of interest Accurate values of derivatives of line shape functions are necessary for creation of energy and temperature grids for interpolation. There have been no standard tabulations for the energy and temperature derivatives of Doppler Broadened functions available in the literature so far. newlineA new non-quadrature method is proposed for evaluation of the Doppler broadening functions in this thesis. Bounds of the functions are obtained using Steffensen s inequality. They provide approximations to any desired accuracy. The bounds of energy and temperature derivatives are derived in terms of the bounds of and#968; and and#967; functions.