Chemical Binding Effects in Neutron Resonance Scattering and Absorption.

The Doppler broadening of neutron absorption and scattering resonances is an effect of considerable importance in calculating reactor parameters. This broadening is known to depend upon the state of the atom from which the scattering of the neutron occurs. This dependence is called the chemical binding effect. A key assumption in the usual computations of Doppler broadening is to ignore the dependence of the total resonance width on the chemical binding state of the compound nucleus. This is an excellent approximation for the gamma line. We derive an expression for the neutron line width as a function of the energy of the compound nucleus for an ideal gas. The influence of energy on the width with energy is examined at two different temperatures 4K and 1000K. It is found that these effects are very small, of the order of 10^{4-} . The assumption of constancy of the resonance width is thus shown to be a good approximation for the neutron line width. Also we examine the influence of the crystalline binding on the 6.67 eV resonance energy of U-238 line shape in uranium carbide and uranium dioxide. This model treats the crystal as a gas with an effective temperature and an effective mass determined by harmonic crystal phonon spectrum developed by Koppel and Houston. Based on this model, the line shape of U-238 is Gaussian plus a recoilless part. We also compute the broadening using a harmonic crystal model. As the temperature of U-238 target is decreased, disagreement between the two models becomes pronounced. However the results agree in the limiting case of high temperature. As the nucleus becomes more tightly bound, shifts in the resonance peak to lower energies are also observed. A general formula for the differential scattering cross section is developed starting from the transition probability (T-matrix). The formalism is applied to the gas and harmonic crystal models to determine the chemical binding effect. Although the resonance broadening is determined in terms of a four point correlation function, it is found that these broadenings are not different from the neutron absorption.