Hyper-Raman scattering from cubic BaTi03 is studied to clarify the controversies about the low-frequency dielectric response in this material. Applying the Auctuation-dissipation theorem, we obtain the imaginary part e"(0) of the dielectric function in the wave-number range from 3 to 150 cm '. e"(0) can be adequately described by a classical singleoscillator dispersion formula. In approaching the Curie temperature, we find a continuous decrease of the mode frequency 00. The relative damping constant y/Qo exceeds 2, so that the mode may be referred to as intermediate between oscillator and relaxator. Because of the high damping e"(0) can be formally written as the sum of two overdamped oscillator contributions. This would lead to the concept of a soft-mode saturation and an extra dispersion mechanism as has been recently inferred from the far-infrared reflectivity spectrum. However, we do not find any evidence for this mode splitting and, so far, regard it as artificial.

We use the fluctuation-dissipation theorem to relate the hyper-Raman scattering efficiency of transverse and longitudinal-optical phonons to the infrared dielectric function e(Q) = e'(D) +i@"(0).The relation is applied to SrTiO, at room temperature in order to clarify the discrepancies between various far-infrared reflectivity studies. We take advantage of the hyper-Raman selection rules allowing the observation of Raman-forbidden modes. e "(0) is derived from-accurately measured hyper-Raman lines and combined with compatible infrared reflectivity data to give e'(Q). Below 100 cm ' the dielectric dispersion can be adequately described by a classical dispersion formula with a quasiharmonic-oscillator frequency of 87.9 cm ' and a single damping constant of 23.7 cm '. This approximation fails above 100 cm '.

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