On the determination of the diffusion constants of H2_{2}O, phenyls, ZRh1,26_{1,26}, and D2_{2}O by neutron single scattering experiments : Preprint

The average thermal diffusion constant is usually determined by integral methods, i.e. by investigating the relaxation of the neutron density in time or in space. In this paper a different approach is described. From measurements of the differential sca ttering cross-section dE ($\theta$) /d$\Omega$ for various neutron energies E and sample temperatures T$_{m}$, the average cosine of the scattering angle $\overline{\mu}$, the diffusion constant D(E,T$_{m}$), and its thermal average $_{Tm}$ was calculated. Investigations were performed on the most important hydrogeneous moderators and on D$_{2}$O. It was found that the scattering cross sections d5/d$\Omega$, are not very sensitive to the temperature. Therefore, the quantity can easily be evaluated within a large temperature range by means of a comparatively small number of d5/d$\Omega$ -measurements. A qualitative explanation of the very streng interference maxima in the d5/d$\Omega$, -curves of D$_{2}$O can be given. Rather strong coherence maxima have been observed in the phenyl-and ZrH-curves, too. Very good agreement was obtained between our -data and the results of conventional relaxation experiments both with light and heavy water. There was also good agreement with theoretical predictions for H$_{2}$O, D$_{2}$O, diphenyl, and reasonable agreement with calculations for ZrH$_{1,26}$. For diphenyl, there was agreement with some of the relaxation experiments cited in literature. The consistency of the results shows that our thermal diffusion parameters as a function of T$_{m}$ and the diffusion constant D as a function of E can be considered as reliable for one-or multigroup-calculations