Measurement of the Doppler Effect in Uranium-238

The Doppler effect of ²³⁸U metal and ²³⁸U in U₃O₈ was studied by using beams of filtered neutrons at 24 ± 0.9 keV and 144 ± 12 keV from the University of Missouri Research Reactor (MURR) Facility. The Doppler effect is the broadening of the widths of the nuclear resonances in the total cross section due to the thermal motion of the nuclei. The effective average total cross sections (EATCS) for both kinds of samples were measured with good geometry transmission measurements as functions of sample thickness and temperature to show the Doppler effect. The temperature of the samples ranged from 38 to 1100 K. Temperature-related density effects were removed by simultaneously measuring the attenuation of gamma rays passing through the samples. The EATCS data as function of sample thickness at room temperature were fit with a nuclear cross section calculated from a ladder of resonances in the center-of-mass system. This ladder was generated from a set of synthesized nuclear parameters. The best fits to the cross sections, when extrapolated to zero thickness, give 13.5 ± 0.2 b at 24 keV and 11.9 ± 0.2 b at 144 keV. Our value at 24 keV agrees with the ENDF/B-IV, while our value at 144 keVis ∼4% greater. An ideal gas model including an effective mass, M_eff, and an effective temperature, T_eff, was used to Doppler broaden the calculated nuclear cross sections. With this model, good agreement was obtained to the EATCS data for all sample thickness at all temperatures with an M_eff of 238 amu for the ²³⁸U metal and 400 amu for ²³⁸U in U₃O₈. The temperature dependence of T_eff was determined by calculating the total energy using Debye frequency θ_v distributions. In these calculations, the Debye temperatures θ_D that provided the best fits were θ_D = 260 K for the metal and θ_D = 545 K for U₃O₈. These results indicate that this Doppler model combined with the calculated nuclear cross sections can provide a good fit to the data with a two-parameter system for the Doppler part, that is, θ_D and M_eff for each state. From these EATCS data, estimates were made for the Doppler coefficient of a fast reactor. The estimate values of the Doppler coefficient have the right sign and magnitude to agree with Doppler Coefficients for particular fast reactor systems.