Slow Neutron Inelastic Scattering from Liquid Sodium

Partial differential cross sections for slow neutron scattering from liquid sodium have been measured at 100, 150, and 200°C. The Materials Testing Reactor phased-chopper velocity selector was used with a 95% transmission sample at incident neutron energies of 0.025, 0.07, and 0.10 eV at eight scattering angles (16 to 85°). In the scattering law obtained from these cross sections, prominent coherent scattering maxima appear for energy transfers $\Delta E\leqq 0.2k_{B}T$, but disappear beyond $\Delta E=0.3\mathrm{}{k}_{B}T$. At each temperature, time-dependent widths $\rho \mathrm{}\left(t\right)\mathrm{}$ of the intermediate scattering function have been obtained by Fourier transformation of the scattering law for large momentum transfers. At times ${10}^{-13\mathrm{}}$ sec these functions confirm the prediction of gas-like behavior, but at larger times are solid-like. The $\rho \mathrm{}\left(t\right)\text{'}\mathrm{s}$ are also momentum-dependent at larger times indicating that the self-correlation function is not Strictly Gaussian. Measurements of the zeroth and first moments of the energy transfer have been obtained from the scattering law at each temperature for several values of momentum transfer. The zeroth moment is in agreement with neutron diffraction experiments, but the first moment is as much as a factor of 2.5 larger than predicted theoretically.