Measurements of the dynamic structure factor near the lambda temperature in liquid helium

The dynamic structure factor S (q, ω) was measured by Brillouin scattering in liquid 4He at q = 1.79 x 105 cm-1. Results were obtained at two densities: rho = 0.175 g/cm3 for which P/sub lambda/ = 23.1 bars and rho = 0.179 g/cm3 for which P/sub lambda/ = 28.5 bar. Values of the reduced temperature epsilon equivalent (T-T/sub lambda/)/T/sub lambda/ varied from -5 x 10-2 to -5 x 10-6 and from 1.3 x 10-5 to 5 x 10-2. This range involves both the hydrodynamic and the critical regions; values of qxi fall between 5 x 10-2 and 21 below T/sub lambda/ and between 4.5 and 2 x 10-2 above T/sub lambda/. This article presents the data on the critical mode, which is second sound below the transition and heat diffusion above. The most striking result is that the damping of the critical mode is essentially independent of epsilon over the entire range of temperatures studied. This behavior is qualitatively different from the strong temperature dependence, consistent with dynamic scaling, which is observed at low frequencies. On the other hand, any dispersion in the velocity of high frequency (approx. several MHz) second sound, if present, is less than 2%. S (q, ω) retains a two-peaked structure well into the critical region below T/sub lambda/; it still appears in the measured spectra (which contain the instrumental width as well) at qxi approx. 4. At T/sub lambda/ and in the critical region just above, there is evidence for a non-Lorentzian shape of S (q, ω). The critical mode contribution to S (q, ω) is compared with a theoretical calculation of Hohenberg, Siggia, and Halperin based on the planar-spin model of 4He. The theory matches both the overall width and the general features of the shape of S (q, ω) to within our spectral resolution at T/sub lambda/. However, closer to qxi = 1 in the critical region, and in the hydrodynamic regions both above and below T/sub lambda/, the theory predicts linewidths which are too small