Resonant Absorption of Neutrons by Crystals

Abstract

A study has been made of the Doppler broadening of resonances in the total cross section for interaction of slow neutrons with nuclei bound in crystals. The resonance at 6.71 eV in Os metal and the resonance at 6.65 eV in U metal were chosen as examples of moderate crystal binding, while the 6.65-eV resonance in ${\mathrm{U}}_{3}$${\mathrm{O}}_{8}$, for which $k{\ensuremath{\theta}}_{0}=0.043$ eV, was chosen as an example of strong binding. The shapes of the resonance lines were determined as a function of temperature by measuring the neutron transmission of thin and thick samples by means of the Argonne fast chopper. These shapes were compared with theoretical line shapes calculated by means of Lamb's theory of Doppler broadening as applied to the spectra of lattice frequencies implied by simple models of the crystal lattices. For moderate binding, a simple Einstein model which reproduces the observed specific-heat behavior of the crystal above 40\ifmmode^\circ\else\textdegree\fi{}K gives accurate resonance-line shapes at all temperatures. However, for ${\mathrm{U}}_{3}$${\mathrm{O}}_{8}$ the line shape implies a generalized Nernst-Lindemann model of the lattice with a frequency spectrum $g(\ensuremath{\nu})=0.9\ensuremath{\delta}(h{\ensuremath{\nu}}_{1}\ensuremath{-}0.013 \mathrm{eV})+0.1\ensuremath{\delta}(h{\ensuremath{\nu}}_{2}\ensuremath{-}0.052 \mathrm{eV})$. The proportions of the high- and low-frequency components are quite different from the values resulting from specific-heat data. Possible interpretations of the ${\mathrm{U}}_{3}$${\mathrm{O}}_{8}$ results in terms of simple lattice models are presented.